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Isotropy Software

Below, default input is given as an example. You may submit this form as given to see the output of this example.

Subgroup space group: 99 C4v-1, P4mm, P4mm (default) 1 C1-1, P1, P1 2 Ci-1, P-1, P-1 3 C2-1, P2, P121, unique axis b 3 C2-1, P2, P112, unique axis c 4 C2-2, P2_1, P12_11, unique axis b 4 C2-2, P2_1, P112_1, unique axis c 5 C2-3, C2, C121, unique axis b, cell choice 1 5 C2-3, C2, A121, unique axis b, cell choice 2 5 C2-3, C2, I121, unique axis b, cell choice 3 5 C2-3, C2, A112, unique axis c, cell choice 1 5 C2-3, C2, B112, unique axis c, cell choice 2 5 C2-3, C2, I112, unique axis c, cell choice 3 6 Cs-1, Pm, P1m1, unique axis b 6 Cs-1, Pm, P11m, unique axis c 7 Cs-2, Pc, P1c1, unique axis b, cell choice 1 7 Cs-2, Pc, P1n1, unique axis b, cell choice 2 7 Cs-2, Pc, P1a1, unique axis b, cell choice 3 7 Cs-2, Pc, P11a, unique axis c, cell choice 1 7 Cs-2, Pc, P11n, unique axis c, cell choice 2 7 Cs-2, Pc, P11b, unique axis c, cell choice 3 8 Cs-3, Cm, C1m1, unique axis b, cell choice 1 8 Cs-3, Cm, A1m1, unique axis b, cell choice 2 8 Cs-3, Cm, I1m1, unique axis b, cell choice 3 8 Cs-3, Cm, A11m, unique axis c, cell choice 1 8 Cs-3, Cm, B11m, unique axis c, cell choice 2 8 Cs-3, Cm, I11m, unique axis c, cell choice 3 9 Cs-4, Cc, C1c1, unique axis b, cell choice 1 9 Cs-4, Cc, A1n1, unique axis b, cell choice 2 9 Cs-4, Cc, I1a1, unique axis b, cell choice 3 9 Cs-4, Cc, A11a, unique axis c, cell choice 1 9 Cs-4, Cc, B11n, unique axis c, cell choice 2 9 Cs-4, Cc, I11b, unique axis c, cell choice 3 10 C2h-1, P2/m, P12/m1, unique axis b 10 C2h-1, P2/m, P112/m, unique axis c 11 C2h-2, P2_1/m, P12_1/m1, unique axis b 11 C2h-2, P2_1/m, P112_1/m, unique axis c 12 C2h-3, C2/m, C12/m1, unique axis b, cell choice 1 12 C2h-3, C2/m, A12/m1, unique axis b, cell choice 2 12 C2h-3, C2/m, I12/m1, unique axis b, cell choice 3 12 C2h-3, C2/m, A112/m, unique axis c, cell choice 1 12 C2h-3, C2/m, B112/m, unique axis c, cell choice 2 12 C2h-3, C2/m, I112/m, unique axis c, cell choice 3 13 C2h-4, P2/c, P12/c1, unique axis b, cell choice 1 13 C2h-4, P2/c, P12/n1, unique axis b, cell choice 2 13 C2h-4, P2/c, P12/a1, unique axis b, cell choice 3 13 C2h-4, P2/c, P112/a, unique axis c, cell choice 1 13 C2h-4, P2/c, P112/n, unique axis c, cell choice 2 13 C2h-4, P2/c, P112/b, unique axis c, cell choice 3 14 C2h-5, P2_1/c, P12_1/c1, unique axis b, cell choice 1 14 C2h-5, P2_1/c, P12_1/n1, unique axis b, cell choice 2 14 C2h-5, P2_1/c, P12_1/a1, unique axis b, cell choice 3 14 C2h-5, P2_1/c, P112_1/a, unique axis c, cell choice 1 14 C2h-5, P2_1/c, P112_1/n, unique axis c, cell choice 2 14 C2h-5, P2_1/c, P112_1/b, unique axis c, cell choice 3 15 C2h-6, C2/c, C12/c1, unique axis b, cell choice 1 15 C2h-6, C2/c, A12/n1, unique axis b, cell choice 2 15 C2h-6, C2/c, I12/a1, unique axis b, cell choice 3 15 C2h-6, C2/c, A112/a, unique axis c, cell choice 1 15 C2h-6, C2/c, B112/n, unique axis c, cell choice 2 15 C2h-6, C2/c, I112/b, unique axis c, cell choice 3 16 D2-1, P222, P222 17 D2-2, P222_1, P222_1 18 D2-3, P2_12_12, P2_12_12 19 D2-4, P2_12_12_1, P2_12_12_1 20 D2-5, C222_1, C222_1 21 D2-6, C222, C222 22 D2-7, F222, F222 23 D2-8, I222, I222 24 D2-9, I2_12_12_1, I2_12_12_1 25 C2v-1, Pmm2, Pmm2 26 C2v-2, Pmc2_1, Pmc2_1 27 C2v-3, Pcc2, Pcc2 28 C2v-4, Pma2, Pma2 29 C2v-5, Pca2_1, Pca2_1 30 C2v-6, Pnc2, Pnc2 31 C2v-7, Pmn2_1, Pmn2_1 32 C2v-8, Pba2, Pba2 33 C2v-9, Pna2_1, Pna2_1 34 C2v-10, Pnn2, Pnn2 35 C2v-11, Cmm2, Cmm2 36 C2v-12, Cmc2_1, Cmc2_1 37 C2v-13, Ccc2, Ccc2 38 C2v-14, Amm2, Amm2 39 C2v-15, Abm2, Abm2 40 C2v-16, Ama2, Ama2 41 C2v-17, Aba2, Aba2 42 C2v-18, Fmm2, Fmm2 43 C2v-19, Fdd2, Fdd2 44 C2v-20, Imm2, Imm2 45 C2v-21, Iba2, Iba2 46 C2v-22, Ima2, Ima2 47 D2h-1, Pmmm, P2/m2/m2/m 48 D2h-2, Pnnn, P2/n2/n2/n, origin choice 1 48 D2h-2, Pnnn, P2/n2/n2/n, origin choice 2 49 D2h-3, Pccm, P2/c2/c2/m 50 D2h-4, Pban, P2/b2/a2/n, origin choice 1 50 D2h-4, Pban, P2/b2/a2/n, origin choice 2 51 D2h-5, Pmma, P2_1/m2/m2/a 52 D2h-6, Pnna, P2/n2_1/n2/a 53 D2h-7, Pmna, P2/m2/n2_1/a 54 D2h-8, Pcca, P2_1/c2/c2/a 55 D2h-9, Pbam, P2_1/b2_1/a2/m 56 D2h-10, Pccn, P2_1/c2_1/c2/n 57 D2h-11, Pbcm, P2/b2_1/c2_1/m 58 D2h-12, Pnnm, P2_1/n2_1/n2/m 59 D2h-13, Pmmn, P2_1/m2_1/m2/n, origin choice 1 59 D2h-13, Pmmn, P2_1/m2_1/m2/n, origin choice 2 60 D2h-14, Pbcn, P2_1/b2/c2_1/n 61 D2h-15, Pbca, P2_1/b2_1/c2_1/a 62 D2h-16, Pnma, P2_1/n2_1/m2_1/a 63 D2h-17, Cmcm, C2/m2/c2_1/m 64 D2h-18, Cmca, C2/m2/c2_1/a 65 D2h-19, Cmmm, C2/m2/m2/m 66 D2h-20, Cccm, C2/c2/c2/m 67 D2h-21, Cmma, C2/m2/m2/a 68 D2h-22, Ccca, C2/c2/c2/a, origin choice 1 68 D2h-22, Ccca, C2/c2/c2/a, origin choice 2 69 D2h-23, Fmmm, F2/m2/m2/m 70 D2h-24, Fddd, F2/d2/d2/d, origin choice 1 70 D2h-24, Fddd, F2/d2/d2/d, origin choice 2 71 D2h-25, Immm, I2/m2/m2/m 72 D2h-26, Ibam, I2/b2/a2/m 73 D2h-27, Ibca, I2_1/b2_1/c2_1/a 74 D2h-28, Imma, I2_1/m2_1/m2_1/a 75 C4-1, P4, P4 76 C4-2, P4_1, P4_1 77 C4-3, P4_2, P4_2 78 C4-4, P4_3, P4_3 79 C4-5, I4, I4 80 C4-6, I4_1, I4_1 81 S4-1, P-4, P-4 82 S4-2, I-4, I-4 83 C4h-1, P4/m, P4/m 84 C4h-2, P4_2/m, P4_2/m 85 C4h-3, P4/n, P4/n, origin choice 1 85 C4h-3, P4/n, P4/n, origin choice 2 86 C4h-4, P4_2/n, P4_2/n, origin choice 1 86 C4h-4, P4_2/n, P4_2/n, origin choice 2 87 C4h-5, I4/m, I4/m 88 C4h-6, I4_1/a, I4_1/a, origin choice 1 88 C4h-6, I4_1/a, I4_1/a, origin choice 2 89 D4-1, P422, P422 90 D4-2, P42_12, P42_12 91 D4-3, P4_122, P4_122 92 D4-4, P4_12_12, P4_12_12 93 D4-5, P4_222, P4_222 94 D4-6, P4_22_12, P4_22_12 95 D4-7, P4_322, P4_322 96 D4-8, P4_32_12, P4_32_12 97 D4-9, I422, I422 98 D4-10, I4_122, I4_122 99 C4v-1, P4mm, P4mm 100 C4v-2, P4bm, P4bm 101 C4v-3, P4_2cm, P4_2cm 102 C4v-4, P4_2nm, P4_2nm 103 C4v-5, P4cc, P4cc 104 C4v-6, P4nc, P4nc 105 C4v-7, P4_2mc, P4_2mc 106 C4v-8, P4_2bc, P4_2bc 107 C4v-9, I4mm, I4mm 108 C4v-10, I4cm, I4cm 109 C4v-11, I4_1md, I4_1md 110 C4v-12, I4_1cd, I4_1cd 111 D2d-1, P-42m, P-42m 112 D2d-2, P-42c, P-42c 113 D2d-3, P-42_1m, P-42_1m 114 D2d-4, P-42_1c, P-42_1c 115 D2d-5, P-4m2, P-4m2 116 D2d-6, P-4c2, P-4c2 117 D2d-7, P-4b2, P-4b2 118 D2d-8, P-4n2, P-4n2 119 D2d-9, I-4m2, I-4m2 120 D2d-10, I-4c2, I-4c2 121 D2d-11, I-42m, I-42m 122 D2d-12, I-42d, I-42d 123 D4h-1, P4/mmm, P4/m2/m2/m 124 D4h-2, P4/mcc, P4/m2/c2/c 125 D4h-3, P4/nbm, P4/n2/b2/m, origin choice 1 125 D4h-3, P4/nbm, P4/n2/b2/m, origin choice 2 126 D4h-4, P4/nnc, P4/n2/n2/c, origin choice 1 126 D4h-4, P4/nnc, P4/n2/n2/c, origin choice 2 127 D4h-5, P4/mbm, P4/m2_1/b2/m 128 D4h-6, P4/mnc, P4/m2_1/n2/c 129 D4h-7, P4/nmm, P4/n2_1/m2/m, origin choice 1 129 D4h-7, P4/nmm, P4/n2_1/m2/m, origin choice 2 130 D4h-8, P4/ncc, P4/n2_1/c2/c, origin choice 1 130 D4h-8, P4/ncc, P4/n2_1/c2/c, origin choice 2 131 D4h-9, P4_2/mmc, P4_2/m2/m2/c 132 D4h-10, P4_2/mcm, P4_2/m2/c2/m 133 D4h-11, P4_2/nbc, P4_2/n2/b2/c, origin choice 1 133 D4h-11, P4_2/nbc, P4_2/n2/b2/c, origin choice 2 134 D4h-12, P4_2/nnm, P4_2/n2/n2/m, origin choice 1 134 D4h-12, P4_2/nnm, P4_2/n2/n2/m, origin choice 2 135 D4h-13, P4_2/mbc, P4_2/m2_1/b2/c 136 D4h-14, P4_2/mnm, P4_2/m2_1/n2/m 137 D4h-15, P4_2/nmc, P4_2/n2_1/m2/c, origin choice 1 137 D4h-15, P4_2/nmc, P4_2/n2_1/m2/c, origin choice 2 138 D4h-16, P4_2/ncm, P4_2/n2_1/c2/m, origin choice 1 138 D4h-16, P4_2/ncm, P4_2/n2_1/c2/m, origin choice 2 139 D4h-17, I4/mmm, I4/m2/m2/m 140 D4h-18, I4/mcm, I4/m2/c2/m 141 D4h-19, I4_1/amd, I4_1/a2/m2/d, origin choice 1 141 D4h-19, I4_1/amd, I4_1/a2/m2/d, origin choice 2 142 D4h-20, I4_1/acd, I4_1/a2/c2/d, origin choice 1 142 D4h-20, I4_1/acd, I4_1/a2/c2/d, origin choice 2 143 C3-1, P3, P3 144 C3-2, P3_1, P3_1 145 C3-3, P3_2, P3_2 146 C3-4, R3, R3, hexangonal axes 146 C3-4, R3, R3 147 C3i-1, P-3, P-3 148 C3i-2, R-3, R-3, hexangonal axes 148 C3i-2, R-3, R-3 149 D3-1, P312, P312 150 D3-2, P321, P321 151 D3-3, P3_112, P3_112 152 D3-4, P3_121, P3_121 153 D3-5, P3_212, P3_212 154 D3-6, P3_221, P3_221 155 D3-7, R32, R32, hexangonal axes 155 D3-7, R32, R32 156 C3v-1, P3m1, P3m1 157 C3v-2, P31m, P31m 158 C3v-3, P3c1, P3c1 159 C3v-4, P31c, P31c 160 C3v-5, R3m, R3m, hexangonal axes 160 C3v-5, R3m, R3m 161 C3v-6, R3c, R3c, hexangonal axes 161 C3v-6, R3c, R3c 162 D3d-1, P-31m, P-312/m 163 D3d-2, P-31c, P-312/c 164 D3d-3, P-3m1, P-32/m1 165 D3d-4, P-3c1, P-32/c1 166 D3d-5, R-3m, R-32/m, hexangonal axes 166 D3d-5, R-3m, R-32/m 167 D3d-6, R-3c, R-32/c, hexangonal axes 167 D3d-6, R-3c, R-32/c 168 C6-1, P6, P6 169 C6-2, P6_1, P6_1 170 C6-3, P6_5, P6_5 171 C6-4, P6_2, P6_2 172 C6-5, P6_4, P6_4 173 C6-6, P6_3, P6_3 174 C3h-1, P-6, P-6 175 C6h-1, P6/m, P6/m 176 C6h-2, P6_3/m, P6_3/m 177 D6-1, P622, P622 178 D6-2, P6_122, P6_122 179 D6-3, P6_522, P6_522 180 D6-4, P6_222, P6_222 181 D6-5, P6_422, P6_422 182 D6-6, P6_322, P6_322 183 C6v-1, P6mm, P6mm 184 C6v-2, P6cc, P6cc 185 C6v-3, P6_3cm, P6_3cm 186 C6v-4, P6_3mc, P6_3mc 187 D3h-1, P-6m2, P-6m2 188 D3h-2, P-6c2, P-6c2 189 D3h-3, P-62m, P-62m 190 D3h-4, P-62c, P-62c 191 D6h-1, P6/mmm, P6/m2/m2/m 192 D6h-2, P6/mcc, P6/m2/c2/c 193 D6h-3, P6_3/mcm, P6_3/m2/c2/m 194 D6h-4, P6_3/mmc, P6_3/m2/m2/c 195 T-1, P23, P23 196 T-2, F23, F23 197 T-3, I23, I23 198 T-4, P2_13, P2_13 199 T-5, I2_13, I2_13 200 Th-1, Pm-3, P2/m-3 201 Th-2, Pn-3, P2/n-3, origin choice 1 201 Th-2, Pn-3, P2/n-3, origin choice 2 202 Th-3, Fm-3, F2/m-3 203 Th-4, Fd-3, F2/d-3, origin choice 1 203 Th-4, Fd-3, F2/d-3, origin choice 2 204 Th-5, Im-3, I2/m-3 205 Th-6, Pa-3, P2_1/a-3 206 Th-7, Ia-3, I2_1/a-3 207 O-1, P432, P432 208 O-2, P4_232, P4_232 209 O-3, F432, F432 210 O-4, F4_132, F4_132 211 O-5, I432, I432 212 O-6, P4_332, P4_332 213 O-7, P4_132, P4_132 214 O-8, I4_132, I4_132 215 Td-1, P-43m, P-43m 216 Td-2, F-43m, F-43m 217 Td-3, I-43m, I-43m 218 Td-4, P-43n, P-43n 219 Td-5, F-43c, F-43c 220 Td-6, I-43d, I-43d 221 Oh-1, Pm-3m, P4/m-32/m 222 Oh-2, Pn-3n, P4/n-32/n, origin choice 1 222 Oh-2, Pn-3n, P4/n-32/n, origin choice 2 223 Oh-3, Pm-3n, P4_2/m-32/n 224 Oh-4, Pn-3m, P4_2/n-32/m, origin choice 1 224 Oh-4, Pn-3m, P4_2/n-32/m, origin choice 2 225 Oh-5, Fm-3m, F4/m-32/m 226 Oh-6, Fm-3c, F4/m-32/c 227 Oh-7, Fd-3m, F4_1/d-32/m, origin choice 1 227 Oh-7, Fd-3m, F4_1/d-32/m, origin choice 2 228 Oh-8, Fd-3c, F4_1/d-32/c, origin choice 1 228 Oh-8, Fd-3c, F4_1/d-32/c, origin choice 2 229 Oh-9, Im-3m, I4/m-32/m 230 Oh-10, Ia-3d, I4_1/a-32/d

Lattice vectors of subgroup in terms of lattice vectors of parent:

Origin of subgroup with respect to parent in terms of lattice vectors of parent:

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