N/A denotes a trivial classification. Full classifications including strong topological insulators can be easily obtained from this table by using the group extension rules given in Results and are also provided as a table in the Supplementary Materials.
1 | 41 | 81 | 121 | 161 | ℤ2 | 201 | |||||
2 | 42 | 82 | 122 | 162 | 202 | ℤ | |||||
3 | 43 | 83 | 123 | ℤ5 | 163 | 203 | ℤ2 | ||||
4 | 44 | ℤ2 × ℤ2 | 84 | 124 | 164 | 204 | ℤ × ℤ2 | ||||
5 | 45 | 85 | 125 | 165 | 205 | ℤ2 | |||||
6 | 46 | 86 | 126 | 166 | 206 | ||||||
7 | 47 | ℤ6 | 87 | 127 | ℤ3 × ℤ2 | 167 | 207 | ||||
8 | 48 | 88 | 128 | 168 | 208 | ||||||
9 | 49 | 89 | 129 | 169 | ℤ2 | 209 | ℤ2 | ||||
10 | 50 | 90 | 130 | 170 | ℤ2 | 210 | ℤ2 | ||||
11 | 51 | 91 | 131 | ℤ3 × ℤ2 | 171 | 211 | |||||
12 | 52 | 92 | 132 | 172 | 212 | ℤ2 | |||||
13 | 53 | 93 | 133 | 173 | ℤ2 | 213 | ℤ2 | ||||
14 | 54 | 94 | 134 | 174 | ℤ2 | 214 | |||||
15 | 55 | 95 | 135 | 175 | ℤ2 × ℤ2 | 215 | ℤ × ℤ2 | ||||
16 | 56 | 96 | 136 | ℤ2 × ℤ2 | 176 | ℤ × ℤ2 | 216 | ℤ | |||
17 | 57 | 97 | 137 | 177 | 217 | ℤ × ℤ2 | |||||
18 | 58 | 98 | 138 | 178 | 218 | ℤ2 | |||||
19 | 59 | 99 | ℤ3 × ℤ2 | 139 | ℤ3 × ℤ2 | 179 | 219 | ℤ2 | |||
20 | 60 | 100 | 140 | 180 | 220 | ℤ2 | |||||
21 | 61 | 101 | 141 | 181 | 221 | ℤ3 | |||||
22 | 62 | 102 | 142 | 182 | 222 | ||||||
23 | 63 | 103 | 143 | ℤ2 | 183 | ℤ2 × ℤ2 | 223 | ℤ × ℤ2 | |||
24 | 64 | 104 | 144 | ℤ2 | 184 | 224 | |||||
25 | ℤ4 × ℤ2 | 65 | ℤ4 × ℤ2 | 105 | ℤ2 × ℤ2 | 145 | ℤ2 | 185 | ℤ × ℤ2 | 225 | ℤ2 |
26 | 66 | 106 | 146 | ℤ2 | 186 | ℤ × ℤ2 | 226 | ℤ × ℤ2 | |||
27 | 67 | 107 | ℤ2 × ℤ2 | 147 | 187 | ℤ3 | 227 | ℤ × ℤ2 | |||
28 | 68 | 108 | 148 | 188 | ℤ × ℤ2 | 228 | |||||
29 | 69 | 109 | ℤ × ℤ2 | 149 | 189 | ℤ3 | 229 | ℤ2 × ℤ2 | |||
30 | 70 | 110 | 150 | 190 | ℤ × ℤ2 | 230 | |||||
31 | 71 | ℤ3 × ℤ2 | 111 | 151 | 191 | ℤ4 | |||||
32 | 72 | 112 | 152 | 192 | |||||||
33 | 73 | 113 | 153 | 193 | ℤ2 × ℤ2 | ||||||
34 | 74 | 114 | 154 | 194 | ℤ2 × ℤ2 | ||||||
35 | 75 | 115 | 155 | 195 | ℤ2 | ||||||
36 | 76 | 116 | 156 | ℤ × ℤ2 | 196 | N/A | |||||
37 | 77 | 117 | 157 | ℤ × ℤ2 | 197 | ℤ2 | |||||
38 | ℤ3 × ℤ2 | 78 | 118 | 158 | ℤ2 | 198 | N/A | ||||
39 | 79 | 119 | 159 | ℤ2 | 199 | ℤ2 | |||||
40 | 80 | 120 | 160 | ℤ × ℤ2 | 200 | ℤ2 |