Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1352 conjugacy classes of subgroups.
The subgroup lattice has 1080 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#13490 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#13156 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #416373 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #413503 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #149054 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #149052 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #148746 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #148571 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #148151 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #148105 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #147953 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #147932 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #147918 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #147440 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #147130 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×#509 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#2148 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#2148 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×#361 | C22 | 1 | 1 | yes | characteristic |
| 20 | C22×#361 | C22 | 1 | 1 | yes | characteristic |
| 21 | C22×#360 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#2140 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#2110 | C22 | 1 | 1 | yes | characteristic |
| 24 | #23731 | — | 2 | 1 | no | — |
| 25 | C2×#1978 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#1978 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#1976 | C22 | 1 | 1 | yes | characteristic |
| 28 | #21240 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#1975 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#1972 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#1951 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#1951 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#1946 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#1833 | C22 | 1 | 1 | yes | characteristic |
| 35 | #20438 | C22 | 1 | 1 | yes | characteristic |
| 36 | #13490 | — | 2 | 4 | no | — |
| 37 | #13156 | — | 2 | 4 | no | — |
| 38 | C2×#1389 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#1389 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#1388 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#1388 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#1388 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×#1388 | C22 | 1 | 1 | yes | characteristic |
| 44 | C2×#1386 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×#1383 | C22 | 1 | 1 | yes | characteristic |
| 46 | C2×#1383 | C22 | 1 | 1 | yes | characteristic |
| 47 | C2×#1378 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×#1378 | C22 | 1 | 1 | yes | characteristic |
| 49 | #12549 | C22 | 1 | 1 | yes | characteristic |
| 50 | C2×#1375 | C22 | 1 | 1 | yes | characteristic |
| 51 | C2×#1375 | C22 | 1 | 1 | yes | characteristic |
| 52 | #11144 | — | 2 | 1 | no | — |
| 53 | #11144 | — | 2 | 1 | no | — |
| 54 | #11088 | — | 2 | 1 | no | — |
| 55 | #11084 | — | 2 | 1 | no | — |
| 56 | #11081 | — | 2 | 1 | no | — |
| 57 | #11080 | — | 2 | 1 | no | — |
| 58 | #11044 | — | 2 | 1 | no | — |
| 59 | #10873 | C22 | 1 | 1 | yes | characteristic |
| 60 | #10865 | C22 | 1 | 1 | yes | characteristic |
| 61 | C22×#135 | C23 | 1 | 1 | yes | characteristic |
| 62 | C23×D8 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×#509 | — | 2 | 2 | no | — |
| 64 | C2×#509 | — | 2 | 2 | no | — |
| 65 | C2×#509 | — | 4 | 1 | no | — |
| 66 | C2×#509 | — | 4 | 1 | no | — |
| 67 | C2×#509 | — | 4 | 1 | no | — |
| 68 | C2×#509 | — | 4 | 1 | no | — |
| 69 | C22×SD32 | — | 2 | 1 | no | — |
| 70 | C22×D16 | — | 2 | 1 | no | — |
| 71 | C22×M32 | C23 | 1 | 1 | yes | characteristic |
| 72 | C22×M32 | C23 | 1 | 1 | yes | characteristic |
| 73 | C22×M32 | C23 | 1 | 1 | yes | characteristic |
| 74 | C22×M32 | C23 | 1 | 1 | yes | characteristic |
| 75 | C22×#108 | C23 | 1 | 1 | yes | characteristic |
| 76 | C22×#108 | C23 | 1 | 1 | yes | characteristic |
| 77 | C22×#108 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×#108 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×#428 | — | 2 | 1 | no | — |
| 80 | C2×#428 | — | 2 | 1 | no | — |
| 81 | C2×#427 | C23 | 1 | 1 | yes | characteristic |
| 82 | C22×#106 | C23 | 1 | 1 | yes | characteristic |
| 83 | C2×#424 | — | 2 | 1 | no | — |
| 84 | C2×#423 | D4 | 1 | 1 | yes | characteristic |
| 85 | C2×#421 | — | 2 | 1 | no | — |
| 86 | C2×#421 | — | 2 | 1 | no | — |
| 87 | C22×#104 | — | 2 | 1 | no | — |
| 88 | C2×#418 | — | 2 | 1 | no | — |
| 89 | C2×#418 | — | 2 | 1 | no | — |
| 90 | C22×#102 | — | 2 | 1 | no | — |
| 91 | C22×#100 | — | 2 | 1 | no | — |
| 92 | C22×#100 | — | 2 | 1 | no | — |
| 93 | C2×#410 | — | 2 | 1 | no | — |
| 94 | #2879 | — | 2 | 1 | no | — |
| 95 | C2×#408 | — | 2 | 1 | no | — |
| 96 | C2×#405 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×#405 | C23 | 1 | 1 | yes | characteristic |
| 98 | C22×#97 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×#390 | — | 2 | 1 | no | — |
| 100 | #2285 | D4 | 1 | 1 | yes | characteristic |
| 101 | #2148 | — | 2 | 2 | no | — |
| 102 | #2148 | — | 2 | 2 | no | — |
| 103 | #2148 | — | 2 | 2 | no | — |
| 104 | #2148 | — | 4 | 1 | no | — |
| 105 | C2×#362 | — | 2 | 1 | no | — |
| 106 | C2×#362 | — | 2 | 1 | no | — |
| 107 | C2×#361 | — | 2 | 2 | no | — |
| 108 | C2×#361 | — | 2 | 2 | no | — |
| 109 | C2×#361 | — | 2 | 1 | no | — |
| 110 | C2×#361 | — | 2 | 2 | no | — |
| 111 | C2×#361 | — | 2 | 1 | no | — |
| 112 | C2×#361 | — | 4 | 1 | no | — |
| 113 | C2×#361 | — | 4 | 1 | no | — |
| 114 | C2×#361 | — | 4 | 1 | no | — |
| 115 | C2×#360 | — | 2 | 2 | no | — |
| 116 | C2×#360 | — | 4 | 1 | no | — |
| 117 | C2×#360 | — | 4 | 1 | no | — |
| 118 | #2140 | — | 2 | 2 | no | — |
| 119 | #2140 | — | 4 | 1 | no | — |
| 120 | C2×#357 | — | 2 | 2 | no | — |
| 121 | #2110 | — | 2 | 2 | no | — |
| 122 | #2110 | — | 4 | 1 | no | — |
| 123 | C2×#347 | — | 4 | 1 | no | — |
| 124 | #2094 | — | 4 | 1 | no | — |
| 125 | #2093 | — | 4 | 1 | no | — |
| 126 | #2092 | — | 4 | 1 | no | — |
| 127 | #2092 | — | 4 | 1 | no | — |
| 128 | #1978 | — | 2 | 2 | no | — |
| 129 | #1978 | — | 2 | 2 | no | — |
| 130 | #1978 | — | 4 | 1 | no | — |
| 131 | #1978 | — | 4 | 1 | no | — |
| 132 | #1976 | — | 2 | 2 | no | — |
| 133 | #1976 | — | 4 | 1 | no | — |
| 134 | #1975 | — | 4 | 1 | no | — |
| 135 | #1975 | — | 4 | 1 | no | — |
| 136 | #1975 | — | 4 | 1 | no | — |
| 137 | #1974 | — | 4 | 1 | no | — |
| 138 | #1972 | — | 4 | 1 | no | — |
| 139 | #1972 | — | 4 | 1 | no | — |
| 140 | #1951 | — | 2 | 2 | no | — |
| 141 | #1951 | — | 2 | 2 | no | — |
| 142 | #1951 | — | 4 | 1 | no | — |
| 143 | #1951 | — | 4 | 1 | no | — |
| 144 | #1946 | — | 4 | 1 | no | — |
| 145 | #1946 | — | 4 | 1 | no | — |
| 146 | #1833 | — | 2 | 2 | no | — |
| 147 | #1833 | — | 4 | 1 | no | — |
| 148 | #1771 | — | 4 | 1 | no | — |
| 149 | #1771 | — | 4 | 1 | no | — |
| 150 | C2×#344 | — | 2 | 1 | no | — |
| 151 | C2×#344 | — | 2 | 1 | no | — |
| 152 | C2×#343 | — | 2 | 1 | no | — |
| 153 | C2×#343 | — | 2 | 1 | no | — |
| 154 | #1738 | — | 2 | 1 | no | — |
| 155 | C2×#341 | — | 2 | 1 | no | — |
| 156 | C2×#339 | — | 2 | 1 | no | — |
| 157 | C2×H(3,ℤ/4) | — | 2 | 1 | no | — |
| 158 | #1729 | D4 | 1 | 1 | yes | characteristic |
| 159 | #1729 | D4 | 1 | 1 | yes | characteristic |
| 160 | #1728 | — | 2 | 1 | no | — |
| 161 | #1389 | — | 4 | 1 | no | — |
| 162 | #1389 | D4 | 1 | 4 | yes | — |
| 163 | #1388 | — | 2 | 2 | no | — |
| 164 | #1388 | — | 2 | 2 | no | — |
| 165 | #1388 | — | 4 | 1 | no | — |
| 166 | #1388 | — | 4 | 1 | no | — |
| 167 | #1386 | — | 2 | 2 | no | — |
| 168 | #1383 | — | 4 | 1 | no | — |
| 169 | #1383 | — | 4 | 1 | no | — |
| 170 | #1378 | — | 2 | 2 | no | — |
| 171 | #1378 | — | 4 | 1 | no | — |
| 172 | #1376 | — | 4 | 1 | no | — |
| 173 | #1375 | — | 2 | 2 | no | — |
| 174 | #1375 | — | 2 | 2 | no | — |
| 175 | C22×#41 | — | 2 | 1 | no | — |
| 176 | C23×D4 | — | 2 | 1 | no | — |
| 177 | C2×#135 | — | 2 | 1 | no | — |
| 178 | C2×#135 | — | 2 | 1 | no | — |
| 179 | C2×#135 | — | 2 | 1 | no | — |
| 180 | C2×#135 | — | 2 | 1 | no | — |
| 181 | C2×#135 | — | 2 | 1 | no | — |
| 182 | C2×#135 | — | 2 | 1 | no | — |
| 183 | C2×#135 | — | 2 | 1 | no | — |
| 184 | C2×#135 | — | 2 | 1 | no | — |
| 185 | C2×#135 | — | 2 | 1 | no | — |
| 186 | C2×#135 | — | 2 | 1 | no | — |
| 187 | C2×#135 | — | 2 | 1 | no | — |
| 188 | C2×#135 | — | 2 | 1 | no | — |
| 189 | C22×Q16 | #41 | 1 | 1 | yes | characteristic |
| 190 | C22×SD16 | — | 2 | 1 | no | — |
| 191 | C22×D8 | — | 2 | 1 | no | — |
| 192 | C22×D8 | — | 2 | 1 | no | — |
| 193 | C22×D8 | — | 2 | 1 | no | — |
| 194 | C22×D8 | — | 2 | 1 | no | — |
| 195 | C22×D8 | — | 2 | 1 | no | — |
| 196 | C22×D8 | — | 2 | 1 | no | — |
| 197 | C22×D8 | — | 2 | 1 | no | — |
| 198 | C22×D8 | — | 2 | 1 | no | — |
| 199 | C22×D8 | — | 2 | 1 | no | — |
| 200 | C22×D8 | — | 2 | 1 | no | — |
| 201 | C22×D8 | — | 2 | 1 | no | — |
| 202 | C22×D8 | — | 2 | 1 | no | — |
| 203 | C22×D8 | — | 2 | 1 | no | — |
| 204 | C22×D8 | #41 | 1 | 1 | yes | characteristic |
| 205 | C22×D8 | #41 | 1 | 2 | yes | — |
| 206 | C22×M16 | — | 2 | 1 | no | — |
| 207 | C22×M16 | — | 2 | 1 | no | — |
| 208 | C22×M16 | — | 2 | 1 | no | — |
| 209 | C22×M16 | — | 2 | 1 | no | — |
| 210 | C22×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | C22×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C23×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | C23×C8 | C24 | 1 | 1 | yes | characteristic |
| 214 | C2×#117 | — | 2 | 1 | no | — |
| 215 | C2×#117 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | C2×#117 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | C22×C4⋊C4 | — | 2 | 1 | no | — |
| 218 | C22×C22⋊C4 | — | 4 | 2 | no | — |
| 219 | C22×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | #509 | — | 4 | 4 | no | — |
| 221 | #509 | — | 4 | 4 | no | — |
| 222 | #509 | — | 4 | 4 | no | — |
| 223 | #509 | — | 4 | 4 | no | — |
| 224 | C2×SD32 | — | 4 | 2 | no | — |
| 225 | C2×SD32 | — | 4 | 2 | no | — |
| 226 | C2×SD32 | — | 4 | 2 | no | — |
| 227 | C2×D16 | — | 4 | 2 | no | — |
| 228 | C2×D16 | — | 4 | 2 | no | — |
| 229 | C2×D16 | — | 4 | 2 | no | — |
| 230 | C2×M32 | — | 2 | 1 | no | — |
| 231 | C2×M32 | — | 2 | 1 | no | — |
| 232 | C2×M32 | — | 2 | 1 | no | — |
| 233 | C2×M32 | — | 2 | 1 | no | — |
| 234 | C2×M32 | — | 2 | 1 | no | — |
| 235 | C2×M32 | — | 2 | 1 | no | — |
| 236 | C2×M32 | — | 2 | 1 | no | — |
| 237 | C2×M32 | — | 2 | 1 | no | — |
| 238 | C2×M32 | — | 2 | 1 | no | — |
| 239 | C2×M32 | — | 2 | 1 | no | — |
| 240 | C2×M32 | — | 2 | 1 | no | — |
| 241 | C2×M32 | — | 2 | 1 | no | — |
| 242 | C2×M32 | — | 2 | 1 | no | — |
| 243 | C2×M32 | — | 2 | 1 | no | — |
| 244 | C2×M32 | — | 2 | 1 | no | — |
| 245 | C2×M32 | — | 2 | 1 | no | — |
| 246 | C2×M32 | — | 2 | 1 | no | — |
| 247 | C2×M32 | — | 2 | 1 | no | — |
| 248 | C2×M32 | — | 2 | 1 | no | — |
| 249 | C2×M32 | — | 2 | 1 | no | — |
| 250 | C2×M32 | — | 2 | 1 | no | — |
| 251 | C2×M32 | C2×D4 | 1 | 2 | yes | — |
| 252 | C2×M32 | #41 | 1 | 2 | yes | — |
| 253 | C2×M32 | #41 | 1 | 2 | yes | — |
| 254 | C22×C16 | — | 2 | 1 | no | — |
| 255 | C22×C16 | — | 2 | 1 | no | — |
| 256 | C22×C16 | — | 2 | 1 | no | — |
| 257 | C22×C16 | — | 2 | 1 | no | — |
| 258 | C2×#108 | — | 2 | 1 | no | — |
| 259 | C2×#108 | — | 2 | 1 | no | — |
| 260 | C2×#108 | — | 2 | 1 | no | — |
| 261 | C2×#108 | — | 2 | 1 | no | — |
| 262 | C2×#108 | — | 2 | 1 | no | — |
| 263 | C2×#108 | — | 2 | 1 | no | — |
| 264 | C2×#108 | — | 2 | 1 | no | — |
| 265 | C2×#108 | — | 2 | 1 | no | — |
| 266 | C2×#108 | — | 2 | 1 | no | — |
| 267 | C2×#108 | — | 2 | 1 | no | — |
| 268 | C2×#108 | — | 2 | 1 | no | — |
| 269 | C2×#108 | — | 2 | 1 | no | — |
| 270 | C2×#108 | — | 2 | 1 | no | — |
| 271 | C2×#108 | — | 2 | 1 | no | — |
| 272 | C2×#108 | — | 2 | 1 | no | — |
| 273 | C2×#108 | — | 2 | 1 | no | — |
| 274 | C2×#108 | — | 2 | 1 | no | — |
| 275 | C2×#108 | — | 2 | 1 | no | — |
| 276 | C2×#108 | — | 2 | 1 | no | — |
| 277 | C2×#108 | — | 2 | 1 | no | — |
| 278 | C2×#108 | — | 2 | 1 | no | — |
| 279 | C2×#108 | — | 2 | 1 | no | — |
| 280 | C2×#108 | C2×D4 | 1 | 2 | yes | — |
| 281 | C2×#108 | #41 | 1 | 2 | yes | — |
| 282 | #428 | — | 4 | 2 | no | — |
| 283 | #428 | — | 4 | 2 | no | — |
| 284 | #428 | — | 8 | 1 | no | — |
| 285 | #428 | — | 8 | 1 | no | — |
| 286 | #427 | — | 2 | 1 | no | — |
| 287 | #427 | — | 2 | 1 | no | — |
| 288 | #427 | — | 2 | 1 | no | — |
| 289 | #427 | C2×D4 | 1 | 2 | yes | — |
| 290 | C2×#107 | — | 2 | 1 | no | — |
| 291 | C2×#107 | — | 4 | 1 | no | — |
| 292 | C2×#107 | — | 4 | 1 | no | — |
| 293 | C2×#106 | — | 2 | 1 | no | — |
| 294 | C2×#106 | — | 2 | 1 | no | — |
| 295 | C2×#106 | — | 2 | 1 | no | — |
| 296 | C2×#106 | — | 2 | 1 | no | — |
| 297 | C2×#106 | — | 2 | 1 | no | — |
| 298 | C2×#106 | — | 2 | 1 | no | — |
| 299 | C2×#106 | — | 2 | 1 | no | — |
| 300 | C2×#106 | — | 4 | 1 | no | — |
| 301 | C2×#106 | — | 4 | 1 | no | — |
| 302 | #424 | — | 4 | 2 | no | — |
| 303 | #424 | — | 8 | 1 | no | — |
| 304 | #423 | — | 4 | 1 | no | — |
| 305 | #423 | — | 4 | 1 | no | — |
| 306 | C2×C4⋊C8 | — | 4 | 1 | no | — |
| 307 | C2×C4⋊C8 | — | 8 | 1 | no | — |
| 308 | #421 | — | 4 | 2 | no | — |
| 309 | #421 | — | 4 | 2 | no | — |
| 310 | #421 | — | 8 | 1 | no | — |
| 311 | #421 | — | 8 | 1 | no | — |
| 312 | C2×#104 | — | 4 | 2 | no | — |
| 313 | C2×#104 | — | 4 | 2 | no | — |
| 314 | C2×#104 | — | 4 | 2 | no | — |
| 315 | C2×#104 | — | 4 | 1 | no | — |
| 316 | C2×#104 | — | 4 | 1 | no | — |
| 317 | C2×#104 | — | 8 | 1 | no | — |
| 318 | #418 | — | 4 | 2 | no | — |
| 319 | #418 | — | 4 | 2 | no | — |
| 320 | #418 | — | 8 | 1 | no | — |
| 321 | #418 | — | 8 | 1 | no | — |
| 322 | C2×#102 | — | 4 | 1 | no | — |
| 323 | C2×#102 | — | 4 | 1 | no | — |
| 324 | C2×#102 | — | 4 | 1 | no | — |
| 325 | C2×#102 | — | 4 | 1 | no | — |
| 326 | C2×#102 | — | 4 | 2 | no | — |
| 327 | C2×#102 | — | 8 | 1 | no | — |
| 328 | C2×#102 | — | 8 | 1 | no | — |
| 329 | C2×#100 | — | 4 | 2 | no | — |
| 330 | C2×#100 | — | 4 | 2 | no | — |
| 331 | C2×#100 | — | 4 | 2 | no | — |
| 332 | C2×#100 | — | 4 | 2 | no | — |
| 333 | C2×#100 | — | 8 | 1 | no | — |
| 334 | C2×#100 | — | 8 | 1 | no | — |
| 335 | #410 | — | 4 | 2 | no | — |
| 336 | #410 | — | 8 | 1 | no | — |
| 337 | C2×#99 | — | 4 | 2 | no | — |
| 338 | #408 | — | 4 | 2 | no | — |
| 339 | #408 | — | 4 | 2 | no | — |
| 340 | #408 | — | 8 | 1 | no | — |
| 341 | #408 | — | 8 | 1 | no | — |
| 342 | #407 | — | 8 | 1 | no | — |
| 343 | C2×C22⋊C8 | — | 8 | 1 | no | — |
| 344 | #405 | — | 2 | 1 | no | — |
| 345 | #405 | — | 2 | 1 | no | — |
| 346 | #405 | — | 2 | 1 | no | — |
| 347 | #405 | — | 2 | 1 | no | — |
| 348 | #405 | — | 2 | 1 | no | — |
| 349 | #405 | — | 2 | 1 | no | — |
| 350 | #405 | — | 2 | 1 | no | — |
| 351 | #405 | — | 2 | 1 | no | — |
| 352 | C2×#97 | — | 2 | 1 | no | — |
| 353 | C2×#97 | — | 2 | 1 | no | — |
| 354 | C2×#97 | — | 2 | 1 | no | — |
| 355 | C2×#97 | — | 2 | 1 | no | — |
| 356 | C2×#97 | — | 2 | 1 | no | — |
| 357 | C2×#97 | — | 2 | 1 | no | — |
| 358 | C2×#97 | — | 2 | 1 | no | — |
| 359 | C2×#97 | — | 2 | 1 | no | — |
| 360 | C2×C4×C8 | — | 2 | 1 | no | — |
| 361 | C2×C4×C8 | — | 2 | 1 | no | — |
| 362 | #390 | — | 4 | 2 | no | — |
| 363 | #390 | — | 4 | 1 | no | — |
| 364 | #390 | — | 4 | 1 | no | — |
| 365 | #384 | — | 2 | 1 | no | — |
| 366 | #382 | — | 2 | 1 | no | — |
| 367 | #380 | — | 4 | 1 | no | — |
| 368 | C4×C4⋊C4 | — | 4 | 1 | no | — |
| 369 | #362 | — | 2 | 4 | no | — |
| 370 | #362 | — | 4 | 2 | no | — |
| 371 | #361 | — | 2 | 4 | no | — |
| 372 | #361 | — | 4 | 2 | no | — |
| 373 | #361 | — | 4 | 4 | no | — |
| 374 | #361 | — | 4 | 4 | no | — |
| 375 | #360 | — | 4 | 4 | no | — |
| 376 | #357 | — | 4 | 4 | no | — |
| 377 | #347 | — | 4 | 4 | no | — |
| 378 | #344 | — | 4 | 2 | no | — |
| 379 | #344 | — | 8 | 1 | no | — |
| 380 | #343 | — | 4 | 2 | no | — |
| 381 | #343 | — | 4 | 2 | no | — |
| 382 | #341 | — | 8 | 1 | no | — |
| 383 | #341 | — | 8 | 1 | no | — |
| 384 | #339 | — | 4 | 2 | no | — |
| 385 | H(3,ℤ/4) | — | 4 | 2 | no | — |
| 386 | #336 | — | 4 | 1 | no | — |
| 387 | #336 | — | 4 | 1 | no | — |
| 388 | #336 | — | 4 | 1 | no | — |
| 389 | #336 | — | 4 | 1 | no | — |
| 390 | C25 | — | 4 | 1 | no | — |
| 391 | C2×#41 | — | 4 | 1 | no | — |
| 392 | C2×#41 | — | 4 | 1 | no | — |
| 393 | C2×#41 | — | 4 | 1 | no | — |
| 394 | C2×#41 | — | 4 | 1 | no | — |
| 395 | C2×#41 | — | 4 | 1 | no | — |
| 396 | C2×#41 | — | 4 | 1 | no | — |
| 397 | C2×#41 | — | 4 | 1 | no | — |
| 398 | C2×#41 | — | 4 | 1 | no | — |
| 399 | C2×#41 | — | 4 | 1 | no | — |
| 400 | C2×#41 | — | 4 | 1 | no | — |
| 401 | C2×#41 | — | 4 | 1 | no | — |
| 402 | C2×#41 | — | 4 | 1 | no | — |
| 403 | C22×Q8 | — | 2 | 1 | no | — |
| 404 | C22×D4 | — | 2 | 2 | no | — |
| 405 | C22×D4 | — | 2 | 1 | no | — |
| 406 | C22×D4 | — | 4 | 1 | no | — |
| 407 | C22×D4 | — | 4 | 1 | no | — |
| 408 | C22×D4 | — | 4 | 1 | no | — |
| 409 | C22×D4 | — | 4 | 1 | no | — |
| 410 | C22×D4 | — | 4 | 1 | no | — |
| 411 | C22×D4 | — | 4 | 1 | no | — |
| 412 | C22×D4 | — | 4 | 1 | no | — |
| 413 | C22×D4 | — | 4 | 1 | no | — |
| 414 | C22×D4 | — | 4 | 1 | no | — |
| 415 | C22×D4 | — | 4 | 1 | no | — |
| 416 | C22×D4 | — | 4 | 1 | no | — |
| 417 | C22×D4 | — | 4 | 1 | no | — |
| 418 | C22×D4 | — | 4 | 1 | no | — |
| 419 | C22×D4 | — | 4 | 1 | no | — |
| 420 | C23×C4 | — | 2 | 1 | no | — |
| 421 | C23×C4 | — | 4 | 1 | no | — |
| 422 | C23×C4 | — | 4 | 1 | no | — |
| 423 | C23×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 424 | #135 | — | 4 | 1 | no | — |
| 425 | #135 | — | 4 | 1 | no | — |
| 426 | #135 | — | 4 | 1 | no | — |
| 427 | #135 | — | 4 | 1 | no | — |
| 428 | #135 | — | 4 | 1 | no | — |
| 429 | #135 | — | 4 | 1 | no | — |
| 430 | #135 | — | 4 | 1 | no | — |
| 431 | #135 | — | 4 | 1 | no | — |
| 432 | #135 | — | 4 | 1 | no | — |
| 433 | #135 | — | 4 | 1 | no | — |
| 434 | #135 | — | 4 | 1 | no | — |
| 435 | #135 | — | 4 | 1 | no | — |
| 436 | #135 | — | 4 | 1 | no | — |
| 437 | #135 | — | 4 | 1 | no | — |
| 438 | #135 | — | 4 | 1 | no | — |
| 439 | #135 | — | 4 | 1 | no | — |
| 440 | C2×Q16 | — | 2 | 1 | no | — |
| 441 | C2×Q16 | — | 2 | 1 | no | — |
| 442 | C2×Q16 | — | 2 | 1 | no | — |
| 443 | C2×Q16 | — | 2 | 1 | no | — |
| 444 | C2×Q16 | — | 2 | 1 | no | — |
| 445 | C2×Q16 | — | 2 | 1 | no | — |
| 446 | C2×SD16 | — | 4 | 1 | no | — |
| 447 | C2×SD16 | — | 4 | 1 | no | — |
| 448 | C2×SD16 | — | 4 | 1 | no | — |
| 449 | C2×SD16 | — | 4 | 1 | no | — |
| 450 | C2×SD16 | — | 4 | 1 | no | — |
| 451 | C2×SD16 | — | 4 | 1 | no | — |
| 452 | C2×D8 | — | 2 | 1 | no | — |
| 453 | C2×D8 | — | 2 | 2 | no | — |
| 454 | C2×D8 | — | 2 | 2 | no | — |
| 455 | C2×D8 | — | 2 | 1 | no | — |
| 456 | C2×D8 | — | 2 | 2 | no | — |
| 457 | C2×D8 | — | 2 | 1 | no | — |
| 458 | C2×D8 | — | 2 | 2 | no | — |
| 459 | C2×D8 | — | 2 | 2 | no | — |
| 460 | C2×D8 | — | 2 | 2 | no | — |
| 461 | C2×D8 | — | 2 | 1 | no | — |
| 462 | C2×D8 | — | 2 | 1 | no | — |
| 463 | C2×D8 | — | 2 | 1 | no | — |
| 464 | C2×D8 | — | 4 | 1 | no | — |
| 465 | C2×D8 | — | 4 | 1 | no | — |
| 466 | C2×D8 | — | 4 | 1 | no | — |
| 467 | C2×D8 | — | 4 | 1 | no | — |
| 468 | C2×D8 | — | 4 | 1 | no | — |
| 469 | C2×D8 | — | 4 | 1 | no | — |
| 470 | C2×D8 | — | 4 | 1 | no | — |
| 471 | C2×D8 | — | 4 | 1 | no | — |
| 472 | C2×D8 | — | 4 | 1 | no | — |
| 473 | C2×D8 | — | 4 | 1 | no | — |
| 474 | C2×D8 | — | 4 | 1 | no | — |
| 475 | C2×D8 | — | 4 | 1 | no | — |
| 476 | C2×D8 | — | 4 | 1 | no | — |
| 477 | C2×D8 | — | 4 | 1 | no | — |
| 478 | C2×D8 | — | 4 | 1 | no | — |
| 479 | C2×D8 | — | 4 | 1 | no | — |
| 480 | C2×D8 | — | 4 | 1 | no | — |
| 481 | C2×D8 | — | 4 | 1 | no | — |
| 482 | C2×D8 | — | 4 | 1 | no | — |
| 483 | C2×D8 | — | 4 | 1 | no | — |
| 484 | C2×D8 | — | 4 | 1 | no | — |
| 485 | C2×D8 | — | 4 | 1 | no | — |
| 486 | C2×M16 | — | 2 | 2 | no | — |
| 487 | C2×M16 | — | 2 | 1 | no | — |
| 488 | C2×M16 | — | 2 | 1 | no | — |
| 489 | C2×M16 | — | 2 | 2 | no | — |
| 490 | C2×M16 | — | 2 | 1 | no | — |
| 491 | C2×M16 | — | 2 | 1 | no | — |
| 492 | C2×M16 | — | 2 | 1 | no | — |
| 493 | C2×M16 | — | 2 | 1 | no | — |
| 494 | C2×M16 | — | 2 | 1 | no | — |
| 495 | C2×M16 | — | 2 | 1 | no | — |
| 496 | C2×M16 | — | 2 | 1 | no | — |
| 497 | C2×M16 | — | 2 | 1 | no | — |
| 498 | C2×M16 | — | 2 | 1 | no | — |
| 499 | C2×M16 | — | 2 | 1 | no | — |
| 500 | C2×M16 | — | 4 | 1 | no | — |
| 501 | C2×M16 | — | 4 | 1 | no | — |
| 502 | C2×M16 | — | 4 | 1 | no | — |
| 503 | C2×M16 | — | 4 | 1 | no | — |
| 504 | C2×M16 | — | 4 | 1 | no | — |
| 505 | C2×M16 | — | 4 | 1 | no | — |
| 506 | C2×M16 | — | 4 | 1 | no | — |
| 507 | C2×M16 | — | 4 | 1 | no | — |
| 508 | C2×M16 | — | 4 | 1 | no | — |
| 509 | C2×M16 | — | 4 | 1 | no | — |
| 510 | C2×M16 | — | 4 | 1 | no | — |
| 511 | C2×M16 | — | 4 | 1 | no | — |
| 512 | C2×M16 | — | 4 | 1 | no | — |
| 513 | C2×M16 | — | 4 | 1 | no | — |
| 514 | C2×M16 | — | 4 | 1 | no | — |
| 515 | C2×M16 | — | 4 | 1 | no | — |
| 516 | C2×M16 | — | 4 | 1 | no | — |
| 517 | C2×M16 | — | 4 | 1 | no | — |
| 518 | C2×M16 | — | 4 | 1 | no | — |
| 519 | C2×M16 | — | 4 | 1 | no | — |
| 520 | C2×M16 | — | 4 | 1 | no | — |
| 521 | C2×M16 | — | 4 | 1 | no | — |
| 522 | C22×C8 | — | 2 | 1 | no | — |
| 523 | C22×C8 | — | 2 | 1 | no | — |
| 524 | C22×C8 | — | 2 | 1 | no | — |
| 525 | C22×C8 | — | 2 | 1 | no | — |
| 526 | C22×C8 | — | 2 | 1 | no | — |
| 527 | C22×C8 | — | 2 | 1 | no | — |
| 528 | C22×C8 | — | 2 | 1 | no | — |
| 529 | C22×C8 | — | 2 | 1 | no | — |
| 530 | C22×C8 | — | 2 | 1 | no | — |
| 531 | C22×C8 | — | 4 | 1 | no | — |
| 532 | C22×C8 | — | 4 | 1 | no | — |
| 533 | C22×C8 | — | 4 | 1 | no | — |
| 534 | C22×C8 | — | 4 | 1 | no | — |
| 535 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 536 | C22×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 537 | C22×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 538 | C22×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 539 | C22×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 540 | C22×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 541 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 542 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 543 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 544 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 545 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 546 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 547 | C22×C8 | 2−1+4 | 1 | 1 | yes | characteristic |
| 548 | C22×C8 | 2−1+4 | 1 | 1 | yes | characteristic |
| 549 | #117 | — | 2 | 2 | no | — |
| 550 | #117 | — | 2 | 1 | no | — |
| 551 | #117 | — | 2 | 1 | no | — |
| 552 | #117 | — | 2 | 1 | no | — |
| 553 | #117 | — | 2 | 1 | no | — |
| 554 | #117 | — | 2 | 1 | no | — |
| 555 | #117 | — | 2 | 1 | no | — |
| 556 | #117 | — | 2 | 1 | no | — |
| 557 | #117 | — | 2 | 1 | no | — |
| 558 | #117 | — | 4 | 1 | no | — |
| 559 | #117 | — | 4 | 1 | no | — |
| 560 | #117 | — | 4 | 1 | no | — |
| 561 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 562 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 563 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 564 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 565 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 566 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 567 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 568 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 569 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 570 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 571 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 572 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 573 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 574 | C2×C22⋊C4 | — | 8 | 2 | no | — |
| 575 | C2×C22⋊C4 | — | 8 | 2 | no | — |
| 576 | C2×C22⋊C4 | — | 16 | 4 | no | — |
| 577 | C2×C42 | — | 2 | 1 | no | — |
| 578 | C2×C42 | — | 2 | 1 | no | — |
| 579 | C2×C42 | — | 2 | 1 | no | — |
| 580 | C2×C42 | — | 2 | 1 | no | — |
| 581 | C2×C42 | — | 2 | 1 | no | — |
| 582 | C2×C42 | — | 2 | 1 | no | — |
| 583 | C2×C42 | — | 2 | 1 | no | — |
| 584 | C2×C42 | — | 4 | 1 | no | — |
| 585 | C2×C42 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 586 | C2×C42 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 587 | SD32 | — | 4 | 8 | no | — |
| 588 | D16 | — | 4 | 8 | no | — |
| 589 | M32 | — | 2 | 2 | no | — |
| 590 | M32 | — | 2 | 2 | no | — |
| 591 | M32 | — | 2 | 2 | no | — |
| 592 | M32 | — | 2 | 2 | no | — |
| 593 | M32 | — | 2 | 2 | no | — |
| 594 | M32 | — | 2 | 2 | no | — |
| 595 | M32 | — | 4 | 1 | no | — |
| 596 | M32 | — | 4 | 1 | no | — |
| 597 | M32 | — | 4 | 1 | no | — |
| 598 | M32 | — | 4 | 1 | no | — |
| 599 | M32 | — | 4 | 1 | no | — |
| 600 | M32 | — | 4 | 1 | no | — |
| 601 | M32 | — | 4 | 1 | no | — |
| 602 | M32 | — | 4 | 1 | no | — |
| 603 | M32 | — | 4 | 1 | no | — |
| 604 | M32 | — | 4 | 1 | no | — |
| 605 | C2×C16 | — | 2 | 2 | no | — |
| 606 | C2×C16 | — | 2 | 2 | no | — |
| 607 | C2×C16 | — | 2 | 2 | no | — |
| 608 | C2×C16 | — | 4 | 1 | no | — |
| 609 | C2×C16 | — | 4 | 1 | no | — |
| 610 | C2×C16 | — | 4 | 1 | no | — |
| 611 | C2×C16 | — | 4 | 1 | no | — |
| 612 | C2×C16 | — | 4 | 1 | no | — |
| 613 | C2×C16 | — | 4 | 1 | no | — |
| 614 | C2×C16 | — | 4 | 1 | no | — |
| 615 | C2×C16 | — | 4 | 1 | no | — |
| 616 | C2×C16 | — | 4 | 1 | no | — |
| 617 | #108 | — | 2 | 2 | no | — |
| 618 | #108 | — | 2 | 2 | no | — |
| 619 | #108 | — | 2 | 2 | no | — |
| 620 | #108 | — | 2 | 2 | no | — |
| 621 | #108 | — | 4 | 1 | no | — |
| 622 | #108 | — | 4 | 1 | no | — |
| 623 | #108 | — | 4 | 1 | no | — |
| 624 | #108 | — | 4 | 1 | no | — |
| 625 | #108 | — | 4 | 1 | no | — |
| 626 | #108 | — | 4 | 1 | no | — |
| 627 | #108 | — | 4 | 1 | no | — |
| 628 | #108 | — | 4 | 1 | no | — |
| 629 | #108 | — | 4 | 1 | no | — |
| 630 | #108 | — | 4 | 1 | no | — |
| 631 | #108 | — | 4 | 1 | no | — |
| 632 | #108 | — | 4 | 1 | no | — |
| 633 | #107 | — | 2 | 2 | no | — |
| 634 | #107 | — | 4 | 1 | no | — |
| 635 | #107 | — | 8 | 2 | no | — |
| 636 | #107 | — | 8 | 2 | no | — |
| 637 | #106 | — | 2 | 2 | no | — |
| 638 | #106 | — | 4 | 1 | no | — |
| 639 | #106 | — | 4 | 1 | no | — |
| 640 | #106 | — | 4 | 1 | no | — |
| 641 | #106 | — | 4 | 1 | no | — |
| 642 | #106 | — | 4 | 1 | no | — |
| 643 | #106 | — | 8 | 2 | no | — |
| 644 | #106 | — | 8 | 2 | no | — |
| 645 | C4⋊C8 | — | 4 | 4 | no | — |
| 646 | C4⋊C8 | — | 8 | 4 | no | — |
| 647 | #104 | — | 8 | 2 | no | — |
| 648 | #104 | — | 8 | 2 | no | — |
| 649 | #104 | — | 8 | 4 | no | — |
| 650 | #104 | — | 8 | 4 | no | — |
| 651 | #102 | — | 8 | 2 | no | — |
| 652 | #102 | — | 8 | 2 | no | — |
| 653 | #102 | — | 8 | 2 | no | — |
| 654 | #102 | — | 8 | 2 | no | — |
| 655 | #102 | — | 8 | 4 | no | — |
| 656 | #100 | — | 8 | 4 | no | — |
| 657 | #100 | — | 8 | 4 | no | — |
| 658 | #99 | — | 8 | 4 | no | — |
| 659 | C22⋊C8 | — | 8 | 4 | no | — |
| 660 | C22⋊C8 | — | 8 | 4 | no | — |
| 661 | #97 | — | 4 | 1 | no | — |
| 662 | #97 | — | 4 | 1 | no | — |
| 663 | #97 | — | 4 | 1 | no | — |
| 664 | #97 | — | 4 | 1 | no | — |
| 665 | #97 | — | 4 | 1 | no | — |
| 666 | #97 | — | 4 | 1 | no | — |
| 667 | #97 | — | 4 | 1 | no | — |
| 668 | #97 | — | 4 | 1 | no | — |
| 669 | C4×C8 | — | 4 | 1 | no | — |
| 670 | C4×C8 | — | 4 | 1 | no | — |
| 671 | C4×C8 | — | 4 | 1 | no | — |
| 672 | C4×C8 | — | 4 | 1 | no | — |
| 673 | #95 | — | 4 | 2 | no | — |
| 674 | C24 | — | 4 | 2 | no | — |
| 675 | C24 | — | 4 | 1 | no | — |
| 676 | C24 | — | 8 | 1 | no | — |
| 677 | C24 | — | 8 | 1 | no | — |
| 678 | C24 | — | 8 | 1 | no | — |
| 679 | C24 | — | 8 | 1 | no | — |
| 680 | C24 | — | 8 | 1 | no | — |
| 681 | C24 | — | 8 | 1 | no | — |
| 682 | C24 | — | 16 | 2 | no | — |
| 683 | C24 | — | 16 | 2 | no | — |
| 684 | C24 | #575 | 1 | 1 | yes | characteristic |
| 685 | #41 | — | 8 | 1 | no | — |
| 686 | #41 | — | 8 | 1 | no | — |
| 687 | #41 | — | 8 | 1 | no | — |
| 688 | #41 | — | 8 | 1 | no | — |
| 689 | #41 | — | 8 | 1 | no | — |
| 690 | #41 | — | 8 | 1 | no | — |
| 691 | #41 | — | 8 | 1 | no | — |
| 692 | #41 | — | 8 | 1 | no | — |
| 693 | #41 | — | 8 | 1 | no | — |
| 694 | #41 | — | 8 | 1 | no | — |
| 695 | #41 | — | 8 | 1 | no | — |
| 696 | #41 | — | 8 | 1 | no | — |
| 697 | #41 | — | 8 | 1 | no | — |
| 698 | #41 | — | 8 | 1 | no | — |
| 699 | #41 | — | 8 | 1 | no | — |
| 700 | #41 | — | 8 | 1 | no | — |
| 701 | C2×Q8 | — | 4 | 1 | no | — |
| 702 | C2×Q8 | — | 4 | 1 | no | — |
| 703 | C2×Q8 | — | 4 | 1 | no | — |
| 704 | C2×Q8 | — | 4 | 1 | no | — |
| 705 | C2×Q8 | — | 4 | 1 | no | — |
| 706 | C2×Q8 | — | 4 | 1 | no | — |
| 707 | C2×D4 | — | 4 | 2 | no | — |
| 708 | C2×D4 | — | 4 | 1 | no | — |
| 709 | C2×D4 | — | 4 | 2 | no | — |
| 710 | C2×D4 | — | 4 | 2 | no | — |
| 711 | C2×D4 | — | 4 | 1 | no | — |
| 712 | C2×D4 | — | 4 | 1 | no | — |
| 713 | C2×D4 | — | 4 | 2 | no | — |
| 714 | C2×D4 | — | 4 | 2 | no | — |
| 715 | C2×D4 | — | 4 | 1 | no | — |
| 716 | C2×D4 | — | 4 | 1 | no | — |
| 717 | C2×D4 | — | 4 | 2 | no | — |
| 718 | C2×D4 | — | 4 | 1 | no | — |
| 719 | C2×D4 | — | 8 | 1 | no | — |
| 720 | C2×D4 | — | 8 | 1 | no | — |
| 721 | C2×D4 | — | 8 | 1 | no | — |
| 722 | C2×D4 | — | 8 | 1 | no | — |
| 723 | C2×D4 | — | 8 | 1 | no | — |
| 724 | C2×D4 | — | 8 | 1 | no | — |
| 725 | C2×D4 | — | 8 | 1 | no | — |
| 726 | C2×D4 | — | 8 | 1 | no | — |
| 727 | C2×D4 | — | 8 | 1 | no | — |
| 728 | C2×D4 | — | 8 | 1 | no | — |
| 729 | C2×D4 | — | 8 | 1 | no | — |
| 730 | C2×D4 | — | 8 | 1 | no | — |
| 731 | C2×D4 | — | 8 | 1 | no | — |
| 732 | C2×D4 | — | 8 | 1 | no | — |
| 733 | C2×D4 | — | 8 | 1 | no | — |
| 734 | C2×D4 | — | 8 | 1 | no | — |
| 735 | C2×D4 | — | 8 | 1 | no | — |
| 736 | C2×D4 | — | 8 | 1 | no | — |
| 737 | C2×D4 | — | 8 | 1 | no | — |
| 738 | C2×D4 | — | 8 | 1 | no | — |
| 739 | C2×D4 | — | 8 | 1 | no | — |
| 740 | C2×D4 | — | 8 | 1 | no | — |
| 741 | C2×D4 | — | 8 | 1 | no | — |
| 742 | C2×D4 | — | 8 | 1 | no | — |
| 743 | C2×D4 | — | 8 | 1 | no | — |
| 744 | C2×D4 | — | 8 | 1 | no | — |
| 745 | C2×D4 | — | 8 | 1 | no | — |
| 746 | C2×D4 | — | 8 | 1 | no | — |
| 747 | C22×C4 | — | 2 | 1 | no | — |
| 748 | C22×C4 | — | 2 | 1 | no | — |
| 749 | C22×C4 | — | 4 | 1 | no | — |
| 750 | C22×C4 | — | 4 | 1 | no | — |
| 751 | C22×C4 | — | 4 | 1 | no | — |
| 752 | C22×C4 | — | 4 | 1 | no | — |
| 753 | C22×C4 | — | 4 | 1 | no | — |
| 754 | C22×C4 | — | 8 | 2 | no | — |
| 755 | C22×C4 | — | 8 | 1 | no | — |
| 756 | C22×C4 | — | 8 | 1 | no | — |
| 757 | C22×C4 | — | 8 | 1 | no | — |
| 758 | C22×C4 | — | 8 | 1 | no | — |
| 759 | C22×C4 | — | 8 | 1 | no | — |
| 760 | C22×C4 | — | 8 | 1 | no | — |
| 761 | C22×C4 | — | 8 | 1 | no | — |
| 762 | C22×C4 | — | 8 | 1 | no | — |
| 763 | C22×C4 | — | 8 | 1 | no | — |
| 764 | C22×C4 | — | 8 | 1 | no | — |
| 765 | C22×C4 | — | 16 | 2 | no | — |
| 766 | C22×C4 | #532 | 1 | 1 | yes | characteristic |
| 767 | C22×C4 | #534 | 1 | 1 | yes | characteristic |
| 768 | C22×C4 | #535 | 1 | 1 | yes | characteristic |
| 769 | C22×C4 | D42 | 1 | 1 | yes | characteristic |
| 770 | C22×C4 | #546 | 1 | 1 | yes | characteristic |
| 771 | C22×C4 | #548 | 1 | 1 | yes | characteristic |
| 772 | C22×C4 | #548 | 1 | 1 | yes | characteristic |
| 773 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 774 | C22×C4 | #575 | 1 | 1 | yes | characteristic |
| 775 | C22×C4 | #575 | 1 | 1 | yes | characteristic |
| 776 | C22×C4 | #576 | 1 | 1 | yes | characteristic |
| 777 | C22×C4 | #576 | 1 | 1 | yes | characteristic |
| 778 | C22×C4 | #576 | 1 | 1 | yes | characteristic |
| 779 | C22×C4 | #577 | 1 | 1 | yes | characteristic |
| 780 | Q16 | — | 4 | 1 | no | — |
| 781 | Q16 | — | 4 | 1 | no | — |
| 782 | Q16 | — | 4 | 1 | no | — |
| 783 | Q16 | — | 4 | 1 | no | — |
| 784 | SD16 | — | 8 | 1 | no | — |
| 785 | SD16 | — | 8 | 1 | no | — |
| 786 | SD16 | — | 8 | 1 | no | — |
| 787 | SD16 | — | 8 | 1 | no | — |
| 788 | D8 | — | 4 | 1 | no | — |
| 789 | D8 | — | 4 | 2 | no | — |
| 790 | D8 | — | 4 | 2 | no | — |
| 791 | D8 | — | 4 | 2 | no | — |
| 792 | D8 | — | 4 | 1 | no | — |
| 793 | D8 | — | 4 | 1 | no | — |
| 794 | D8 | — | 4 | 2 | no | — |
| 795 | D8 | — | 4 | 1 | no | — |
| 796 | D8 | — | 8 | 1 | no | — |
| 797 | D8 | — | 8 | 1 | no | — |
| 798 | D8 | — | 8 | 1 | no | — |
| 799 | D8 | — | 8 | 1 | no | — |
| 800 | M16 | — | 4 | 2 | no | — |
| 801 | M16 | — | 4 | 2 | no | — |
| 802 | M16 | — | 4 | 1 | no | — |
| 803 | M16 | — | 4 | 1 | no | — |
| 804 | M16 | — | 4 | 1 | no | — |
| 805 | M16 | — | 4 | 2 | no | — |
| 806 | M16 | — | 4 | 1 | no | — |
| 807 | M16 | — | 4 | 1 | no | — |
| 808 | M16 | — | 4 | 2 | no | — |
| 809 | M16 | — | 4 | 1 | no | — |
| 810 | M16 | — | 4 | 1 | no | — |
| 811 | M16 | — | 4 | 1 | no | — |
| 812 | M16 | — | 8 | 1 | no | — |
| 813 | M16 | — | 8 | 1 | no | — |
| 814 | M16 | — | 8 | 1 | no | — |
| 815 | M16 | — | 8 | 1 | no | — |
| 816 | M16 | — | 8 | 1 | no | — |
| 817 | M16 | — | 8 | 1 | no | — |
| 818 | M16 | — | 8 | 1 | no | — |
| 819 | M16 | — | 8 | 1 | no | — |
| 820 | M16 | — | 8 | 1 | no | — |
| 821 | M16 | — | 8 | 1 | no | — |
| 822 | M16 | — | 8 | 1 | no | — |
| 823 | M16 | — | 8 | 1 | no | — |
| 824 | C2×C8 | — | 4 | 1 | no | — |
| 825 | C2×C8 | — | 4 | 1 | no | — |
| 826 | C2×C8 | — | 4 | 1 | no | — |
| 827 | C2×C8 | — | 4 | 1 | no | — |
| 828 | C2×C8 | — | 4 | 1 | no | — |
| 829 | C2×C8 | — | 4 | 1 | no | — |
| 830 | C2×C8 | — | 4 | 1 | no | — |
| 831 | C2×C8 | — | 4 | 1 | no | — |
| 832 | C2×C8 | — | 4 | 1 | no | — |
| 833 | C2×C8 | — | 4 | 1 | no | — |
| 834 | C2×C8 | — | 4 | 1 | no | — |
| 835 | C2×C8 | — | 4 | 1 | no | — |
| 836 | C2×C8 | — | 4 | 1 | no | — |
| 837 | C2×C8 | — | 4 | 2 | no | — |
| 838 | C2×C8 | — | 4 | 2 | no | — |
| 839 | C2×C8 | — | 8 | 1 | no | — |
| 840 | C2×C8 | — | 8 | 1 | no | — |
| 841 | C2×C8 | — | 8 | 1 | no | — |
| 842 | C2×C8 | — | 8 | 1 | no | — |
| 843 | C2×C8 | — | 8 | 1 | no | — |
| 844 | C2×C8 | — | 8 | 1 | no | — |
| 845 | C2×C8 | — | 8 | 1 | no | — |
| 846 | C2×C8 | — | 8 | 1 | no | — |
| 847 | C2×C8 | — | 8 | 1 | no | — |
| 848 | C2×C8 | — | 8 | 1 | no | — |
| 849 | C2×C8 | #525 | 1 | 1 | yes | characteristic |
| 850 | C2×C8 | #529 | 1 | 1 | yes | characteristic |
| 851 | C2×C8 | #535 | 1 | 1 | yes | characteristic |
| 852 | C2×C8 | #537 | 1 | 1 | yes | characteristic |
| 853 | C2×C8 | #538 | 1 | 1 | yes | characteristic |
| 854 | C2×C8 | #538 | 1 | 1 | yes | characteristic |
| 855 | C2×C8 | #538 | 1 | 1 | yes | characteristic |
| 856 | C2×C8 | #538 | 1 | 1 | yes | characteristic |
| 857 | C2×C8 | #539 | 1 | 1 | yes | characteristic |
| 858 | C2×C8 | #539 | 1 | 1 | yes | characteristic |
| 859 | C2×C8 | #539 | 1 | 1 | yes | characteristic |
| 860 | C2×C8 | #539 | 1 | 1 | yes | characteristic |
| 861 | C2×C8 | #540 | 1 | 1 | yes | characteristic |
| 862 | C2×C8 | #540 | 1 | 1 | yes | characteristic |
| 863 | C2×C8 | #540 | 1 | 1 | yes | characteristic |
| 864 | C2×C8 | #542 | 1 | 1 | yes | characteristic |
| 865 | C2×C8 | #546 | 1 | 1 | yes | characteristic |
| 866 | C2×C8 | #547 | 1 | 1 | yes | characteristic |
| 867 | C2×C8 | #550 | 1 | 1 | yes | characteristic |
| 868 | C2×C8 | #551 | 1 | 1 | yes | characteristic |
| 869 | C2×C8 | #551 | 1 | 1 | yes | characteristic |
| 870 | C2×C8 | #551 | 1 | 1 | yes | characteristic |
| 871 | C2×C8 | #551 | 1 | 1 | yes | characteristic |
| 872 | C2×C8 | #556 | 1 | 1 | yes | characteristic |
| 873 | C2×C8 | #560 | 1 | 1 | yes | characteristic |
| 874 | C2×C8 | #562 | 1 | 1 | yes | characteristic |
| 875 | C2×C8 | #562 | 1 | 1 | yes | characteristic |
| 876 | C2×C8 | #563 | 1 | 1 | yes | characteristic |
| 877 | C4⋊C4 | — | 4 | 2 | no | — |
| 878 | C4⋊C4 | — | 4 | 1 | no | — |
| 879 | C4⋊C4 | — | 4 | 1 | no | — |
| 880 | C4⋊C4 | — | 4 | 1 | no | — |
| 881 | C4⋊C4 | — | 4 | 1 | no | — |
| 882 | C4⋊C4 | — | 8 | 1 | no | — |
| 883 | C4⋊C4 | — | 8 | 1 | no | — |
| 884 | C4⋊C4 | — | 8 | 1 | no | — |
| 885 | C4⋊C4 | — | 8 | 1 | no | — |
| 886 | C4⋊C4 | — | 8 | 1 | no | — |
| 887 | C4⋊C4 | — | 16 | 2 | no | — |
| 888 | C22⋊C4 | — | 4 | 1 | no | — |
| 889 | C22⋊C4 | — | 4 | 2 | no | — |
| 890 | C22⋊C4 | — | 4 | 1 | no | — |
| 891 | C22⋊C4 | — | 4 | 1 | no | — |
| 892 | C22⋊C4 | — | 4 | 1 | no | — |
| 893 | C22⋊C4 | — | 8 | 1 | no | — |
| 894 | C22⋊C4 | — | 16 | 4 | no | — |
| 895 | C22⋊C4 | — | 16 | 4 | no | — |
| 896 | C42 | — | 2 | 1 | no | — |
| 897 | C42 | — | 2 | 1 | no | — |
| 898 | C42 | — | 2 | 1 | no | — |
| 899 | C42 | — | 2 | 1 | no | — |
| 900 | C42 | — | 4 | 1 | no | — |
| 901 | C42 | — | 4 | 1 | no | — |
| 902 | C42 | — | 4 | 1 | no | — |
| 903 | C42 | — | 4 | 1 | no | — |
| 904 | C42 | — | 4 | 1 | no | — |
| 905 | C42 | — | 4 | 1 | no | — |
| 906 | C42 | — | 4 | 2 | no | — |
| 907 | C42 | — | 8 | 1 | no | — |
| 908 | C16 | — | 4 | 2 | no | — |
| 909 | C16 | — | 4 | 2 | no | — |
| 910 | C16 | — | 4 | 2 | no | — |
| 911 | C16 | — | 8 | 1 | no | — |
| 912 | C23 | — | 4 | 2 | no | — |
| 913 | C23 | — | 8 | 1 | no | — |
| 914 | C23 | — | 8 | 2 | no | — |
| 915 | C23 | — | 8 | 1 | no | — |
| 916 | C23 | — | 8 | 2 | no | — |
| 917 | C23 | — | 8 | 2 | no | — |
| 918 | C23 | — | 8 | 1 | no | — |
| 919 | C23 | — | 16 | 2 | no | — |
| 920 | C23 | — | 16 | 2 | no | — |
| 921 | C23 | — | 16 | 2 | no | — |
| 922 | C23 | — | 16 | 4 | no | — |
| 923 | C23 | — | 16 | 4 | no | — |
| 924 | C23 | — | 16 | 1 | no | — |
| 925 | C23 | — | 16 | 1 | no | — |
| 926 | C23 | — | 16 | 1 | no | — |
| 927 | C23 | — | 16 | 1 | no | — |
| 928 | C23 | — | 32 | 2 | no | — |
| 929 | C23 | — | 32 | 2 | no | — |
| 930 | C23 | — | 32 | 1 | no | — |
| 931 | C23 | — | 32 | 1 | no | — |
| 932 | C23 | — | 32 | 1 | no | — |
| 933 | C23 | — | 32 | 1 | no | — |
| 934 | C23 | #3183 | 1 | 1 | yes | characteristic |
| 935 | C23 | #3194 | 1 | 1 | yes | characteristic |
| 936 | C23 | #3219 | 1 | 1 | yes | characteristic |
| 937 | C23 | #3268 | 1 | 1 | yes | characteristic |
| 938 | C23 | #3309 | 1 | 1 | yes | characteristic |
| 939 | C23 | #3370 | 1 | 1 | yes | characteristic |
| 940 | C23 | #3376 | 1 | 1 | yes | characteristic |
| 941 | Q8 | — | 8 | 1 | no | — |
| 942 | Q8 | — | 8 | 1 | no | — |
| 943 | Q8 | — | 8 | 1 | no | — |
| 944 | Q8 | — | 8 | 1 | no | — |
| 945 | D4 | — | 8 | 2 | no | — |
| 946 | D4 | — | 8 | 1 | no | — |
| 947 | D4 | — | 8 | 2 | no | — |
| 948 | D4 | — | 8 | 2 | no | — |
| 949 | D4 | — | 8 | 1 | no | — |
| 950 | D4 | — | 8 | 1 | no | — |
| 951 | D4 | — | 8 | 2 | no | — |
| 952 | D4 | — | 8 | 1 | no | — |
| 953 | D4 | — | 16 | 1 | no | — |
| 954 | D4 | — | 16 | 1 | no | — |
| 955 | D4 | — | 16 | 1 | no | — |
| 956 | D4 | — | 16 | 1 | no | — |
| 957 | D4 | — | 16 | 1 | no | — |
| 958 | D4 | — | 16 | 1 | no | — |
| 959 | D4 | — | 16 | 1 | no | — |
| 960 | D4 | — | 16 | 1 | no | — |
| 961 | C2×C4 | — | 4 | 2 | no | — |
| 962 | C2×C4 | — | 4 | 2 | no | — |
| 963 | C2×C4 | — | 4 | 1 | no | — |
| 964 | C2×C4 | — | 4 | 1 | no | — |
| 965 | C2×C4 | — | 8 | 2 | no | — |
| 966 | C2×C4 | — | 8 | 2 | no | — |
| 967 | C2×C4 | — | 8 | 1 | no | — |
| 968 | C2×C4 | — | 8 | 1 | no | — |
| 969 | C2×C4 | — | 8 | 1 | no | — |
| 970 | C2×C4 | — | 8 | 1 | no | — |
| 971 | C2×C4 | — | 8 | 2 | no | — |
| 972 | C2×C4 | — | 8 | 1 | no | — |
| 973 | C2×C4 | — | 16 | 1 | no | — |
| 974 | C2×C4 | — | 16 | 1 | no | — |
| 975 | C2×C4 | — | 16 | 2 | no | — |
| 976 | C2×C4 | — | 16 | 1 | no | — |
| 977 | C2×C4 | — | 16 | 1 | no | — |
| 978 | C2×C4 | — | 16 | 1 | no | — |
| 979 | C2×C4 | — | 16 | 1 | no | — |
| 980 | C2×C4 | — | 16 | 2 | no | — |
| 981 | C2×C4 | — | 16 | 1 | no | — |
| 982 | C2×C4 | — | 32 | 1 | no | — |
| 983 | C2×C4 | — | 32 | 1 | no | — |
| 984 | C2×C4 | #2461 | 1 | 1 | yes | characteristic |
| 985 | C2×C4 | #2560 | 1 | 1 | yes | characteristic |
| 986 | C2×C4 | #2661 | 1 | 1 | yes | characteristic |
| 987 | C2×C4 | #2673 | 1 | 1 | yes | characteristic |
| 988 | C2×C4 | #2676 | 1 | 1 | yes | characteristic |
| 989 | C2×C4 | #2696 | 1 | 1 | yes | characteristic |
| 990 | C2×C4 | #2728 | 1 | 1 | yes | characteristic |
| 991 | C2×C4 | #3176 | 1 | 1 | yes | characteristic |
| 992 | C2×C4 | #3179 | 1 | 1 | yes | characteristic |
| 993 | C2×C4 | #3180 | 1 | 1 | yes | characteristic |
| 994 | C2×C4 | #3197 | 1 | 1 | yes | characteristic |
| 995 | C2×C4 | #3198 | 1 | 1 | yes | characteristic |
| 996 | C2×C4 | #3199 | 1 | 1 | yes | characteristic |
| 997 | C2×C4 | #3213 | 1 | 1 | yes | characteristic |
| 998 | C2×C4 | #3220 | 1 | 1 | yes | characteristic |
| 999 | C2×C4 | #3224 | 1 | 1 | yes | characteristic |
| 1000 | C2×C4 | #3271 | 1 | 1 | yes | characteristic |
| 1001 | C2×C4 | #3273 | 1 | 1 | yes | characteristic |
| 1002 | C2×C4 | #3274 | 1 | 1 | yes | characteristic |
| 1003 | C2×C4 | #3319 | 1 | 1 | yes | characteristic |
| 1004 | C2×C4 | #3325 | 1 | 1 | yes | characteristic |
| 1005 | C2×C4 | #3326 | 1 | 1 | yes | characteristic |
| 1006 | C2×C4 | #3366 | 1 | 1 | yes | characteristic |
| 1007 | C2×C4 | #3370 | 1 | 1 | yes | characteristic |
| 1008 | C2×C4 | #3370 | 1 | 1 | yes | characteristic |
| 1009 | C2×C4 | #3370 | 1 | 1 | yes | characteristic |
| 1010 | C2×C4 | #3370 | 1 | 1 | yes | characteristic |
| 1011 | C2×C4 | #3373 | 1 | 1 | yes | characteristic |
| 1012 | C8 | — | 8 | 1 | no | — |
| 1013 | C8 | — | 8 | 1 | no | — |
| 1014 | C8 | — | 8 | 1 | no | — |
| 1015 | C8 | — | 8 | 2 | no | — |
| 1016 | C8 | — | 8 | 2 | no | — |
| 1017 | C8 | — | 16 | 1 | no | — |
| 1018 | C8 | — | 16 | 1 | no | — |
| 1019 | C8 | #2471 | 1 | 1 | yes | characteristic |
| 1020 | C8 | #2636 | 1 | 1 | yes | characteristic |
| 1021 | C8 | #2649 | 1 | 1 | yes | characteristic |
| 1022 | C8 | #2706 | 1 | 1 | yes | characteristic |
| 1023 | C8 | #2727 | 1 | 1 | yes | characteristic |
| 1024 | C8 | #2735 | 1 | 1 | yes | characteristic |
| 1025 | C8 | #2740 | 1 | 1 | yes | characteristic |
| 1026 | C8 | #2837 | 1 | 1 | yes | characteristic |
| 1027 | C22 | — | 2 | 2 | no | — |
| 1028 | C22 | — | 2 | 2 | no | — |
| 1029 | C22 | — | 2 | 2 | no | — |
| 1030 | C22 | — | 4 | 1 | no | — |
| 1031 | C22 | — | 4 | 1 | no | — |
| 1032 | C22 | — | 4 | 1 | no | — |
| 1033 | C22 | — | 4 | 1 | no | — |
| 1034 | C22 | — | 16 | 2 | no | — |
| 1035 | C22 | — | 16 | 1 | no | — |
| 1036 | C22 | — | 16 | 2 | no | — |
| 1037 | C22 | — | 16 | 2 | no | — |
| 1038 | C22 | — | 16 | 4 | no | — |
| 1039 | C22 | — | 32 | 1 | no | — |
| 1040 | C22 | — | 32 | 2 | no | — |
| 1041 | C22 | — | 32 | 2 | no | — |
| 1042 | C22 | — | 32 | 2 | no | — |
| 1043 | C22 | — | 32 | 1 | no | — |
| 1044 | C22 | — | 32 | 1 | no | — |
| 1045 | C22 | — | 32 | 2 | no | — |
| 1046 | C22 | — | 32 | 2 | no | — |
| 1047 | C22 | #26837 | 1 | 1 | yes | characteristic |
| 1048 | C22 | #29096 | 1 | 1 | yes | characteristic |
| 1049 | C22 | #30322 | 1 | 1 | yes | characteristic |
| 1050 | C22 | #30732 | 1 | 1 | yes | characteristic |
| 1051 | C22 | #30891 | 1 | 1 | yes | characteristic |
| 1052 | C22 | #31651 | 1 | 1 | yes | characteristic |
| 1053 | C22 | #32554 | 1 | 1 | yes | characteristic |
| 1054 | C4 | — | 8 | 1 | no | — |
| 1055 | C4 | — | 8 | 1 | no | — |
| 1056 | C4 | — | 16 | 1 | no | — |
| 1057 | C4 | — | 16 | 1 | no | — |
| 1058 | C4 | — | 16 | 2 | no | — |
| 1059 | C4 | — | 16 | 1 | no | — |
| 1060 | C4 | — | 32 | 1 | no | — |
| 1061 | C4 | #16548 | 1 | 1 | yes | characteristic |
| 1062 | C4 | #26843 | 1 | 1 | yes | characteristic |
| 1063 | C4 | #29079 | 1 | 1 | yes | characteristic |
| 1064 | C4 | #30329 | 1 | 1 | yes | characteristic |
| 1065 | C4 | #30722 | 1 | 1 | yes | characteristic |
| 1066 | C4 | #30903 | 1 | 1 | yes | characteristic |
| 1067 | C4 | #31665 | 1 | 1 | yes | characteristic |
| 1068 | C4 | #32558 | 1 | 1 | yes | characteristic |
| 1069 | C2 | — | 2 | 1 | no | — |
| 1070 | C2 | — | 2 | 1 | no | — |
| 1071 | C2 | — | 2 | 1 | no | — |
| 1072 | C2 | — | 2 | 1 | no | — |
| 1073 | C2 | — | 2 | 1 | no | — |
| 1074 | C2 | — | 2 | 1 | no | — |
| 1075 | C2 | — | 32 | 1 | no | — |
| 1076 | C2 | — | 32 | 2 | no | — |
| 1077 | C2 | #466562 | 1 | 1 | yes | characteristic |
| 1078 | C2 | #511427 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #32554 |
| commutator, Frattini, cosocle | C23×C8 | C24 |
| prime radical | C22×#509 | C22 |
| LCS | G ▷ C23×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #20438 ◁ G | |
| LECS | G ▷ C23×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13490 | C2 | semidirect |
| 2. C2×#13156 | C2 | semidirect |
| 3. #416373 | C2 | semidirect |
| 4. #413503 | C2 | semidirect |
| 5. #149054 | C2 | semidirect |
| 6. #149052 | C2 | semidirect |
| 7. #148746 | C2 | semidirect |
| 8. #148571 | C2 | semidirect |
| 9. #148151 | C2 | semidirect |
| 10. #148105 | C2 | semidirect |
| 14. #147440 | C2 | semidirect |
| 15. #147130 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#13490 | 2 |
| C2×#13156 | 2 |
| #416373 | 2 |
| #413503 | 2 |
| #149054 | 2 |
| #149052 | 2 |
| #148746 | 2 |
| #148571 | 2 |
| #148151 | 2 |
| #148105 | 2 |
| #147953 | 2 |
| #147932 | 2 |
| #147918 | 2 |
| #147440 | 2 |
| #147130 | 2 |