Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
5782 conjugacy classes of subgroups.
The subgroup lattice has 499 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #63070 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #63067 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #62491 | C2 | 1 | 10 | yes | maximal, complemented |
| 4 | #62371 | C2 | 1 | 5 | yes | maximal, complemented |
| 5 | #62241 | C2 | 1 | 10 | yes | maximal, complemented |
| 6 | #62238 | C2 | 1 | 10 | yes | maximal, complemented |
| 7 | #61877 | C2 | 1 | 5 | yes | maximal, complemented |
| 8 | #61876 | C2 | 1 | 5 | yes | maximal, complemented |
| 9 | #61476 | C2 | 1 | 10 | yes | maximal, complemented |
| 10 | #61375 | C2 | 1 | 5 | yes | maximal, complemented |
| 11 | #60332 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #3563 | — | 2 | 10 | no | — |
| 13 | #3563 | C22 | 1 | 10 | yes | — |
| 14 | #3559 | — | 2 | 10 | no | — |
| 15 | #3559 | C22 | 1 | 10 | yes | — |
| 16 | #3556 | C22 | 1 | 5 | yes | — |
| 17 | #3553 | — | 2 | 5 | no | — |
| 18 | #3548 | — | 2 | 5 | no | — |
| 19 | #3548 | C22 | 1 | 5 | yes | — |
| 20 | #3531 | — | 2 | 1 | no | — |
| 21 | #3531 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#564 | — | 2 | 1 | no | — |
| 23 | #3517 | C22 | 1 | 10 | yes | — |
| 24 | #3515 | C22 | 1 | 10 | yes | — |
| 25 | #3504 | C22 | 1 | 5 | yes | — |
| 26 | #3504 | C22 | 1 | 5 | yes | — |
| 27 | #3392 | C22 | 1 | 10 | yes | — |
| 28 | #3390 | C22 | 1 | 20 | yes | — |
| 29 | #3389 | C22 | 1 | 20 | yes | — |
| 30 | #3388 | C22 | 1 | 20 | yes | — |
| 31 | #3381 | C22 | 1 | 20 | yes | — |
| 32 | #3381 | C22 | 1 | 10 | yes | — |
| 33 | #3374 | C22 | 1 | 10 | yes | — |
| 34 | #3372 | C22 | 1 | 20 | yes | — |
| 35 | #3368 | C22 | 1 | 20 | yes | — |
| 36 | #3366 | C22 | 1 | 10 | yes | — |
| 37 | #3351 | C22 | 1 | 20 | yes | — |
| 38 | #3346 | C22 | 1 | 20 | yes | — |
| 39 | #3343 | C22 | 1 | 20 | yes | — |
| 40 | #3337 | C22 | 1 | 20 | yes | — |
| 41 | #3335 | C22 | 1 | 10 | yes | — |
| 42 | #3333 | C22 | 1 | 10 | yes | — |
| 43 | #3330 | C22 | 1 | 10 | yes | — |
| 44 | #3317 | C22 | 1 | 20 | yes | — |
| 45 | #3307 | C22 | 1 | 20 | yes | — |
| 46 | #3284 | C22 | 1 | 10 | yes | — |
| 47 | #3260 | C22 | 1 | 20 | yes | — |
| 48 | #3254 | C22 | 1 | 10 | yes | — |
| 49 | #3242 | C22 | 1 | 20 | yes | — |
| 50 | #3241 | C22 | 1 | 20 | yes | — |
| 51 | #3236 | C22 | 1 | 10 | yes | — |
| 52 | #3234 | C22 | 1 | 10 | yes | — |
| 53 | #3174 | C22 | 1 | 20 | yes | — |
| 54 | #3167 | C22 | 1 | 10 | yes | — |
| 55 | #3163 | C22 | 1 | 10 | yes | — |
| 56 | C2×#499 | C22 | 1 | 5 | yes | — |
| 57 | #3120 | C22 | 1 | 20 | yes | — |
| 58 | #3119 | C22 | 1 | 20 | yes | — |
| 59 | #3116 | C22 | 1 | 10 | yes | — |
| 60 | #3115 | C22 | 1 | 10 | yes | — |
| 61 | #3083 | C22 | 1 | 10 | yes | — |
| 62 | #3083 | C22 | 1 | 10 | yes | — |
| 63 | #3080 | C22 | 1 | 5 | yes | — |
| 64 | #3080 | C22 | 1 | 5 | yes | — |
| 65 | #2995 | C22 | 1 | 10 | yes | — |
| 66 | #2987 | C22 | 1 | 5 | yes | — |
| 67 | #2966 | C22 | 1 | 10 | yes | — |
| 68 | #2960 | C22 | 1 | 5 | yes | — |
| 69 | #2952 | C22 | 1 | 10 | yes | — |
| 70 | C4×#135 | C22 | 1 | 5 | yes | — |
| 71 | C2×#135 | C23 | 1 | 5 | yes | — |
| 72 | #564 | — | 2 | 5 | no | — |
| 73 | #564 | — | 2 | 10 | no | — |
| 74 | #564 | — | 2 | 5 | no | — |
| 75 | #564 | D4 | 1 | 1 | yes | characteristic |
| 76 | #563 | — | 2 | 10 | no | — |
| 77 | #563 | — | 2 | 10 | no | — |
| 78 | #563 | D4 | 1 | 10 | yes | — |
| 79 | #562 | — | 2 | 5 | no | — |
| 80 | #562 | — | 2 | 5 | no | — |
| 81 | #562 | — | 2 | 10 | no | — |
| 82 | #562 | D4 | 1 | 5 | yes | — |
| 83 | #557 | — | 2 | 10 | no | — |
| 84 | #557 | C23 | 1 | 10 | yes | — |
| 85 | #557 | C23 | 1 | 20 | yes | — |
| 86 | #557 | C23 | 1 | 10 | yes | — |
| 87 | #554 | — | 2 | 20 | no | — |
| 88 | #554 | — | 2 | 20 | no | — |
| 89 | #554 | C23 | 1 | 10 | yes | — |
| 90 | #554 | C23 | 1 | 20 | yes | — |
| 91 | #554 | C23 | 1 | 10 | yes | — |
| 92 | #553 | — | 2 | 20 | no | — |
| 93 | #553 | — | 2 | 10 | no | — |
| 94 | #553 | C23 | 1 | 20 | yes | — |
| 95 | #552 | — | 2 | 20 | no | — |
| 96 | #552 | — | 2 | 20 | no | — |
| 97 | #552 | — | 2 | 10 | no | — |
| 98 | #552 | C23 | 1 | 20 | yes | — |
| 99 | #550 | — | 2 | 10 | no | — |
| 100 | #550 | C23 | 1 | 10 | yes | — |
| 101 | #550 | C23 | 1 | 10 | yes | — |
| 102 | #547 | — | 2 | 10 | no | — |
| 103 | #547 | — | 2 | 20 | no | — |
| 104 | #547 | — | 2 | 10 | no | — |
| 105 | #547 | C23 | 1 | 10 | yes | — |
| 106 | #547 | C23 | 1 | 10 | yes | — |
| 107 | #544 | — | 2 | 10 | no | — |
| 108 | #544 | — | 2 | 10 | no | — |
| 109 | #544 | — | 2 | 10 | no | — |
| 110 | #544 | C23 | 1 | 10 | yes | — |
| 111 | #544 | C23 | 1 | 10 | yes | — |
| 112 | #541 | — | 2 | 20 | no | — |
| 113 | #541 | — | 2 | 20 | no | — |
| 114 | #541 | C23 | 1 | 20 | yes | — |
| 115 | #540 | — | 2 | 20 | no | — |
| 116 | #540 | C23 | 1 | 20 | yes | — |
| 117 | #539 | — | 2 | 20 | no | — |
| 118 | #539 | — | 2 | 20 | no | — |
| 119 | #539 | — | 2 | 10 | no | — |
| 120 | #539 | — | 2 | 10 | no | — |
| 121 | #537 | — | 2 | 20 | no | — |
| 122 | #537 | — | 2 | 10 | no | — |
| 123 | #533 | — | 2 | 5 | no | — |
| 124 | #533 | — | 2 | 5 | no | — |
| 125 | #533 | C23 | 1 | 10 | yes | — |
| 126 | #533 | C23 | 1 | 5 | yes | — |
| 127 | #532 | — | 2 | 10 | no | — |
| 128 | #532 | C23 | 1 | 10 | yes | — |
| 129 | #529 | — | 2 | 10 | no | — |
| 130 | #529 | — | 2 | 10 | no | — |
| 131 | #529 | C23 | 1 | 10 | yes | — |
| 132 | C2×#125 | — | 2 | 5 | no | — |
| 133 | C2×#125 | — | 2 | 5 | no | — |
| 134 | C2×#125 | — | 2 | 10 | no | — |
| 135 | C2×#125 | C23 | 1 | 5 | yes | — |
| 136 | C2×#125 | C23 | 1 | 5 | yes | — |
| 137 | #520 | C23 | 1 | 10 | yes | — |
| 138 | #520 | C23 | 1 | 10 | yes | — |
| 139 | C4×#41 | C23 | 1 | 5 | yes | — |
| 140 | C4×#41 | C23 | 1 | 5 | yes | — |
| 141 | #501 | C23 | 1 | 20 | yes | — |
| 142 | #501 | C23 | 1 | 20 | yes | — |
| 143 | #499 | C23 | 1 | 20 | yes | — |
| 144 | #499 | C23 | 1 | 20 | yes | — |
| 145 | #498 | C23 | 1 | 10 | yes | — |
| 146 | #492 | C23 | 1 | 10 | yes | — |
| 147 | #491 | C23 | 1 | 20 | yes | — |
| 148 | #490 | C23 | 1 | 20 | yes | — |
| 149 | #487 | C23 | 1 | 10 | yes | — |
| 150 | #486 | C23 | 1 | 10 | yes | — |
| 151 | #485 | C23 | 1 | 20 | yes | — |
| 152 | #484 | C23 | 1 | 20 | yes | — |
| 153 | #483 | C23 | 1 | 20 | yes | — |
| 154 | #482 | C23 | 1 | 20 | yes | — |
| 155 | #481 | C23 | 1 | 20 | yes | — |
| 156 | #480 | C23 | 1 | 20 | yes | — |
| 157 | #479 | C23 | 1 | 20 | yes | — |
| 158 | #479 | C23 | 1 | 20 | yes | — |
| 159 | #479 | C23 | 1 | 20 | yes | — |
| 160 | #479 | C23 | 1 | 20 | yes | — |
| 161 | #478 | C23 | 1 | 20 | yes | — |
| 162 | #478 | C23 | 1 | 20 | yes | — |
| 163 | #478 | C23 | 1 | 20 | yes | — |
| 164 | #478 | C23 | 1 | 20 | yes | — |
| 165 | #477 | C23 | 1 | 10 | yes | — |
| 166 | #477 | C23 | 1 | 20 | yes | — |
| 167 | #476 | C23 | 1 | 10 | yes | — |
| 168 | #475 | C23 | 1 | 10 | yes | — |
| 169 | #474 | C23 | 1 | 10 | yes | — |
| 170 | #474 | C23 | 1 | 20 | yes | — |
| 171 | #468 | C23 | 1 | 20 | yes | — |
| 172 | #468 | C23 | 1 | 20 | yes | — |
| 173 | #465 | C23 | 1 | 20 | yes | — |
| 174 | #465 | C23 | 1 | 20 | yes | — |
| 175 | #462 | C23 | 1 | 10 | yes | — |
| 176 | #461 | C23 | 1 | 10 | yes | — |
| 177 | #461 | C23 | 1 | 20 | yes | — |
| 178 | #460 | C23 | 1 | 10 | yes | — |
| 179 | #460 | C23 | 1 | 20 | yes | — |
| 180 | #459 | C23 | 1 | 10 | yes | — |
| 181 | #452 | C23 | 1 | 20 | yes | — |
| 182 | #449 | C23 | 1 | 20 | yes | — |
| 183 | #446 | C23 | 1 | 10 | yes | — |
| 184 | #446 | C23 | 1 | 20 | yes | — |
| 185 | C8×Q8 | C23 | 1 | 10 | yes | — |
| 186 | #442 | C23 | 1 | 20 | yes | — |
| 187 | #441 | C23 | 1 | 20 | yes | — |
| 188 | #440 | C23 | 1 | 20 | yes | — |
| 189 | #440 | C23 | 1 | 20 | yes | — |
| 190 | C4×Q16 | C23 | 1 | 10 | yes | — |
| 191 | C4×SD16 | C23 | 1 | 10 | yes | — |
| 192 | C4×SD16 | C23 | 1 | 20 | yes | — |
| 193 | C4×SD16 | C23 | 1 | 20 | yes | — |
| 194 | C4×SD16 | C23 | 1 | 10 | yes | — |
| 195 | C4×D8 | C23 | 1 | 10 | yes | — |
| 196 | #436 | C23 | 1 | 10 | yes | — |
| 197 | #435 | C23 | 1 | 20 | yes | — |
| 198 | C8×D4 | C23 | 1 | 10 | yes | — |
| 199 | #433 | C23 | 1 | 20 | yes | — |
| 200 | #432 | C23 | 1 | 10 | yes | — |
| 201 | #428 | C23 | 1 | 10 | yes | — |
| 202 | #428 | C23 | 1 | 10 | yes | — |
| 203 | #427 | C23 | 1 | 5 | yes | — |
| 204 | C2×#107 | C23 | 1 | 10 | yes | — |
| 205 | C2×#106 | C23 | 1 | 10 | yes | — |
| 206 | #424 | C23 | 1 | 10 | yes | — |
| 207 | #423 | C23 | 1 | 5 | yes | — |
| 208 | #417 | C23 | 1 | 10 | yes | — |
| 209 | #417 | C23 | 1 | 10 | yes | — |
| 210 | #416 | C23 | 1 | 5 | yes | — |
| 211 | #416 | C23 | 1 | 5 | yes | — |
| 212 | #405 | C23 | 1 | 10 | yes | — |
| 213 | C2×C4×C8 | C23 | 1 | 5 | yes | — |
| 214 | C2×#41 | — | 2 | 10 | no | — |
| 215 | C2×#41 | — | 2 | 10 | no | — |
| 216 | C2×#41 | — | 2 | 10 | no | — |
| 217 | C2×#41 | C24 | 1 | 5 | yes | — |
| 218 | C2×#41 | C24 | 1 | 5 | yes | — |
| 219 | #135 | — | 2 | 20 | no | — |
| 220 | C2×Q16 | C24 | 1 | 5 | yes | — |
| 221 | C2×SD16 | C24 | 1 | 5 | yes | — |
| 222 | C2×SD16 | C24 | 1 | 20 | yes | — |
| 223 | C2×SD16 | C24 | 1 | 1 | yes | characteristic |
| 224 | C2×D8 | C24 | 1 | 5 | yes | — |
| 225 | C2×M16 | C24 | 1 | 10 | yes | — |
| 226 | C22×C8 | C24 | 1 | 5 | yes | — |
| 227 | C22×C8 | C24 | 1 | 5 | yes | — |
| 228 | C4⋊Q8 | — | 2 | 10 | no | — |
| 229 | C4⋊Q8 | — | 2 | 20 | no | — |
| 230 | C4⋊Q8 | — | 2 | 10 | no | — |
| 231 | C4⋊Q8 | — | 2 | 10 | no | — |
| 232 | C4⋊Q8 | C2×D4 | 1 | 10 | yes | — |
| 233 | C4⋊Q8 | C24 | 1 | 10 | yes | — |
| 234 | C4⋊Q8 | C24 | 1 | 10 | yes | — |
| 235 | C4⋊Q8 | C24 | 1 | 10 | yes | — |
| 236 | #127 | — | 2 | 10 | no | — |
| 237 | #127 | C24 | 1 | 10 | yes | — |
| 238 | #126 | — | 2 | 20 | no | — |
| 239 | #126 | — | 2 | 20 | no | — |
| 240 | #126 | — | 2 | 20 | no | — |
| 241 | #126 | — | 2 | 20 | no | — |
| 242 | #126 | C2×D4 | 1 | 20 | yes | — |
| 243 | #125 | — | 2 | 10 | no | — |
| 244 | #125 | — | 2 | 20 | no | — |
| 245 | #125 | — | 2 | 20 | no | — |
| 246 | #125 | — | 2 | 20 | no | — |
| 247 | #125 | — | 2 | 10 | no | — |
| 248 | #125 | — | 2 | 10 | no | — |
| 249 | #125 | — | 2 | 20 | no | — |
| 250 | #125 | — | 2 | 10 | no | — |
| 251 | #125 | — | 2 | 20 | no | — |
| 252 | #125 | — | 2 | 20 | no | — |
| 253 | #125 | — | 2 | 20 | no | — |
| 254 | #125 | — | 2 | 5 | no | — |
| 255 | #125 | — | 2 | 5 | no | — |
| 256 | #125 | — | 2 | 10 | no | — |
| 257 | #125 | — | 2 | 5 | no | — |
| 258 | #125 | — | 2 | 5 | no | — |
| 259 | #125 | C2×D4 | 1 | 10 | yes | — |
| 260 | #125 | C2×D4 | 1 | 5 | yes | — |
| 261 | #125 | C2×D4 | 1 | 5 | yes | — |
| 262 | #125 | C24 | 1 | 20 | yes | — |
| 263 | #125 | C24 | 1 | 20 | yes | — |
| 264 | #124 | — | 2 | 10 | no | — |
| 265 | #124 | C2×D4 | 1 | 10 | yes | — |
| 266 | #123 | — | 2 | 20 | no | — |
| 267 | #123 | — | 2 | 20 | no | — |
| 268 | #123 | — | 2 | 20 | no | — |
| 269 | #123 | — | 2 | 20 | no | — |
| 270 | #123 | — | 2 | 20 | no | — |
| 271 | #123 | — | 2 | 20 | no | — |
| 272 | #123 | C2×D4 | 1 | 20 | yes | — |
| 273 | C22⋊Q8 | — | 2 | 10 | no | — |
| 274 | C22⋊Q8 | — | 2 | 20 | no | — |
| 275 | C22⋊Q8 | — | 2 | 10 | no | — |
| 276 | C22⋊Q8 | — | 2 | 10 | no | — |
| 277 | C22⋊Q8 | — | 2 | 20 | no | — |
| 278 | C22⋊Q8 | — | 2 | 20 | no | — |
| 279 | C22⋊Q8 | — | 2 | 20 | no | — |
| 280 | C22⋊Q8 | — | 2 | 20 | no | — |
| 281 | C22⋊Q8 | — | 2 | 20 | no | — |
| 282 | C22⋊Q8 | — | 2 | 20 | no | — |
| 283 | C22⋊Q8 | C2×D4 | 1 | 10 | yes | — |
| 284 | C22⋊Q8 | C2×D4 | 1 | 20 | yes | — |
| 285 | C22⋊Q8 | C24 | 1 | 20 | yes | — |
| 286 | #121 | — | 2 | 10 | no | — |
| 287 | #121 | — | 2 | 20 | no | — |
| 288 | #121 | — | 2 | 10 | no | — |
| 289 | #121 | — | 2 | 10 | no | — |
| 290 | #121 | — | 2 | 20 | no | — |
| 291 | #121 | — | 2 | 20 | no | — |
| 292 | #121 | — | 2 | 20 | no | — |
| 293 | #121 | — | 2 | 20 | no | — |
| 294 | #121 | C2×D4 | 1 | 10 | yes | — |
| 295 | #121 | C24 | 1 | 20 | yes | — |
| 296 | C4×Q8 | — | 2 | 10 | no | — |
| 297 | C4×Q8 | — | 2 | 10 | no | — |
| 298 | C4×Q8 | — | 2 | 20 | no | — |
| 299 | C4×Q8 | — | 2 | 10 | no | — |
| 300 | C4×Q8 | C24 | 1 | 10 | yes | — |
| 301 | C4×Q8 | C24 | 1 | 10 | yes | — |
| 302 | C4×Q8 | C24 | 1 | 20 | yes | — |
| 303 | C4×Q8 | C24 | 1 | 10 | yes | — |
| 304 | C4×D4 | — | 2 | 10 | no | — |
| 305 | C4×D4 | — | 2 | 10 | no | — |
| 306 | C4×D4 | — | 2 | 10 | no | — |
| 307 | C4×D4 | — | 2 | 10 | no | — |
| 308 | C4×D4 | — | 2 | 20 | no | — |
| 309 | C4×D4 | — | 2 | 20 | no | — |
| 310 | C4×D4 | — | 2 | 20 | no | — |
| 311 | C4×D4 | — | 2 | 10 | no | — |
| 312 | C4×D4 | C24 | 1 | 10 | yes | — |
| 313 | C4×D4 | C24 | 1 | 10 | yes | — |
| 314 | C4×D4 | C24 | 1 | 20 | yes | — |
| 315 | C4×D4 | C24 | 1 | 10 | yes | — |
| 316 | #117 | — | 2 | 10 | no | — |
| 317 | #117 | — | 2 | 10 | no | — |
| 318 | #117 | — | 2 | 10 | no | — |
| 319 | #117 | — | 2 | 20 | no | — |
| 320 | #117 | — | 2 | 5 | no | — |
| 321 | #117 | — | 2 | 5 | no | — |
| 322 | #117 | C24 | 1 | 5 | yes | — |
| 323 | #117 | C24 | 1 | 5 | yes | — |
| 324 | #117 | C24 | 1 | 10 | yes | — |
| 325 | C2×C4⋊C4 | — | 2 | 10 | no | — |
| 326 | C2×C4⋊C4 | — | 2 | 10 | no | — |
| 327 | C2×C4⋊C4 | — | 2 | 10 | no | — |
| 328 | C2×C4⋊C4 | — | 2 | 10 | no | — |
| 329 | C2×C4⋊C4 | — | 2 | 10 | no | — |
| 330 | C2×C4⋊C4 | — | 2 | 10 | no | — |
| 331 | C2×C4⋊C4 | — | 2 | 20 | no | — |
| 332 | C2×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 333 | C2×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 334 | C2×C42 | — | 2 | 5 | no | — |
| 335 | C2×C42 | — | 2 | 5 | no | — |
| 336 | C2×C42 | C24 | 1 | 5 | yes | — |
| 337 | #107 | C24 | 1 | 20 | yes | — |
| 338 | #107 | C24 | 1 | 20 | yes | — |
| 339 | #107 | C24 | 1 | 10 | yes | — |
| 340 | #106 | C24 | 1 | 10 | yes | — |
| 341 | #106 | C24 | 1 | 20 | yes | — |
| 342 | #106 | C24 | 1 | 20 | yes | — |
| 343 | C4⋊C8 | C24 | 1 | 20 | yes | — |
| 344 | C4⋊C8 | C24 | 1 | 10 | yes | — |
| 345 | C4⋊C8 | C24 | 1 | 10 | yes | — |
| 346 | #103 | C24 | 1 | 10 | yes | — |
| 347 | #103 | C24 | 1 | 10 | yes | — |
| 348 | #103 | C24 | 1 | 20 | yes | — |
| 349 | #103 | C24 | 1 | 20 | yes | — |
| 350 | #102 | C24 | 1 | 10 | yes | — |
| 351 | #102 | C24 | 1 | 10 | yes | — |
| 352 | #102 | C24 | 1 | 20 | yes | — |
| 353 | #102 | C24 | 1 | 20 | yes | — |
| 354 | C22⋊C8 | C24 | 1 | 20 | yes | — |
| 355 | #97 | C24 | 1 | 20 | yes | — |
| 356 | C4×C8 | C24 | 1 | 10 | yes | — |
| 357 | C4×C8 | C24 | 1 | 10 | yes | — |
| 358 | #41 | — | 2 | 10 | no | — |
| 359 | #41 | — | 2 | 10 | no | — |
| 360 | #41 | — | 4 | 5 | no | — |
| 361 | #41 | — | 4 | 5 | no | — |
| 362 | #41 | — | 16 | 10 | no | — |
| 363 | #41 | — | 16 | 10 | no | — |
| 364 | #41 | — | 16 | 10 | no | — |
| 365 | C2×Q8 | — | 2 | 10 | no | — |
| 366 | C2×Q8 | — | 2 | 10 | no | — |
| 367 | C2×Q8 | C22×D4 | 1 | 10 | yes | — |
| 368 | C2×Q8 | C25 | 1 | 5 | yes | — |
| 369 | C2×Q8 | C25 | 1 | 1 | yes | characteristic |
| 370 | C2×D4 | — | 2 | 5 | no | — |
| 371 | C2×D4 | — | 2 | 5 | no | — |
| 372 | C2×D4 | — | 2 | 20 | no | — |
| 373 | C2×D4 | — | 2 | 10 | no | — |
| 374 | C2×D4 | — | 2 | 10 | no | — |
| 375 | C2×D4 | C22×D4 | 1 | 10 | yes | — |
| 376 | C2×D4 | C25 | 1 | 5 | yes | — |
| 377 | C2×D4 | C25 | 1 | 1 | yes | characteristic |
| 378 | C22×C4 | — | 2 | 10 | no | — |
| 379 | C22×C4 | — | 2 | 10 | no | — |
| 380 | C22×C4 | — | 2 | 5 | no | — |
| 381 | C22×C4 | — | 2 | 5 | no | — |
| 382 | C22×C4 | — | 2 | 10 | no | — |
| 383 | C22×C4 | — | 2 | 10 | no | — |
| 384 | C22×C4 | — | 2 | 20 | no | — |
| 385 | C22×C4 | C22×D4 | 1 | 10 | yes | — |
| 386 | C22×C4 | C25 | 1 | 5 | yes | — |
| 387 | Q16 | — | 2 | 10 | no | — |
| 388 | SD16 | — | 2 | 10 | no | — |
| 389 | SD16 | — | 4 | 20 | no | — |
| 390 | SD16 | 2−1+4 | 1 | 4 | yes | — |
| 391 | D8 | — | 2 | 10 | no | — |
| 392 | M16 | — | 4 | 10 | no | — |
| 393 | C2×C8 | — | 2 | 10 | no | — |
| 394 | C2×C8 | — | 4 | 5 | no | — |
| 395 | C2×C8 | C25 | 1 | 5 | yes | — |
| 396 | C2×C8 | C25 | 1 | 10 | yes | — |
| 397 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 398 | C4⋊C4 | — | 2 | 10 | no | — |
| 399 | C4⋊C4 | — | 2 | 10 | no | — |
| 400 | C4⋊C4 | — | 2 | 20 | no | — |
| 401 | C4⋊C4 | — | 2 | 20 | no | — |
| 402 | C4⋊C4 | — | 2 | 20 | no | — |
| 403 | C4⋊C4 | — | 2 | 10 | no | — |
| 404 | C4⋊C4 | — | 2 | 10 | no | — |
| 405 | C4⋊C4 | — | 2 | 10 | no | — |
| 406 | C4⋊C4 | — | 2 | 10 | no | — |
| 407 | C4⋊C4 | — | 2 | 20 | no | — |
| 408 | C4⋊C4 | — | 2 | 20 | no | — |
| 409 | C4⋊C4 | — | 2 | 20 | no | — |
| 410 | C4⋊C4 | — | 2 | 10 | no | — |
| 411 | C4⋊C4 | — | 2 | 10 | no | — |
| 412 | C4⋊C4 | C22×D4 | 1 | 10 | yes | — |
| 413 | C4⋊C4 | C22×D4 | 1 | 10 | yes | — |
| 414 | C4⋊C4 | C22×D4 | 1 | 10 | yes | — |
| 415 | C4⋊C4 | C22×D4 | 1 | 10 | yes | — |
| 416 | C4⋊C4 | C22×D4 | 1 | 20 | yes | — |
| 417 | C4⋊C4 | C25 | 1 | 10 | yes | — |
| 418 | C4⋊C4 | C25 | 1 | 10 | yes | — |
| 419 | C22⋊C4 | — | 2 | 20 | no | — |
| 420 | C22⋊C4 | — | 2 | 5 | no | — |
| 421 | C22⋊C4 | — | 2 | 5 | no | — |
| 422 | C22⋊C4 | — | 2 | 10 | no | — |
| 423 | C22⋊C4 | — | 2 | 20 | no | — |
| 424 | C22⋊C4 | — | 2 | 10 | no | — |
| 425 | C22⋊C4 | — | 2 | 20 | no | — |
| 426 | C22⋊C4 | C22×D4 | 1 | 20 | yes | — |
| 427 | C22⋊C4 | C22×D4 | 1 | 20 | yes | — |
| 428 | C42 | — | 2 | 5 | no | — |
| 429 | C42 | — | 2 | 10 | no | — |
| 430 | C42 | — | 2 | 5 | no | — |
| 431 | C42 | — | 2 | 10 | no | — |
| 432 | C42 | — | 2 | 20 | no | — |
| 433 | C42 | C22×D4 | 1 | 5 | yes | — |
| 434 | C42 | C22×D4 | 1 | 5 | yes | — |
| 435 | C42 | C25 | 1 | 10 | yes | — |
| 436 | C23 | — | 2 | 1 | no | — |
| 437 | C23 | — | 2 | 5 | no | — |
| 438 | C23 | C23×D4 | 1 | 5 | yes | — |
| 439 | Q8 | — | 2 | 1 | no | — |
| 440 | Q8 | — | 2 | 5 | no | — |
| 441 | Q8 | — | 2 | 5 | no | — |
| 442 | Q8 | — | 4 | 10 | no | — |
| 443 | Q8 | — | 8 | 10 | no | — |
| 444 | Q8 | — | 8 | 10 | no | — |
| 445 | Q8 | C2×2−1+4 | 1 | 2 | yes | — |
| 446 | D4 | — | 2 | 5 | no | — |
| 447 | D4 | — | 2 | 1 | no | — |
| 448 | D4 | — | 2 | 5 | no | — |
| 449 | D4 | — | 4 | 10 | no | — |
| 450 | D4 | — | 4 | 10 | no | — |
| 451 | D4 | — | 4 | 10 | no | — |
| 452 | D4 | — | 8 | 10 | no | — |
| 453 | D4 | — | 8 | 10 | no | — |
| 454 | D4 | — | 8 | 20 | no | — |
| 455 | D4 | C2×2−1+4 | 1 | 2 | yes | — |
| 456 | C2×C4 | — | 2 | 1 | no | — |
| 457 | C2×C4 | — | 2 | 5 | no | — |
| 458 | C2×C4 | — | 2 | 5 | no | — |
| 459 | C2×C4 | — | 2 | 5 | no | — |
| 460 | C2×C4 | — | 2 | 10 | no | — |
| 461 | C2×C4 | — | 2 | 10 | no | — |
| 462 | C2×C4 | — | 4 | 10 | no | — |
| 463 | C2×C4 | — | 4 | 10 | no | — |
| 464 | C2×C4 | — | 4 | 10 | no | — |
| 465 | C2×C4 | — | 8 | 10 | no | — |
| 466 | C2×C4 | — | 8 | 10 | no | — |
| 467 | C2×C4 | — | 8 | 20 | no | — |
| 468 | C2×C4 | — | 8 | 10 | no | — |
| 469 | C2×C4 | — | 8 | 10 | no | — |
| 470 | C2×C4 | C23×D4 | 1 | 5 | yes | — |
| 471 | C2×C4 | C23×D4 | 1 | 10 | yes | — |
| 472 | C2×C4 | C23×D4 | 1 | 10 | yes | — |
| 473 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 474 | C8 | — | 2 | 5 | no | — |
| 475 | C8 | — | 2 | 10 | no | — |
| 476 | C8 | C2×2−1+4 | 1 | 2 | yes | — |
| 477 | C22 | — | 2 | 5 | no | — |
| 478 | C22 | — | 2 | 2 | no | — |
| 479 | C22 | — | 2 | 10 | no | — |
| 480 | C22 | — | 4 | 2 | no | — |
| 481 | C22 | — | 4 | 5 | no | — |
| 482 | C22 | — | 4 | 10 | no | — |
| 483 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 484 | C4 | — | 2 | 5 | no | — |
| 485 | C4 | — | 2 | 2 | no | — |
| 486 | C4 | — | 2 | 10 | no | — |
| 487 | C4 | — | 2 | 10 | no | — |
| 488 | C4 | — | 4 | 5 | no | — |
| 489 | C4 | — | 4 | 10 | no | — |
| 490 | C4 | — | 4 | 10 | no | — |
| 491 | C4 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 492 | C4 | 2−1+6 | 1 | 1 | yes | characteristic |
| 493 | C2 | — | 4 | 5 | no | — |
| 494 | C2 | — | 4 | 2 | no | — |
| 495 | C2 | — | 8 | 5 | no | — |
| 496 | C2 | D4×2−1+4 | 1 | 1 | yes | characteristic |
| 497 | C2 | #63092 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ #3531 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63070 | C2 | semidirect |
| 2. #63067 | C2 | semidirect |
| 3. #62491 | C2 | semidirect |
| 4. #62371 | C2 | semidirect |
| 5. #62241 | C2 | semidirect |
| 6. #62238 | C2 | semidirect |
| 7. #61877 | C2 | semidirect |
| 8. #61876 | C2 | semidirect |
| 9. #61476 | C2 | semidirect |
| 10. #61375 | C2 | semidirect |
| 11. #60332 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63070 | 2 |
| #63067 | 2 |
| #62491 | 2 |
| #62371 | 2 |
| #62241 | 2 |
| #62238 | 2 |
| #61877 | 2 |
| #61876 | 2 |
| #61476 | 2 |
| #61375 | 2 |
| #60332 | 2 |