← #12089593
Subgroups — #12089593
Order 1280.
554 conjugacy classes of subgroups.
The subgroup lattice has 534 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C5×#3363 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10615440 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10615413 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10611442 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #10602734 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #10602730 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #10602034 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #10602019 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #10601955 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #10601941 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #10601857 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #10601850 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #10601735 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #10601725 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #10601696 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | C5×Q82 | C22 | 1 | 1 | yes | characteristic |
| 17 | C5×#557 | C22 | 1 | 1 | yes | characteristic |
| 18 | #65901 | C22 | 1 | 1 | yes | characteristic |
| 19 | #65901 | C22 | 1 | 1 | yes | characteristic |
| 20 | C5×#487 | — | 2 | 1 | no | — |
| 21 | C5×#487 | C22 | 1 | 1 | yes | characteristic |
| 22 | C5×#477 | — | 2 | 1 | no | — |
| 23 | C5×#477 | C22 | 1 | 1 | yes | characteristic |
| 24 | C5×#462 | — | 2 | 1 | no | — |
| 25 | C5×#462 | C22 | 1 | 1 | yes | characteristic |
| 26 | C5×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 27 | C4×C5×Q16 | — | 2 | 1 | no | — |
| 28 | C4×C5×Q16 | C22 | 1 | 1 | yes | characteristic |
| 29 | #65470 | — | 2 | 1 | no | — |
| 30 | #65383 | — | 2 | 1 | no | — |
| 31 | #65383 | C22 | 1 | 1 | yes | characteristic |
| 32 | #65380 | C22 | 1 | 1 | yes | characteristic |
| 33 | #65370 | C22 | 1 | 1 | yes | characteristic |
| 34 | #65369 | — | 2 | 1 | no | — |
| 35 | #65368 | C22 | 1 | 1 | yes | characteristic |
| 36 | #65367 | C22 | 1 | 1 | yes | characteristic |
| 37 | #65367 | C22 | 1 | 1 | yes | characteristic |
| 38 | #65353 | — | 2 | 1 | no | — |
| 39 | #65352 | — | 2 | 1 | no | — |
| 40 | #65320 | C22 | 1 | 1 | yes | characteristic |
| 41 | #65320 | C22 | 1 | 1 | yes | characteristic |
| 42 | #65319 | — | 2 | 1 | no | — |
| 43 | C4×#689 | — | 2 | 1 | no | — |
| 44 | C4×#689 | C22 | 1 | 1 | yes | characteristic |
| 45 | #65313 | C22 | 1 | 1 | yes | characteristic |
| 46 | Q8×#168 | C22 | 1 | 1 | yes | characteristic |
| 47 | #65311 | — | 2 | 1 | no | — |
| 48 | #65311 | — | 2 | 1 | no | — |
| 49 | #65309 | C22 | 1 | 1 | yes | characteristic |
| 50 | #65309 | C22 | 1 | 1 | yes | characteristic |
| 51 | #65162 | — | 2 | 1 | no | — |
| 52 | #65082 | — | 2 | 1 | no | — |
| 53 | #65082 | — | 2 | 1 | no | — |
| 54 | #64988 | C22 | 1 | 1 | yes | characteristic |
| 55 | C8×Dic10 | C22 | 1 | 1 | yes | characteristic |
| 56 | #64767 | C22 | 1 | 1 | yes | characteristic |
| 57 | #64766 | C22 | 1 | 1 | yes | characteristic |
| 58 | Q8⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 59 | Q8⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 60 | Q8⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 61 | #64704 | C22 | 1 | 1 | yes | characteristic |
| 62 | #64702 | C22 | 1 | 1 | yes | characteristic |
| 63 | #64702 | C22 | 1 | 1 | yes | characteristic |
| 64 | #64700 | C22 | 1 | 1 | yes | characteristic |
| 65 | #64678 | C22 | 1 | 1 | yes | characteristic |
| 66 | #64674 | C22 | 1 | 1 | yes | characteristic |
| 67 | #19818 | — | 5 | 1 | no | maximal, Sylow |
| 68 | C2×C5×Q16 | — | 2 | 1 | no | — |
| 69 | C2×C5×Q16 | D4 | 1 | 1 | yes | characteristic |
| 70 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 71 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 72 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 73 | C5×C4⋊Q8 | — | 4 | 1 | no | — |
| 74 | C5×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 75 | C5×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 76 | C5×#125 | — | 2 | 1 | no | — |
| 77 | C5×#125 | — | 4 | 1 | no | — |
| 78 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 79 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 80 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 81 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 82 | C4×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 83 | C4×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 84 | C4×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 85 | #4090 | — | 2 | 1 | no | — |
| 86 | #4090 | — | 2 | 1 | no | — |
| 87 | C2×#689 | — | 2 | 1 | no | — |
| 88 | C2×#689 | — | 2 | 1 | no | — |
| 89 | C2×#689 | D4 | 1 | 1 | yes | characteristic |
| 90 | C2×Dic20 | — | 2 | 1 | no | — |
| 91 | C2×Dic20 | — | 2 | 1 | no | — |
| 92 | #4035 | — | 4 | 1 | no | — |
| 93 | #4035 | — | 4 | 1 | no | — |
| 94 | #4033 | — | 2 | 1 | no | — |
| 95 | #4033 | — | 2 | 1 | no | — |
| 96 | #4016 | — | 2 | 1 | no | — |
| 97 | #4016 | — | 2 | 1 | no | — |
| 98 | #4015 | C23 | 1 | 1 | yes | characteristic |
| 99 | #4015 | C23 | 1 | 1 | yes | characteristic |
| 100 | C4×Dic10 | — | 2 | 1 | no | — |
| 101 | C4×Dic10 | — | 2 | 1 | no | — |
| 102 | C4×Dic10 | C23 | 1 | 1 | yes | characteristic |
| 103 | C5×#107 | — | 2 | 1 | no | — |
| 104 | C5×#107 | D4 | 1 | 1 | yes | characteristic |
| 105 | C5×C4⋊C8 | — | 2 | 1 | no | — |
| 106 | C5×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 107 | C5×#103 | — | 2 | 1 | no | — |
| 108 | C5×#103 | — | 2 | 1 | no | — |
| 109 | C5×#103 | — | 2 | 1 | no | — |
| 110 | C5×#103 | — | 2 | 1 | no | — |
| 111 | C5×#103 | D4 | 1 | 1 | yes | characteristic |
| 112 | C5×#103 | D4 | 1 | 1 | yes | characteristic |
| 113 | C4×C5×C8 | — | 2 | 1 | no | — |
| 114 | C4×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 115 | #3967 | — | 2 | 1 | no | — |
| 116 | #3967 | — | 2 | 1 | no | — |
| 117 | #3967 | — | 4 | 1 | no | — |
| 118 | #3967 | D4 | 1 | 1 | yes | characteristic |
| 119 | #3946 | — | 2 | 1 | no | — |
| 120 | C8×Dic5 | — | 2 | 1 | no | — |
| 121 | #3942 | — | 2 | 1 | no | — |
| 122 | #3942 | — | 2 | 1 | no | — |
| 123 | #3942 | — | 2 | 1 | no | — |
| 124 | #3942 | — | 2 | 1 | no | — |
| 125 | #3942 | D4 | 1 | 1 | yes | characteristic |
| 126 | #3940 | — | 2 | 1 | no | — |
| 127 | #3940 | — | 2 | 1 | no | — |
| 128 | #3940 | — | 2 | 1 | no | — |
| 129 | #3940 | — | 2 | 1 | no | — |
| 130 | #3940 | — | 2 | 1 | no | — |
| 131 | #3939 | — | 2 | 1 | no | — |
| 132 | #3939 | — | 2 | 1 | no | — |
| 133 | #3939 | — | 2 | 1 | no | — |
| 134 | #3939 | — | 4 | 1 | no | — |
| 135 | #3939 | D4 | 1 | 1 | yes | characteristic |
| 136 | C4⋊#168 | — | 2 | 1 | no | — |
| 137 | C4⋊#168 | — | 2 | 1 | no | — |
| 138 | C4⋊#168 | C23 | 1 | 1 | yes | characteristic |
| 139 | C4⋊#168 | C23 | 1 | 1 | yes | characteristic |
| 140 | C4⋊#168 | C23 | 1 | 1 | yes | characteristic |
| 141 | #3935 | — | 2 | 1 | no | — |
| 142 | C4×#168 | — | 2 | 1 | no | — |
| 143 | C4×#168 | C23 | 1 | 1 | yes | characteristic |
| 144 | C4×#168 | C23 | 1 | 1 | yes | characteristic |
| 145 | #3395 | — | 5 | 1 | no | — |
| 146 | #3387 | — | 5 | 1 | no | — |
| 147 | #3383 | — | 5 | 1 | no | — |
| 148 | #3363 | D5 | 1 | 1 | yes | characteristic |
| 149 | #1723 | — | 5 | 1 | no | — |
| 150 | #1694 | — | 5 | 1 | no | — |
| 151 | #1684 | — | 5 | 1 | no | — |
| 152 | #1672 | — | 5 | 1 | no | — |
| 153 | #1670 | — | 5 | 1 | no | — |
| 154 | #1648 | — | 5 | 1 | no | — |
| 155 | #1648 | — | 5 | 1 | no | — |
| 156 | #1645 | — | 5 | 1 | no | — |
| 157 | #1636 | — | 5 | 1 | no | — |
| 158 | #1584 | — | 5 | 1 | no | — |
| 159 | #1579 | — | 5 | 1 | no | — |
| 160 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 161 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 162 | C2×C5×Q8 | — | 4 | 1 | no | — |
| 163 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C2×Dic10 | — | 2 | 1 | no | — |
| 167 | C2×Dic10 | — | 2 | 1 | no | — |
| 168 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C5×Q16 | — | 4 | 1 | no | — |
| 170 | C5×Q16 | — | 4 | 2 | no | — |
| 171 | C2×C5×C8 | — | 2 | 1 | no | — |
| 172 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 175 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 176 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 177 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 178 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 179 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 180 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 181 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 182 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 183 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 184 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 185 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 186 | C5×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C5×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C5×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C42×C5 | — | 2 | 1 | no | — |
| 190 | C42×C5 | — | 2 | 1 | no | — |
| 191 | C42×C5 | — | 2 | 1 | no | — |
| 192 | C42×C5 | — | 4 | 1 | no | — |
| 193 | C42×C5 | — | 4 | 1 | no | — |
| 194 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 195 | #689 | — | 8 | 1 | no | — |
| 196 | #689 | — | 8 | 1 | no | — |
| 197 | #689 | Q16 | 1 | 4 | yes | complemented |
| 198 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 199 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 200 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 201 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 202 | C4⋊Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | #683 | — | 2 | 1 | no | — |
| 204 | #683 | — | 4 | 1 | no | — |
| 205 | #683 | — | 4 | 1 | no | — |
| 206 | #683 | — | 4 | 1 | no | — |
| 207 | #683 | — | 4 | 1 | no | — |
| 208 | #683 | — | 4 | 1 | no | — |
| 209 | #683 | — | 4 | 1 | no | — |
| 210 | C4×Dic5 | — | 2 | 1 | no | — |
| 211 | C4×Dic5 | — | 4 | 1 | no | — |
| 212 | C4×Dic5 | — | 4 | 1 | no | — |
| 213 | C2×#168 | — | 2 | 1 | no | — |
| 214 | C2×#168 | — | 2 | 1 | no | — |
| 215 | C2×#168 | — | 2 | 1 | no | — |
| 216 | C2×#168 | — | 2 | 1 | no | — |
| 217 | C2×#168 | C2×D4 | 1 | 1 | yes | characteristic |
| 218 | C2×#168 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | Dic20 | — | 4 | 2 | no | — |
| 220 | Dic20 | — | 8 | 1 | no | — |
| 221 | Q82 | C2×D5 | 1 | 1 | yes | characteristic |
| 222 | #557 | — | 5 | 1 | no | — |
| 223 | #557 | — | 5 | 1 | no | — |
| 224 | #557 | C2×D5 | 1 | 1 | yes | characteristic |
| 225 | #501 | — | 10 | 1 | no | — |
| 226 | #500 | — | 5 | 1 | no | — |
| 227 | #500 | — | 5 | 1 | no | — |
| 228 | #499 | — | 10 | 1 | no | — |
| 229 | #498 | — | 5 | 1 | no | — |
| 230 | #494 | — | 5 | 1 | no | — |
| 231 | #494 | — | 10 | 1 | no | — |
| 232 | #487 | — | 2 | 1 | no | — |
| 233 | #487 | — | 5 | 1 | no | — |
| 234 | #487 | C2×D5 | 1 | 1 | yes | characteristic |
| 235 | #479 | — | 10 | 1 | no | — |
| 236 | #479 | — | 10 | 1 | no | — |
| 237 | #479 | — | 10 | 1 | no | — |
| 238 | #477 | — | 2 | 1 | no | — |
| 239 | #477 | — | 5 | 1 | no | — |
| 240 | #477 | C2×D5 | 1 | 1 | yes | characteristic |
| 241 | #475 | — | 5 | 1 | no | — |
| 242 | #475 | — | 5 | 1 | no | — |
| 243 | #475 | — | 5 | 1 | no | — |
| 244 | #475 | — | 10 | 1 | no | — |
| 245 | #462 | — | 2 | 1 | no | — |
| 246 | #462 | — | 5 | 1 | no | — |
| 247 | #462 | — | 5 | 1 | no | — |
| 248 | #462 | — | 10 | 1 | no | — |
| 249 | #462 | — | 10 | 1 | no | — |
| 250 | #462 | C2×D5 | 1 | 1 | yes | characteristic |
| 251 | #446 | — | 5 | 1 | no | — |
| 252 | C8×Q8 | — | 5 | 1 | no | — |
| 253 | C8×Q8 | — | 5 | 1 | no | — |
| 254 | C8×Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 255 | #441 | — | 10 | 1 | no | — |
| 256 | C4×Q16 | — | 2 | 1 | no | — |
| 257 | C4×Q16 | — | 5 | 1 | no | — |
| 258 | C4×Q16 | — | 10 | 1 | no | — |
| 259 | C4×Q16 | — | 10 | 1 | no | — |
| 260 | C4×Q16 | C2×D5 | 1 | 1 | yes | characteristic |
| 261 | #335 | — | 5 | 1 | no | — |
| 262 | #334 | — | 5 | 1 | no | — |
| 263 | #333 | — | 5 | 1 | no | — |
| 264 | #332 | — | 5 | 1 | no | — |
| 265 | #332 | — | 5 | 1 | no | — |
| 266 | #332 | — | 5 | 1 | no | — |
| 267 | Q8⋊C8 | — | 5 | 1 | no | — |
| 268 | Q8⋊C8 | — | 5 | 1 | no | — |
| 269 | Q8⋊C8 | — | 5 | 1 | no | — |
| 270 | Q8⋊C8 | — | 5 | 1 | no | — |
| 271 | #322 | — | 5 | 1 | no | — |
| 272 | C5×Q8 | — | 2 | 1 | no | — |
| 273 | C5×Q8 | — | 2 | 1 | no | — |
| 274 | C5×Q8 | — | 2 | 1 | no | — |
| 275 | C5×Q8 | — | 2 | 1 | no | — |
| 276 | C5×Q8 | — | 2 | 1 | no | — |
| 277 | C5×Q8 | — | 4 | 1 | no | — |
| 278 | C5×Q8 | — | 4 | 1 | no | — |
| 279 | C5×Q8 | — | 8 | 1 | no | — |
| 280 | C5×Q8 | — | 16 | 1 | no | — |
| 281 | C5×Q8 | C2×Q16 | 1 | 2 | yes | — |
| 282 | C2×C4×C5 | — | 2 | 1 | no | — |
| 283 | C2×C4×C5 | — | 2 | 1 | no | — |
| 284 | C2×C4×C5 | — | 2 | 1 | no | — |
| 285 | C2×C4×C5 | — | 2 | 1 | no | — |
| 286 | C2×C4×C5 | — | 2 | 1 | no | — |
| 287 | C2×C4×C5 | — | 2 | 1 | no | — |
| 288 | C2×C4×C5 | — | 4 | 1 | no | — |
| 289 | C2×C4×C5 | — | 4 | 1 | no | — |
| 290 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 291 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 292 | C2×C4×C5 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 293 | C2×Dic5 | — | 2 | 1 | no | — |
| 294 | C2×Dic5 | — | 2 | 1 | no | — |
| 295 | C2×Dic5 | — | 4 | 1 | no | — |
| 296 | C2×Dic5 | — | 4 | 1 | no | — |
| 297 | Dic10 | — | 2 | 1 | no | — |
| 298 | Dic10 | — | 4 | 1 | no | — |
| 299 | Dic10 | — | 4 | 1 | no | — |
| 300 | Dic10 | — | 4 | 1 | no | — |
| 301 | Dic10 | — | 4 | 1 | no | — |
| 302 | Dic10 | C2×Q16 | 1 | 2 | yes | — |
| 303 | C5×C8 | — | 2 | 1 | no | — |
| 304 | C5×C8 | — | 2 | 1 | no | — |
| 305 | C5×C8 | — | 4 | 1 | no | — |
| 306 | #168 | — | 2 | 1 | no | — |
| 307 | #168 | — | 4 | 1 | no | — |
| 308 | #168 | — | 4 | 1 | no | — |
| 309 | #168 | — | 4 | 1 | no | — |
| 310 | #168 | — | 4 | 1 | no | — |
| 311 | #168 | C2×Q16 | 1 | 2 | yes | — |
| 312 | C2×Q16 | — | 2 | 1 | no | — |
| 313 | C2×Q16 | — | 5 | 1 | no | — |
| 314 | C2×Q16 | — | 10 | 1 | no | — |
| 315 | C2×Q16 | — | 10 | 1 | no | — |
| 316 | C2×Q16 | — | 10 | 1 | no | — |
| 317 | C2×Q16 | — | 10 | 1 | no | — |
| 318 | C2×Q16 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 319 | C4⋊Q8 | — | 2 | 1 | no | — |
| 320 | C4⋊Q8 | — | 2 | 1 | no | — |
| 321 | C4⋊Q8 | — | 2 | 1 | no | — |
| 322 | C4⋊Q8 | — | 4 | 1 | no | — |
| 323 | C4⋊Q8 | — | 5 | 1 | no | — |
| 324 | C4⋊Q8 | — | 5 | 1 | no | — |
| 325 | C4⋊Q8 | — | 10 | 1 | no | — |
| 326 | C4⋊Q8 | — | 10 | 1 | no | — |
| 327 | C4⋊Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 328 | C4⋊Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 329 | #125 | — | 2 | 1 | no | — |
| 330 | #125 | — | 4 | 1 | no | — |
| 331 | #125 | — | 10 | 1 | no | — |
| 332 | #125 | — | 10 | 1 | no | — |
| 333 | #125 | — | 20 | 1 | no | — |
| 334 | #125 | — | 20 | 1 | no | — |
| 335 | C4×Q8 | — | 2 | 1 | no | — |
| 336 | C4×Q8 | — | 2 | 1 | no | — |
| 337 | C4×Q8 | — | 2 | 1 | no | — |
| 338 | C4×Q8 | — | 2 | 1 | no | — |
| 339 | C4×Q8 | — | 5 | 1 | no | — |
| 340 | C4×Q8 | — | 10 | 1 | no | — |
| 341 | C4×Q8 | — | 10 | 1 | no | — |
| 342 | C4×Q8 | — | 10 | 1 | no | — |
| 343 | C4×Q8 | — | 10 | 1 | no | — |
| 344 | C4×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 345 | C4×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 346 | C4×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 347 | #107 | — | 2 | 1 | no | — |
| 348 | #107 | — | 5 | 1 | no | — |
| 349 | #107 | — | 10 | 1 | no | — |
| 350 | #107 | — | 10 | 1 | no | — |
| 351 | #107 | — | 10 | 1 | no | — |
| 352 | #107 | — | 20 | 1 | no | — |
| 353 | #107 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 354 | #106 | — | 10 | 1 | no | — |
| 355 | #106 | — | 10 | 1 | no | — |
| 356 | #106 | — | 10 | 1 | no | — |
| 357 | #106 | — | 10 | 1 | no | — |
| 358 | #106 | — | 10 | 1 | no | — |
| 359 | C4⋊C8 | — | 2 | 1 | no | — |
| 360 | C4⋊C8 | — | 5 | 1 | no | — |
| 361 | C4⋊C8 | — | 5 | 1 | no | — |
| 362 | C4⋊C8 | — | 5 | 1 | no | — |
| 363 | C4⋊C8 | — | 10 | 1 | no | — |
| 364 | C4⋊C8 | — | 10 | 1 | no | — |
| 365 | C4⋊C8 | — | 10 | 1 | no | — |
| 366 | C4⋊C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 367 | #103 | — | 2 | 1 | no | — |
| 368 | #103 | — | 2 | 1 | no | — |
| 369 | #103 | — | 2 | 1 | no | — |
| 370 | #103 | — | 2 | 1 | no | — |
| 371 | #103 | — | 5 | 1 | no | — |
| 372 | #103 | — | 5 | 1 | no | — |
| 373 | #103 | — | 10 | 1 | no | — |
| 374 | #103 | — | 10 | 1 | no | — |
| 375 | #103 | — | 10 | 1 | no | — |
| 376 | #103 | — | 10 | 1 | no | — |
| 377 | #103 | — | 10 | 1 | no | — |
| 378 | #103 | — | 10 | 1 | no | — |
| 379 | #103 | — | 20 | 1 | no | — |
| 380 | #103 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 381 | #103 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 382 | #97 | — | 10 | 1 | no | — |
| 383 | C4×C8 | — | 2 | 1 | no | — |
| 384 | C4×C8 | — | 5 | 1 | no | — |
| 385 | C4×C8 | — | 5 | 1 | no | — |
| 386 | C4×C8 | — | 10 | 1 | no | — |
| 387 | C4×C8 | — | 10 | 1 | no | — |
| 388 | C4×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 389 | C22×C5 | D42 | 1 | 1 | yes | characteristic |
| 390 | C4×C5 | — | 2 | 2 | no | — |
| 391 | C4×C5 | — | 2 | 1 | no | — |
| 392 | C4×C5 | — | 4 | 1 | no | — |
| 393 | C4×C5 | — | 4 | 1 | no | — |
| 394 | C4×C5 | — | 4 | 1 | no | — |
| 395 | C4×C5 | — | 4 | 1 | no | — |
| 396 | C4×C5 | — | 4 | 1 | no | — |
| 397 | C4×C5 | — | 8 | 1 | no | — |
| 398 | C4×C5 | — | 8 | 1 | no | — |
| 399 | C4×C5 | C22×Q16 | 1 | 1 | yes | characteristic |
| 400 | C4×C5 | #575 | 1 | 1 | yes | characteristic |
| 401 | C4×C5 | #577 | 1 | 1 | yes | characteristic |
| 402 | C4×C5 | #578 | 1 | 1 | yes | characteristic |
| 403 | Dic5 | — | 2 | 2 | no | — |
| 404 | Dic5 | — | 4 | 1 | no | — |
| 405 | Dic5 | — | 8 | 1 | no | — |
| 406 | Dic5 | — | 8 | 1 | no | — |
| 407 | C2×Q8 | — | 2 | 1 | no | — |
| 408 | C2×Q8 | — | 2 | 1 | no | — |
| 409 | C2×Q8 | — | 4 | 1 | no | — |
| 410 | C2×Q8 | — | 5 | 1 | no | — |
| 411 | C2×Q8 | — | 10 | 1 | no | — |
| 412 | C2×Q8 | — | 10 | 1 | no | — |
| 413 | C2×Q8 | D4×D5 | 1 | 1 | yes | characteristic |
| 414 | C2×Q8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 415 | C2×Q8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 416 | Q16 | — | 4 | 1 | no | — |
| 417 | Q16 | — | 4 | 2 | no | — |
| 418 | Q16 | — | 5 | 4 | no | — |
| 419 | Q16 | — | 20 | 2 | no | — |
| 420 | Q16 | — | 40 | 1 | no | — |
| 421 | Q16 | — | 40 | 1 | no | — |
| 422 | Q16 | — | 40 | 1 | no | — |
| 423 | C2×C8 | — | 2 | 1 | no | — |
| 424 | C2×C8 | — | 5 | 1 | no | — |
| 425 | C2×C8 | — | 5 | 1 | no | — |
| 426 | C2×C8 | — | 10 | 1 | no | — |
| 427 | C2×C8 | — | 10 | 1 | no | — |
| 428 | C2×C8 | — | 10 | 1 | no | — |
| 429 | C2×C8 | — | 10 | 1 | no | — |
| 430 | C2×C8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 431 | C2×C8 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 432 | C4⋊C4 | — | 2 | 1 | no | — |
| 433 | C4⋊C4 | — | 2 | 1 | no | — |
| 434 | C4⋊C4 | — | 2 | 1 | no | — |
| 435 | C4⋊C4 | — | 2 | 1 | no | — |
| 436 | C4⋊C4 | — | 2 | 1 | no | — |
| 437 | C4⋊C4 | — | 2 | 1 | no | — |
| 438 | C4⋊C4 | — | 2 | 1 | no | — |
| 439 | C4⋊C4 | — | 4 | 1 | no | — |
| 440 | C4⋊C4 | — | 4 | 1 | no | — |
| 441 | C4⋊C4 | — | 4 | 1 | no | — |
| 442 | C4⋊C4 | — | 4 | 1 | no | — |
| 443 | C4⋊C4 | — | 4 | 1 | no | — |
| 444 | C4⋊C4 | — | 5 | 1 | no | — |
| 445 | C4⋊C4 | — | 10 | 1 | no | — |
| 446 | C4⋊C4 | — | 10 | 1 | no | — |
| 447 | C4⋊C4 | — | 10 | 1 | no | — |
| 448 | C4⋊C4 | — | 10 | 1 | no | — |
| 449 | C4⋊C4 | — | 10 | 1 | no | — |
| 450 | C4⋊C4 | — | 20 | 1 | no | — |
| 451 | C4⋊C4 | — | 20 | 1 | no | — |
| 452 | C4⋊C4 | — | 20 | 1 | no | — |
| 453 | C4⋊C4 | — | 20 | 1 | no | — |
| 454 | C4⋊C4 | — | 20 | 1 | no | — |
| 455 | C4⋊C4 | — | 20 | 1 | no | — |
| 456 | C4⋊C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 457 | C4⋊C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 458 | C4⋊C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 459 | C42 | — | 2 | 1 | no | — |
| 460 | C42 | — | 2 | 1 | no | — |
| 461 | C42 | — | 2 | 1 | no | — |
| 462 | C42 | — | 4 | 1 | no | — |
| 463 | C42 | — | 4 | 1 | no | — |
| 464 | C42 | — | 10 | 1 | no | — |
| 465 | C42 | — | 20 | 1 | no | — |
| 466 | C42 | — | 20 | 1 | no | — |
| 467 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 468 | C2×C5 | #3271 | 1 | 1 | yes | characteristic |
| 469 | C2×C5 | D4×Q16 | 1 | 1 | yes | characteristic |
| 470 | C2×C5 | #3289 | 1 | 1 | yes | characteristic |
| 471 | Q8 | — | 2 | 1 | no | — |
| 472 | Q8 | — | 2 | 1 | no | — |
| 473 | Q8 | — | 2 | 1 | no | — |
| 474 | Q8 | — | 2 | 1 | no | — |
| 475 | Q8 | — | 2 | 1 | no | — |
| 476 | Q8 | — | 4 | 1 | no | — |
| 477 | Q8 | — | 4 | 1 | no | — |
| 478 | Q8 | — | 5 | 2 | no | — |
| 479 | Q8 | — | 8 | 1 | no | — |
| 480 | Q8 | — | 10 | 1 | no | — |
| 481 | Q8 | — | 16 | 1 | no | — |
| 482 | Q8 | — | 20 | 1 | no | — |
| 483 | Q8 | — | 20 | 1 | no | — |
| 484 | Q8 | — | 20 | 1 | no | — |
| 485 | Q8 | — | 20 | 1 | no | — |
| 486 | Q8 | D5×Q16 | 1 | 2 | yes | — |
| 487 | C2×C4 | — | 2 | 1 | no | — |
| 488 | C2×C4 | — | 2 | 1 | no | — |
| 489 | C2×C4 | — | 2 | 1 | no | — |
| 490 | C2×C4 | — | 2 | 1 | no | — |
| 491 | C2×C4 | — | 2 | 1 | no | — |
| 492 | C2×C4 | — | 2 | 1 | no | — |
| 493 | C2×C4 | — | 4 | 1 | no | — |
| 494 | C2×C4 | — | 4 | 1 | no | — |
| 495 | C2×C4 | — | 10 | 1 | no | — |
| 496 | C2×C4 | — | 10 | 1 | no | — |
| 497 | C2×C4 | — | 20 | 1 | no | — |
| 498 | C2×C4 | — | 20 | 1 | no | — |
| 499 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 500 | C2×C4 | #4144 | 1 | 1 | yes | characteristic |
| 501 | C2×C4 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 502 | C8 | — | 2 | 1 | no | — |
| 503 | C8 | — | 2 | 1 | no | — |
| 504 | C8 | — | 4 | 1 | no | — |
| 505 | C8 | — | 5 | 2 | no | — |
| 506 | C8 | — | 10 | 1 | no | — |
| 507 | C8 | — | 20 | 1 | no | — |
| 508 | C8 | — | 20 | 1 | no | — |
| 509 | C8 | — | 20 | 1 | no | — |
| 510 | C8 | — | 20 | 1 | no | — |
| 511 | C5 | #19818 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 512 | C22 | D4×C22⋊D5 | 1 | 1 | yes | characteristic |
| 513 | C4 | — | 2 | 2 | no | — |
| 514 | C4 | — | 2 | 1 | no | — |
| 515 | C4 | — | 4 | 1 | no | — |
| 516 | C4 | — | 4 | 1 | no | — |
| 517 | C4 | — | 4 | 1 | no | — |
| 518 | C4 | — | 4 | 1 | no | — |
| 519 | C4 | — | 4 | 1 | no | — |
| 520 | C4 | — | 8 | 1 | no | — |
| 521 | C4 | — | 8 | 1 | no | — |
| 522 | C4 | — | 10 | 2 | no | — |
| 523 | C4 | — | 20 | 1 | no | — |
| 524 | C4 | — | 40 | 1 | no | — |
| 525 | C4 | — | 40 | 1 | no | — |
| 526 | C4 | C2×D5×Q16 | 1 | 1 | yes | characteristic |
| 527 | C4 | #66100 | 1 | 1 | yes | characteristic |
| 528 | C4 | #66156 | 1 | 1 | yes | characteristic |
| 529 | C4 | #66171 | 1 | 1 | yes | characteristic |
| 530 | C2 | #10615278 | 1 | 1 | yes | characteristic |
| 531 | C2 | Q16×C22⋊D5 | 1 | 1 | yes | characteristic |
| 532 | C2 | #10615744 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta