Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
500 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10614175 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10614173 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10611081 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C5×#1467 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10601604 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10601594 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10598248 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×C4×C5×Q8 | C22 | 1 | 1 | yes | characteristic |
| 9 | #65811 | C22 | 1 | 1 | yes | characteristic |
| 10 | #65811 | C22 | 1 | 1 | yes | characteristic |
| 11 | C5×#432 | C22 | 1 | 1 | yes | characteristic |
| 12 | C5×#432 | C22 | 1 | 1 | yes | characteristic |
| 13 | #65516 | — | 2 | 1 | no | — |
| 14 | #65516 | — | 2 | 1 | no | — |
| 15 | #65316 | — | 2 | 1 | no | — |
| 16 | #65316 | — | 2 | 1 | no | — |
| 17 | #65315 | — | 2 | 2 | no | — |
| 18 | C4×#688 | — | 2 | 2 | no | — |
| 19 | #65310 | — | 2 | 1 | no | — |
| 20 | #65309 | — | 2 | 1 | no | — |
| 21 | #65257 | — | 2 | 1 | no | — |
| 22 | #65256 | — | 2 | 1 | no | — |
| 23 | #65215 | C22 | 1 | 1 | yes | characteristic |
| 24 | #65214 | C22 | 1 | 1 | yes | characteristic |
| 25 | #65132 | — | 2 | 1 | no | — |
| 26 | #65130 | — | 2 | 1 | no | — |
| 27 | #65023 | — | 2 | 2 | no | — |
| 28 | #65003 | — | 2 | 1 | no | — |
| 29 | #65001 | — | 2 | 1 | no | — |
| 30 | C5×#324 | — | 2 | 2 | no | — |
| 31 | #64703 | — | 2 | 2 | no | — |
| 32 | #64684 | — | 2 | 2 | no | — |
| 33 | #10040 | — | 5 | 1 | no | maximal, Sylow |
| 34 | C22×C5×Q8 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×#709 | — | 2 | 1 | no | — |
| 36 | C2×#709 | — | 2 | 1 | no | — |
| 37 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 38 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 39 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 40 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 41 | C2×C5×C4⋊C4 | — | 2 | 1 | no | — |
| 42 | C2×C5×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 43 | C2×C42×C5 | — | 2 | 1 | no | — |
| 44 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 45 | C2×#688 | — | 2 | 2 | no | — |
| 46 | C2×#688 | — | 2 | 2 | no | — |
| 47 | #4076 | — | 2 | 1 | no | — |
| 48 | #4076 | — | 2 | 1 | no | — |
| 49 | #4076 | — | 2 | 1 | no | — |
| 50 | #4076 | — | 2 | 1 | no | — |
| 51 | C2×D40 | — | 2 | 2 | no | — |
| 52 | C2×#677 | — | 2 | 2 | no | — |
| 53 | #4021 | — | 2 | 1 | no | — |
| 54 | #4021 | — | 2 | 1 | no | — |
| 55 | #4020 | D4 | 1 | 1 | yes | characteristic |
| 56 | #4020 | D4 | 1 | 1 | yes | characteristic |
| 57 | C4×D20 | — | 2 | 1 | no | — |
| 58 | C4×D20 | — | 2 | 1 | no | — |
| 59 | C4×D20 | — | 2 | 1 | no | — |
| 60 | C4×D20 | — | 2 | 1 | no | — |
| 61 | #4015 | D4 | 1 | 1 | yes | characteristic |
| 62 | #4015 | D4 | 1 | 1 | yes | characteristic |
| 63 | C5×C4⋊C8 | — | 2 | 1 | no | — |
| 64 | C5×C4⋊C8 | — | 2 | 1 | no | — |
| 65 | C5×C22⋊C8 | — | 2 | 1 | no | — |
| 66 | C5×C22⋊C8 | D4 | 1 | 2 | yes | — |
| 67 | C5×#97 | — | 2 | 1 | no | — |
| 68 | C5×#97 | — | 2 | 1 | no | — |
| 69 | #3967 | — | 2 | 2 | no | — |
| 70 | #3967 | — | 2 | 2 | no | — |
| 71 | C22⋊#168 | — | 2 | 1 | no | — |
| 72 | C22⋊#168 | — | 2 | 1 | no | — |
| 73 | #3953 | — | 2 | 2 | no | — |
| 74 | #3948 | — | 2 | 2 | no | — |
| 75 | #3941 | — | 2 | 2 | no | — |
| 76 | #3941 | — | 2 | 2 | no | — |
| 77 | #3940 | — | 2 | 2 | no | — |
| 78 | #3939 | — | 2 | 2 | no | — |
| 79 | C4⋊#168 | — | 2 | 1 | no | — |
| 80 | C4⋊#168 | — | 2 | 1 | no | — |
| 81 | #3935 | D4 | 1 | 2 | yes | — |
| 82 | C4×#168 | D4 | 1 | 2 | yes | — |
| 83 | #3214 | — | 5 | 1 | no | — |
| 84 | #3112 | — | 5 | 1 | no | — |
| 85 | #3103 | — | 5 | 1 | no | — |
| 86 | #1536 | — | 5 | 1 | no | — |
| 87 | #1496 | — | 5 | 1 | no | — |
| 88 | #1467 | D5 | 1 | 1 | yes | characteristic, complemented |
| 89 | #1287 | — | 5 | 1 | no | — |
| 90 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 91 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 92 | C2×C5×Q8 | — | 4 | 2 | no | — |
| 93 | C22×C4×C5 | — | 2 | 1 | no | — |
| 94 | C22×C4×C5 | — | 2 | 1 | no | — |
| 95 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C22×C4×C5 | #41 | 1 | 1 | yes | characteristic |
| 98 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 99 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 100 | #709 | — | 8 | 2 | no | — |
| 101 | #709 | — | 8 | 2 | no | — |
| 102 | C2×D20 | — | 2 | 1 | no | — |
| 103 | C2×D20 | — | 2 | 1 | no | — |
| 104 | C2×D20 | — | 2 | 1 | no | — |
| 105 | C2×D20 | — | 2 | 1 | no | — |
| 106 | C2×D20 | — | 2 | 1 | no | — |
| 107 | C2×D20 | — | 2 | 1 | no | — |
| 108 | C2×C4×D5 | — | 4 | 1 | no | — |
| 109 | C2×C4×D5 | — | 4 | 1 | no | — |
| 110 | C2×Dic10 | — | 2 | 1 | no | — |
| 111 | C2×Dic10 | — | 2 | 1 | no | — |
| 112 | C2×C5×C8 | — | 2 | 2 | no | — |
| 113 | C2×C5×C8 | — | 4 | 1 | no | — |
| 114 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 115 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 116 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 117 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 118 | C42×C5 | — | 4 | 1 | no | — |
| 119 | C42×C5 | — | 4 | 1 | no | — |
| 120 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 123 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | #688 | — | 4 | 4 | no | — |
| 125 | #688 | — | 4 | 4 | no | — |
| 126 | #685 | — | 4 | 1 | no | — |
| 127 | #685 | — | 4 | 1 | no | — |
| 128 | #685 | — | 4 | 1 | no | — |
| 129 | #685 | — | 4 | 1 | no | — |
| 130 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 131 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 132 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 133 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 134 | C2×#168 | — | 2 | 2 | no | — |
| 135 | C2×#168 | — | 2 | 2 | no | — |
| 136 | D40 | — | 8 | 2 | no | — |
| 137 | #677 | — | 8 | 2 | no | — |
| 138 | #532 | — | 5 | 1 | no | — |
| 139 | #532 | — | 5 | 1 | no | — |
| 140 | C2×C4×Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 141 | #496 | — | 10 | 1 | no | — |
| 142 | #489 | — | 10 | 1 | no | — |
| 143 | #481 | — | 10 | 1 | no | — |
| 144 | #480 | — | 10 | 1 | no | — |
| 145 | #477 | — | 10 | 1 | no | — |
| 146 | #475 | — | 10 | 1 | no | — |
| 147 | #461 | — | 10 | 1 | no | — |
| 148 | #460 | — | 10 | 1 | no | — |
| 149 | #460 | — | 10 | 1 | no | — |
| 150 | #459 | — | 10 | 1 | no | — |
| 151 | #449 | — | 10 | 2 | no | — |
| 152 | #448 | — | 10 | 1 | no | — |
| 153 | #448 | — | 10 | 1 | no | — |
| 154 | #440 | — | 10 | 2 | no | — |
| 155 | C4×SD16 | — | 10 | 2 | no | — |
| 156 | #432 | — | 5 | 1 | no | — |
| 157 | #432 | C2×D5 | 1 | 1 | yes | characteristic |
| 158 | #432 | C2×D5 | 1 | 1 | yes | characteristic |
| 159 | #431 | — | 5 | 1 | no | — |
| 160 | #329 | — | 10 | 2 | no | — |
| 161 | D4⋊C8 | — | 10 | 2 | no | — |
| 162 | #324 | — | 2 | 2 | no | — |
| 163 | C23×C5 | #121 | 1 | 1 | yes | characteristic |
| 164 | C22×D5 | — | 4 | 1 | no | — |
| 165 | C22×D5 | — | 4 | 1 | no | — |
| 166 | C5×Q8 | — | 2 | 2 | no | — |
| 167 | C5×Q8 | — | 2 | 2 | no | — |
| 168 | C5×Q8 | — | 4 | 1 | no | — |
| 169 | C5×Q8 | — | 4 | 1 | no | — |
| 170 | C2×C4×C5 | — | 2 | 2 | no | — |
| 171 | C2×C4×C5 | — | 2 | 2 | no | — |
| 172 | C2×C4×C5 | — | 4 | 1 | no | — |
| 173 | C2×C4×C5 | — | 4 | 1 | no | — |
| 174 | C2×C4×C5 | — | 4 | 1 | no | — |
| 175 | C2×C4×C5 | — | 4 | 1 | no | — |
| 176 | C2×C4×C5 | — | 4 | 1 | no | — |
| 177 | C2×C4×C5 | — | 8 | 1 | no | — |
| 178 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 179 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 180 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 181 | C2×C4×C5 | #121 | 1 | 1 | yes | characteristic |
| 182 | C2×C4×C5 | #121 | 1 | 1 | yes | characteristic |
| 183 | C2×C4×C5 | #127 | 1 | 1 | yes | characteristic |
| 184 | C22⋊D5 | — | 8 | 2 | no | — |
| 185 | C22⋊D5 | — | 8 | 2 | no | — |
| 186 | C2×Dic5 | — | 4 | 1 | no | — |
| 187 | C2×Dic5 | — | 4 | 1 | no | — |
| 188 | D20 | — | 4 | 1 | no | — |
| 189 | D20 | — | 4 | 1 | no | — |
| 190 | D20 | — | 4 | 2 | no | — |
| 191 | D20 | — | 4 | 2 | no | — |
| 192 | D20 | — | 4 | 2 | no | — |
| 193 | D20 | — | 4 | 2 | no | — |
| 194 | D20 | — | 8 | 1 | no | — |
| 195 | C4×D5 | — | 8 | 2 | no | — |
| 196 | C4×D5 | — | 8 | 2 | no | — |
| 197 | Dic10 | — | 4 | 2 | no | — |
| 198 | Dic10 | — | 8 | 1 | no | — |
| 199 | C5×C8 | — | 4 | 2 | no | — |
| 200 | C5×C8 | — | 8 | 1 | no | — |
| 201 | #168 | — | 4 | 2 | no | — |
| 202 | #168 | — | 4 | 2 | no | — |
| 203 | C2×#41 | — | 10 | 1 | no | — |
| 204 | C2×#41 | — | 10 | 1 | no | — |
| 205 | C22×Q8 | D20 | 1 | 1 | yes | characteristic |
| 206 | C2×SD16 | — | 10 | 2 | no | — |
| 207 | C2×SD16 | — | 10 | 2 | no | — |
| 208 | C2×SD16 | — | 10 | 2 | no | — |
| 209 | C2×D8 | — | 10 | 2 | no | — |
| 210 | C4⋊Q8 | — | 5 | 1 | no | — |
| 211 | C4⋊Q8 | — | 5 | 1 | no | — |
| 212 | #127 | — | 5 | 1 | no | — |
| 213 | #127 | — | 5 | 1 | no | — |
| 214 | #124 | — | 10 | 1 | no | — |
| 215 | #124 | — | 10 | 1 | no | — |
| 216 | #121 | — | 10 | 1 | no | — |
| 217 | #121 | — | 10 | 1 | no | — |
| 218 | #121 | — | 10 | 1 | no | — |
| 219 | #121 | — | 10 | 1 | no | — |
| 220 | C4×Q8 | — | 2 | 1 | no | — |
| 221 | C4×Q8 | — | 2 | 1 | no | — |
| 222 | C4×Q8 | — | 2 | 1 | no | — |
| 223 | C4×Q8 | — | 2 | 1 | no | — |
| 224 | C4×D4 | — | 10 | 1 | no | — |
| 225 | C4×D4 | — | 10 | 1 | no | — |
| 226 | C4×D4 | — | 10 | 1 | no | — |
| 227 | C4×D4 | — | 10 | 1 | no | — |
| 228 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 229 | C2×C4⋊C4 | D20 | 1 | 1 | yes | characteristic |
| 230 | C2×C42 | — | 2 | 1 | no | — |
| 231 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 232 | #107 | — | 10 | 2 | no | — |
| 233 | #106 | — | 10 | 2 | no | — |
| 234 | C4⋊C8 | — | 2 | 1 | no | — |
| 235 | C4⋊C8 | — | 2 | 1 | no | — |
| 236 | C4⋊C8 | — | 10 | 1 | no | — |
| 237 | C4⋊C8 | — | 10 | 1 | no | — |
| 238 | #103 | — | 10 | 2 | no | — |
| 239 | #103 | — | 10 | 2 | no | — |
| 240 | #103 | — | 10 | 2 | no | — |
| 241 | #102 | — | 10 | 2 | no | — |
| 242 | #102 | — | 10 | 2 | no | — |
| 243 | #102 | — | 10 | 2 | no | — |
| 244 | C22⋊C8 | — | 2 | 1 | no | — |
| 245 | C22⋊C8 | — | 10 | 1 | no | — |
| 246 | C22⋊C8 | — | 10 | 1 | no | — |
| 247 | C22⋊C8 | C22⋊D5 | 1 | 2 | yes | — |
| 248 | #97 | — | 2 | 1 | no | — |
| 249 | #97 | — | 2 | 1 | no | — |
| 250 | #97 | — | 5 | 2 | no | — |
| 251 | C4×C8 | — | 5 | 2 | no | — |
| 252 | C22×C5 | — | 2 | 1 | no | — |
| 253 | C22×C5 | — | 2 | 1 | no | — |
| 254 | C22×C5 | — | 2 | 1 | no | — |
| 255 | C22×C5 | #392 | 1 | 1 | yes | characteristic |
| 256 | C2×D5 | — | 8 | 1 | no | — |
| 257 | C2×D5 | — | 8 | 1 | no | — |
| 258 | C2×D5 | — | 8 | 1 | no | — |
| 259 | C2×D5 | — | 8 | 1 | no | — |
| 260 | C2×D5 | — | 8 | 1 | no | — |
| 261 | C2×D5 | — | 8 | 1 | no | — |
| 262 | C4×C5 | — | 2 | 1 | no | — |
| 263 | C4×C5 | — | 2 | 1 | no | — |
| 264 | C4×C5 | — | 2 | 1 | no | — |
| 265 | C4×C5 | — | 2 | 1 | no | — |
| 266 | C4×C5 | — | 2 | 1 | no | — |
| 267 | C4×C5 | — | 4 | 2 | no | — |
| 268 | C4×C5 | — | 8 | 1 | no | — |
| 269 | C4×C5 | #471 | 1 | 2 | yes | — |
| 270 | Dic5 | — | 8 | 1 | no | — |
| 271 | Dic5 | — | 8 | 1 | no | — |
| 272 | #41 | — | 40 | 2 | no | — |
| 273 | #41 | — | 40 | 2 | no | — |
| 274 | C2×Q8 | — | 2 | 1 | no | — |
| 275 | C2×Q8 | — | 2 | 1 | no | — |
| 276 | C2×Q8 | — | 4 | 2 | no | — |
| 277 | C2×Q8 | — | 10 | 1 | no | — |
| 278 | C2×Q8 | — | 10 | 1 | no | — |
| 279 | C2×D4 | — | 10 | 1 | no | — |
| 280 | C2×D4 | — | 10 | 1 | no | — |
| 281 | C2×D4 | — | 10 | 1 | no | — |
| 282 | C2×D4 | — | 10 | 1 | no | — |
| 283 | C2×D4 | — | 10 | 1 | no | — |
| 284 | C2×D4 | — | 10 | 1 | no | — |
| 285 | C2×D4 | — | 20 | 1 | no | — |
| 286 | C2×D4 | — | 20 | 1 | no | — |
| 287 | C22×C4 | — | 2 | 1 | no | — |
| 288 | C22×C4 | — | 2 | 1 | no | — |
| 289 | C22×C4 | — | 20 | 1 | no | — |
| 290 | C22×C4 | — | 20 | 1 | no | — |
| 291 | C22×C4 | C2×D20 | 1 | 1 | yes | characteristic |
| 292 | C22×C4 | #709 | 1 | 1 | yes | characteristic |
| 293 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 294 | SD16 | — | 20 | 4 | no | — |
| 295 | SD16 | — | 20 | 4 | no | — |
| 296 | SD16 | — | 40 | 2 | no | — |
| 297 | D8 | — | 40 | 2 | no | — |
| 298 | C2×C8 | — | 2 | 2 | no | — |
| 299 | C2×C8 | — | 4 | 1 | no | — |
| 300 | C2×C8 | — | 10 | 2 | no | — |
| 301 | C2×C8 | — | 10 | 2 | no | — |
| 302 | C4⋊C4 | — | 2 | 1 | no | — |
| 303 | C4⋊C4 | — | 2 | 1 | no | — |
| 304 | C4⋊C4 | — | 4 | 1 | no | — |
| 305 | C4⋊C4 | — | 4 | 1 | no | — |
| 306 | C4⋊C4 | — | 10 | 1 | no | — |
| 307 | C4⋊C4 | — | 10 | 1 | no | — |
| 308 | C4⋊C4 | — | 10 | 1 | no | — |
| 309 | C4⋊C4 | — | 10 | 1 | no | — |
| 310 | C22⋊C4 | — | 20 | 1 | no | — |
| 311 | C22⋊C4 | — | 20 | 1 | no | — |
| 312 | C22⋊C4 | — | 20 | 1 | no | — |
| 313 | C22⋊C4 | — | 20 | 1 | no | — |
| 314 | C42 | — | 4 | 1 | no | — |
| 315 | C42 | — | 4 | 1 | no | — |
| 316 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 317 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 318 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 319 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 320 | C2×C5 | — | 4 | 1 | no | — |
| 321 | C2×C5 | #2008 | 1 | 1 | yes | characteristic |
| 322 | C2×C5 | #2010 | 1 | 1 | yes | characteristic |
| 323 | C2×C5 | #2019 | 1 | 1 | yes | characteristic |
| 324 | D5 | — | 16 | 1 | no | — |
| 325 | D5 | — | 16 | 1 | no | — |
| 326 | C23 | — | 20 | 1 | no | — |
| 327 | C23 | — | 20 | 1 | no | — |
| 328 | C23 | #4076 | 1 | 1 | yes | characteristic |
| 329 | Q8 | — | 2 | 2 | no | — |
| 330 | Q8 | — | 2 | 2 | no | — |
| 331 | Q8 | — | 4 | 1 | no | — |
| 332 | Q8 | — | 4 | 1 | no | — |
| 333 | Q8 | — | 20 | 2 | no | — |
| 334 | Q8 | — | 40 | 1 | no | — |
| 335 | D4 | — | 20 | 1 | no | — |
| 336 | D4 | — | 20 | 2 | no | — |
| 337 | D4 | — | 20 | 2 | no | — |
| 338 | D4 | — | 20 | 2 | no | — |
| 339 | D4 | — | 20 | 1 | no | — |
| 340 | D4 | — | 20 | 2 | no | — |
| 341 | D4 | — | 40 | 1 | no | — |
| 342 | D4 | — | 40 | 2 | no | — |
| 343 | D4 | — | 40 | 2 | no | — |
| 344 | C2×C4 | — | 2 | 2 | no | — |
| 345 | C2×C4 | — | 2 | 2 | no | — |
| 346 | C2×C4 | — | 4 | 1 | no | — |
| 347 | C2×C4 | — | 4 | 1 | no | — |
| 348 | C2×C4 | — | 4 | 1 | no | — |
| 349 | C2×C4 | — | 4 | 1 | no | — |
| 350 | C2×C4 | — | 4 | 1 | no | — |
| 351 | C2×C4 | — | 8 | 1 | no | — |
| 352 | C2×C4 | — | 20 | 1 | no | — |
| 353 | C2×C4 | — | 20 | 1 | no | — |
| 354 | C2×C4 | — | 40 | 2 | no | — |
| 355 | C2×C4 | — | 40 | 2 | no | — |
| 356 | C2×C4 | #4028 | 1 | 1 | yes | characteristic |
| 357 | C2×C4 | #4028 | 1 | 1 | yes | characteristic |
| 358 | C2×C4 | #4030 | 1 | 1 | yes | characteristic |
| 359 | C2×C4 | #4030 | 1 | 1 | yes | characteristic |
| 360 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 361 | C2×C4 | #4086 | 1 | 1 | yes | characteristic |
| 362 | C8 | — | 4 | 2 | no | — |
| 363 | C8 | — | 8 | 1 | no | — |
| 364 | C8 | — | 20 | 2 | no | — |
| 365 | C8 | — | 20 | 2 | no | — |
| 366 | C5 | #10040 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 367 | C22 | — | 2 | 1 | no | — |
| 368 | C22 | — | 2 | 1 | no | — |
| 369 | C22 | — | 2 | 1 | no | — |
| 370 | C22 | — | 40 | 1 | no | — |
| 371 | C22 | — | 40 | 1 | no | — |
| 372 | C22 | — | 40 | 1 | no | — |
| 373 | C22 | — | 40 | 1 | no | — |
| 374 | C22 | — | 40 | 1 | no | — |
| 375 | C22 | — | 40 | 1 | no | — |
| 376 | C22 | #65249 | 1 | 1 | yes | characteristic |
| 377 | C4 | — | 2 | 1 | no | — |
| 378 | C4 | — | 2 | 1 | no | — |
| 379 | C4 | — | 2 | 1 | no | — |
| 380 | C4 | — | 2 | 1 | no | — |
| 381 | C4 | — | 2 | 1 | no | — |
| 382 | C4 | — | 4 | 2 | no | — |
| 383 | C4 | — | 8 | 1 | no | — |
| 384 | C4 | — | 40 | 1 | no | — |
| 385 | C4 | — | 40 | 1 | no | — |
| 386 | C4 | #65043 | 1 | 2 | yes | — |
| 387 | C2 | — | 4 | 1 | no | — |
| 388 | C2 | — | 80 | 1 | no | — |
| 389 | C2 | — | 80 | 1 | no | — |
| 390 | C2 | #10600786 | 1 | 1 | yes | characteristic |
| 391 | C2 | #10600843 | 1 | 1 | yes | characteristic |
| 392 | C2 | #10600910 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10614175 | C2 | semidirect |
| 2. #10614173 | C2 | semidirect |
| 4. C5×#1467 | C2 | semidirect |
| 5. #10601604 | C2 | semidirect |
| 6. #10601594 | C2 | semidirect |
| 7. #10598248 | C2 | semidirect |
| 88. #1467 | D5 | semidirect |
| 366. C5 | #10040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614175 | 2 |
| #10614173 | 2 |
| #10611081 | 2 |
| C5×#1467 | 2 |
| #10601604 | 2 |
| #10601594 | 2 |
| #10598248 | 2 |
| #10040 | 5 |