Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
994 conjugacy classes of subgroups.
The subgroup lattice has 536 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C5×#3548 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10615092 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10615038 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10615017 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10602746 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10602745 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10602615 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10602592 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10602591 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C5×#562 | C22 | 1 | 4 | yes | — |
| 11 | C5×#554 | — | 2 | 1 | no | — |
| 12 | C5×#554 | — | 2 | 1 | no | — |
| 13 | C5×#550 | — | 2 | 1 | no | — |
| 14 | C5×#550 | — | 2 | 1 | no | — |
| 15 | C5×#547 | — | 2 | 1 | no | — |
| 16 | C5×#547 | — | 2 | 1 | no | — |
| 17 | C5×#540 | — | 2 | 2 | no | — |
| 18 | C5×#537 | — | 2 | 2 | no | — |
| 19 | C5×#537 | — | 2 | 2 | no | — |
| 20 | C5×#533 | C22 | 1 | 1 | yes | characteristic |
| 21 | C5×#532 | C22 | 1 | 1 | yes | characteristic |
| 22 | C5×#532 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#4096 | — | 2 | 2 | no | — |
| 24 | #65811 | C22 | 1 | 1 | yes | characteristic |
| 25 | #65527 | — | 2 | 2 | no | — |
| 26 | #65376 | — | 2 | 1 | no | — |
| 27 | #65375 | — | 2 | 1 | no | — |
| 28 | #65373 | — | 2 | 1 | no | — |
| 29 | #65372 | — | 2 | 1 | no | — |
| 30 | #65363 | — | 2 | 1 | no | — |
| 31 | #65361 | — | 2 | 1 | no | — |
| 32 | #65356 | C22 | 1 | 2 | yes | — |
| 33 | #65354 | C22 | 1 | 2 | yes | — |
| 34 | #65349 | C22 | 1 | 2 | yes | — |
| 35 | #65347 | C22 | 1 | 2 | yes | — |
| 36 | #65347 | C22 | 1 | 2 | yes | — |
| 37 | #65344 | C22 | 1 | 2 | yes | — |
| 38 | #65292 | — | 2 | 2 | no | — |
| 39 | #65215 | C22 | 1 | 1 | yes | characteristic |
| 40 | #65215 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#3935 | C22 | 1 | 1 | yes | characteristic |
| 42 | #64763 | C22 | 1 | 4 | yes | — |
| 43 | #64760 | C22 | 1 | 4 | yes | — |
| 44 | #64760 | C22 | 1 | 4 | yes | — |
| 45 | #19053 | — | 5 | 1 | no | maximal, Sylow |
| 46 | C2×C5×#41 | — | 2 | 2 | no | — |
| 47 | C2×C5×#41 | — | 2 | 2 | no | — |
| 48 | C2×C5×#41 | D4 | 1 | 2 | yes | — |
| 49 | C2×C5×#41 | D4 | 1 | 2 | yes | — |
| 50 | C2×#709 | — | 2 | 1 | no | — |
| 51 | C5×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 52 | C5×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 53 | C5×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 54 | C5×C4⋊Q8 | D4 | 1 | 1 | yes | characteristic |
| 55 | C5×#127 | — | 2 | 2 | no | — |
| 56 | C5×#127 | D4 | 1 | 1 | yes | characteristic |
| 57 | C5×#127 | D4 | 1 | 1 | yes | characteristic |
| 58 | C5×#125 | — | 2 | 2 | no | — |
| 59 | C5×#125 | C23 | 1 | 2 | yes | — |
| 60 | C5×#124 | C23 | 1 | 2 | yes | — |
| 61 | C5×#124 | C23 | 1 | 2 | yes | — |
| 62 | C5×#123 | — | 2 | 4 | no | — |
| 63 | C5×#123 | — | 2 | 4 | no | — |
| 64 | C5×C22⋊Q8 | — | 2 | 2 | no | — |
| 65 | C5×C22⋊Q8 | — | 2 | 2 | no | — |
| 66 | C5×C22⋊Q8 | — | 2 | 4 | no | — |
| 67 | C5×C22⋊Q8 | — | 2 | 4 | no | — |
| 68 | C5×C22⋊Q8 | — | 2 | 1 | no | — |
| 69 | C5×C22⋊Q8 | — | 2 | 1 | no | — |
| 70 | C5×#121 | — | 2 | 4 | no | — |
| 71 | C5×#121 | — | 2 | 4 | no | — |
| 72 | C5×#121 | — | 2 | 2 | no | — |
| 73 | C5×#121 | — | 2 | 2 | no | — |
| 74 | C5×#121 | — | 2 | 4 | no | — |
| 75 | C5×#121 | — | 2 | 4 | no | — |
| 76 | C5×#121 | — | 2 | 1 | no | — |
| 77 | C5×#121 | — | 2 | 1 | no | — |
| 78 | C5×#121 | — | 2 | 1 | no | — |
| 79 | C5×#121 | — | 2 | 1 | no | — |
| 80 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 81 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 82 | C4×C5×D4 | — | 2 | 2 | no | — |
| 83 | C4×C5×D4 | — | 2 | 2 | no | — |
| 84 | C4×C5×D4 | — | 2 | 1 | no | — |
| 85 | C4×C5×D4 | — | 2 | 1 | no | — |
| 86 | C4×C5×D4 | — | 2 | 1 | no | — |
| 87 | C4×C5×D4 | — | 2 | 1 | no | — |
| 88 | C5×#117 | D4 | 1 | 2 | yes | — |
| 89 | C2×C5×C4⋊C4 | — | 2 | 2 | no | — |
| 90 | C2×C5×C4⋊C4 | — | 2 | 2 | no | — |
| 91 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 92 | #4096 | — | 4 | 8 | no | — |
| 93 | C2×#689 | — | 2 | 2 | no | — |
| 94 | C2×#688 | — | 2 | 2 | no | — |
| 95 | C2×#688 | — | 2 | 2 | no | — |
| 96 | C2×#687 | — | 2 | 2 | no | — |
| 97 | C2×#686 | — | 2 | 2 | no | — |
| 98 | C2×#686 | — | 2 | 2 | no | — |
| 99 | #4076 | — | 2 | 1 | no | — |
| 100 | #4076 | — | 2 | 1 | no | — |
| 101 | C22×#168 | — | 2 | 1 | no | — |
| 102 | #4021 | — | 2 | 1 | no | — |
| 103 | #4020 | C23 | 1 | 1 | yes | characteristic |
| 104 | C4×D20 | — | 2 | 1 | no | — |
| 105 | C4×D20 | — | 2 | 1 | no | — |
| 106 | #4015 | C23 | 1 | 1 | yes | characteristic |
| 107 | #3967 | — | 2 | 2 | no | — |
| 108 | #3964 | — | 2 | 2 | no | — |
| 109 | C22⋊#168 | — | 2 | 1 | no | — |
| 110 | C22⋊#168 | — | 2 | 1 | no | — |
| 111 | #3941 | — | 2 | 2 | no | — |
| 112 | #3941 | — | 2 | 2 | no | — |
| 113 | #3940 | — | 2 | 2 | no | — |
| 114 | #3939 | — | 2 | 2 | no | — |
| 115 | C4⋊#168 | — | 2 | 1 | no | — |
| 116 | C4⋊#168 | — | 2 | 1 | no | — |
| 117 | #3935 | — | 2 | 1 | no | — |
| 118 | #3935 | C23 | 1 | 2 | yes | — |
| 119 | #3935 | C23 | 1 | 2 | yes | — |
| 120 | #3935 | C23 | 1 | 2 | yes | — |
| 121 | #3548 | D5 | 1 | 1 | yes | characteristic, complemented |
| 122 | #3235 | — | 5 | 1 | no | — |
| 123 | #3214 | — | 5 | 1 | no | — |
| 124 | #3150 | — | 5 | 1 | no | — |
| 125 | #1661 | — | 5 | 4 | no | — |
| 126 | #1656 | — | 5 | 4 | no | — |
| 127 | #1536 | — | 5 | 1 | no | — |
| 128 | #1531 | — | 5 | 1 | no | — |
| 129 | #1530 | — | 5 | 1 | no | — |
| 130 | C5×#41 | — | 4 | 4 | no | — |
| 131 | C5×#41 | — | 8 | 2 | no | — |
| 132 | C5×#41 | — | 8 | 4 | no | — |
| 133 | C5×#41 | — | 8 | 4 | no | — |
| 134 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 135 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 136 | C2×C5×Q8 | C2×D4 | 1 | 2 | yes | — |
| 137 | C2×C5×Q8 | C2×D4 | 1 | 2 | yes | — |
| 138 | C2×C5×D4 | — | 2 | 4 | no | — |
| 139 | C2×C5×D4 | — | 2 | 4 | no | — |
| 140 | C2×C5×D4 | — | 2 | 2 | no | — |
| 141 | C2×C5×D4 | — | 2 | 2 | no | — |
| 142 | C2×C5×D4 | — | 2 | 1 | no | — |
| 143 | C2×C5×D4 | — | 2 | 1 | no | — |
| 144 | C2×C5×D4 | — | 2 | 1 | no | — |
| 145 | C2×C5×D4 | — | 2 | 1 | no | — |
| 146 | C2×C5×D4 | C2×D4 | 1 | 2 | yes | — |
| 147 | C2×C5×D4 | C2×D4 | 1 | 2 | yes | — |
| 148 | C22×C4×C5 | — | 2 | 4 | no | — |
| 149 | C22×C4×C5 | — | 2 | 4 | no | — |
| 150 | C22×C4×C5 | — | 2 | 2 | no | — |
| 151 | C22×C4×C5 | — | 2 | 2 | no | — |
| 152 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×C22⋊D5 | — | 4 | 1 | no | — |
| 156 | #709 | — | 4 | 4 | no | — |
| 157 | C2×D20 | — | 2 | 1 | no | — |
| 158 | C2×D20 | — | 2 | 1 | no | — |
| 159 | C2×D20 | — | 2 | 1 | no | — |
| 160 | C2×C4×D5 | — | 4 | 1 | no | — |
| 161 | C2×Dic10 | — | 2 | 1 | no | — |
| 162 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 163 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 164 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 165 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 166 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 167 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 168 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 169 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 170 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 171 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 172 | C5×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 173 | C5×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 174 | C5×C22⋊C4 | — | 2 | 4 | no | — |
| 175 | C5×C22⋊C4 | — | 2 | 4 | no | — |
| 176 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 177 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 178 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 179 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 180 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 181 | C42×C5 | — | 2 | 2 | no | — |
| 182 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 186 | #689 | — | 4 | 4 | no | — |
| 187 | #688 | — | 4 | 4 | no | — |
| 188 | #688 | — | 8 | 2 | no | — |
| 189 | #687 | — | 4 | 4 | no | — |
| 190 | #686 | — | 4 | 4 | no | — |
| 191 | #686 | — | 8 | 2 | no | — |
| 192 | #685 | — | 4 | 1 | no | — |
| 193 | #685 | — | 4 | 1 | no | — |
| 194 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 195 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 196 | C2×#168 | — | 2 | 4 | no | — |
| 197 | C2×#168 | — | 2 | 2 | no | — |
| 198 | C2×#168 | — | 2 | 2 | no | — |
| 199 | C2×#168 | — | 2 | 2 | no | — |
| 200 | C2×#135 | — | 10 | 2 | no | — |
| 201 | #562 | C2×D5 | 1 | 4 | yes | — |
| 202 | #554 | — | 2 | 1 | no | — |
| 203 | #554 | — | 2 | 1 | no | — |
| 204 | #550 | — | 2 | 1 | no | — |
| 205 | #550 | — | 2 | 1 | no | — |
| 206 | #547 | — | 2 | 1 | no | — |
| 207 | #547 | — | 2 | 1 | no | — |
| 208 | #540 | — | 2 | 2 | no | — |
| 209 | #537 | — | 2 | 2 | no | — |
| 210 | #537 | — | 2 | 2 | no | — |
| 211 | #533 | C2×D5 | 1 | 1 | yes | characteristic |
| 212 | #532 | — | 5 | 1 | no | — |
| 213 | #532 | C2×D5 | 1 | 1 | yes | characteristic |
| 214 | #532 | C2×D5 | 1 | 1 | yes | characteristic |
| 215 | #501 | — | 5 | 2 | no | — |
| 216 | #497 | — | 5 | 2 | no | — |
| 217 | #497 | — | 10 | 1 | no | — |
| 218 | #496 | — | 5 | 2 | no | — |
| 219 | #496 | — | 5 | 2 | no | — |
| 220 | #496 | — | 10 | 1 | no | — |
| 221 | #490 | — | 5 | 2 | no | — |
| 222 | #489 | — | 5 | 2 | no | — |
| 223 | #482 | — | 10 | 2 | no | — |
| 224 | #476 | — | 10 | 1 | no | — |
| 225 | #474 | — | 10 | 1 | no | — |
| 226 | #461 | — | 10 | 1 | no | — |
| 227 | #459 | — | 10 | 1 | no | — |
| 228 | #449 | — | 10 | 2 | no | — |
| 229 | #432 | — | 5 | 1 | no | — |
| 230 | #432 | — | 5 | 1 | no | — |
| 231 | C2×#97 | — | 5 | 1 | no | — |
| 232 | #330 | — | 5 | 4 | no | — |
| 233 | #329 | — | 5 | 4 | no | — |
| 234 | #329 | — | 5 | 4 | no | — |
| 235 | C23×C5 | — | 2 | 2 | no | — |
| 236 | C23×C5 | — | 2 | 2 | no | — |
| 237 | C23×C5 | #120 | 1 | 1 | yes | characteristic |
| 238 | C22×D5 | — | 4 | 1 | no | — |
| 239 | C5×Q8 | — | 4 | 2 | no | — |
| 240 | C5×Q8 | — | 4 | 2 | no | — |
| 241 | C5×Q8 | — | 4 | 2 | no | — |
| 242 | C5×Q8 | — | 4 | 2 | no | — |
| 243 | C5×D4 | — | 4 | 2 | no | — |
| 244 | C5×D4 | — | 4 | 2 | no | — |
| 245 | C5×D4 | — | 4 | 2 | no | — |
| 246 | C5×D4 | — | 4 | 2 | no | — |
| 247 | C5×D4 | — | 4 | 2 | no | — |
| 248 | C5×D4 | — | 4 | 2 | no | — |
| 249 | C5×D4 | — | 8 | 2 | no | — |
| 250 | C5×D4 | — | 8 | 2 | no | — |
| 251 | C5×D4 | — | 8 | 4 | no | — |
| 252 | C5×D4 | — | 8 | 4 | no | — |
| 253 | C2×C4×C5 | — | 2 | 2 | no | — |
| 254 | C2×C4×C5 | — | 2 | 2 | no | — |
| 255 | C2×C4×C5 | — | 2 | 2 | no | — |
| 256 | C2×C4×C5 | — | 2 | 2 | no | — |
| 257 | C2×C4×C5 | — | 2 | 2 | no | — |
| 258 | C2×C4×C5 | — | 4 | 1 | no | — |
| 259 | C2×C4×C5 | — | 4 | 1 | no | — |
| 260 | C2×C4×C5 | — | 4 | 4 | no | — |
| 261 | C2×C4×C5 | — | 4 | 4 | no | — |
| 262 | C2×C4×C5 | — | 8 | 4 | no | — |
| 263 | C2×C4×C5 | — | 8 | 4 | no | — |
| 264 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 265 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 266 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 267 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 268 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 269 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 270 | C22⋊D5 | — | 8 | 2 | no | — |
| 271 | C2×Dic5 | — | 4 | 1 | no | — |
| 272 | D20 | — | 4 | 2 | no | — |
| 273 | D20 | — | 4 | 1 | no | — |
| 274 | D20 | — | 4 | 1 | no | — |
| 275 | D20 | — | 4 | 2 | no | — |
| 276 | C4×D5 | — | 8 | 2 | no | — |
| 277 | Dic10 | — | 4 | 2 | no | — |
| 278 | #168 | — | 2 | 4 | no | — |
| 279 | #168 | — | 4 | 2 | no | — |
| 280 | #168 | — | 4 | 2 | no | — |
| 281 | C2×#41 | — | 2 | 2 | no | — |
| 282 | C2×#41 | — | 2 | 2 | no | — |
| 283 | C2×#41 | — | 10 | 1 | no | — |
| 284 | C2×#41 | C22⋊D5 | 1 | 2 | yes | — |
| 285 | C2×#41 | C22⋊D5 | 1 | 2 | yes | — |
| 286 | #135 | — | 20 | 8 | no | — |
| 287 | C2×Q16 | — | 10 | 2 | no | — |
| 288 | C2×SD16 | — | 10 | 2 | no | — |
| 289 | C2×SD16 | — | 10 | 2 | no | — |
| 290 | C2×SD16 | — | 10 | 2 | no | — |
| 291 | C2×D8 | — | 10 | 2 | no | — |
| 292 | C2×D8 | — | 10 | 2 | no | — |
| 293 | C22×C8 | — | 10 | 1 | no | — |
| 294 | C4⋊Q8 | — | 5 | 1 | no | — |
| 295 | C4⋊Q8 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 296 | C4⋊Q8 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 297 | C4⋊Q8 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 298 | C4⋊Q8 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 299 | #127 | — | 2 | 2 | no | — |
| 300 | #127 | — | 5 | 1 | no | — |
| 301 | #127 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 302 | #127 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 303 | #125 | — | 2 | 2 | no | — |
| 304 | #125 | C22×D5 | 1 | 2 | yes | — |
| 305 | #124 | — | 10 | 1 | no | — |
| 306 | #124 | C22×D5 | 1 | 2 | yes | — |
| 307 | #124 | C22×D5 | 1 | 2 | yes | — |
| 308 | #123 | — | 2 | 4 | no | — |
| 309 | #123 | — | 2 | 4 | no | — |
| 310 | C22⋊Q8 | — | 2 | 2 | no | — |
| 311 | C22⋊Q8 | — | 2 | 2 | no | — |
| 312 | C22⋊Q8 | — | 2 | 4 | no | — |
| 313 | C22⋊Q8 | — | 2 | 4 | no | — |
| 314 | C22⋊Q8 | — | 2 | 1 | no | — |
| 315 | C22⋊Q8 | — | 2 | 1 | no | — |
| 316 | #121 | — | 2 | 4 | no | — |
| 317 | #121 | — | 2 | 4 | no | — |
| 318 | #121 | — | 2 | 2 | no | — |
| 319 | #121 | — | 2 | 2 | no | — |
| 320 | #121 | — | 2 | 4 | no | — |
| 321 | #121 | — | 2 | 4 | no | — |
| 322 | #121 | — | 2 | 1 | no | — |
| 323 | #121 | — | 2 | 1 | no | — |
| 324 | #121 | — | 2 | 1 | no | — |
| 325 | #121 | — | 2 | 1 | no | — |
| 326 | #121 | — | 10 | 1 | no | — |
| 327 | #121 | — | 10 | 1 | no | — |
| 328 | C4×Q8 | — | 2 | 1 | no | — |
| 329 | C4×Q8 | — | 2 | 1 | no | — |
| 330 | C4×D4 | — | 2 | 2 | no | — |
| 331 | C4×D4 | — | 2 | 2 | no | — |
| 332 | C4×D4 | — | 2 | 1 | no | — |
| 333 | C4×D4 | — | 2 | 1 | no | — |
| 334 | C4×D4 | — | 2 | 1 | no | — |
| 335 | C4×D4 | — | 2 | 1 | no | — |
| 336 | C4×D4 | — | 10 | 1 | no | — |
| 337 | C4×D4 | — | 10 | 1 | no | — |
| 338 | #117 | C22⋊D5 | 1 | 2 | yes | — |
| 339 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 340 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 341 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 342 | #107 | — | 10 | 2 | no | — |
| 343 | #106 | — | 10 | 2 | no | — |
| 344 | C4⋊C8 | — | 10 | 1 | no | — |
| 345 | C4⋊C8 | — | 10 | 1 | no | — |
| 346 | #103 | — | 10 | 2 | no | — |
| 347 | #102 | — | 10 | 2 | no | — |
| 348 | #102 | — | 10 | 2 | no | — |
| 349 | #102 | — | 10 | 2 | no | — |
| 350 | C22⋊C8 | — | 10 | 1 | no | — |
| 351 | C22⋊C8 | — | 10 | 1 | no | — |
| 352 | #97 | — | 5 | 2 | no | — |
| 353 | #97 | — | 5 | 2 | no | — |
| 354 | #97 | — | 5 | 2 | no | — |
| 355 | #97 | — | 10 | 1 | no | — |
| 356 | C22×C5 | — | 2 | 1 | no | — |
| 357 | C22×C5 | — | 2 | 1 | no | — |
| 358 | C22×C5 | — | 2 | 1 | no | — |
| 359 | C22×C5 | — | 4 | 2 | no | — |
| 360 | C22×C5 | — | 4 | 2 | no | — |
| 361 | C22×C5 | — | 4 | 2 | no | — |
| 362 | C22×C5 | — | 4 | 2 | no | — |
| 363 | C22×C5 | — | 4 | 2 | no | — |
| 364 | C22×C5 | — | 4 | 2 | no | — |
| 365 | C22×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 366 | C2×D5 | — | 8 | 1 | no | — |
| 367 | C2×D5 | — | 8 | 1 | no | — |
| 368 | C2×D5 | — | 8 | 1 | no | — |
| 369 | C4×C5 | — | 2 | 1 | no | — |
| 370 | C4×C5 | — | 2 | 1 | no | — |
| 371 | C4×C5 | — | 2 | 1 | no | — |
| 372 | C4×C5 | — | 2 | 1 | no | — |
| 373 | C4×C5 | — | 2 | 1 | no | — |
| 374 | C4×C5 | — | 4 | 2 | no | — |
| 375 | C4×C5 | — | 4 | 2 | no | — |
| 376 | C4×C5 | — | 4 | 2 | no | — |
| 377 | C4×C5 | — | 4 | 2 | no | — |
| 378 | C4×C5 | #453 | 1 | 2 | yes | — |
| 379 | Dic5 | — | 8 | 1 | no | — |
| 380 | #41 | — | 4 | 4 | no | — |
| 381 | #41 | — | 8 | 2 | no | — |
| 382 | #41 | — | 8 | 4 | no | — |
| 383 | #41 | — | 8 | 4 | no | — |
| 384 | #41 | — | 20 | 4 | no | — |
| 385 | C2×Q8 | — | 2 | 1 | no | — |
| 386 | C2×Q8 | — | 2 | 1 | no | — |
| 387 | C2×Q8 | — | 10 | 1 | no | — |
| 388 | C2×Q8 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 389 | C2×Q8 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 390 | C2×D4 | — | 2 | 4 | no | — |
| 391 | C2×D4 | — | 2 | 4 | no | — |
| 392 | C2×D4 | — | 2 | 2 | no | — |
| 393 | C2×D4 | — | 2 | 2 | no | — |
| 394 | C2×D4 | — | 2 | 1 | no | — |
| 395 | C2×D4 | — | 2 | 1 | no | — |
| 396 | C2×D4 | — | 2 | 1 | no | — |
| 397 | C2×D4 | — | 2 | 1 | no | — |
| 398 | C2×D4 | — | 10 | 1 | no | — |
| 399 | C2×D4 | — | 10 | 1 | no | — |
| 400 | C2×D4 | — | 10 | 1 | no | — |
| 401 | C2×D4 | — | 20 | 1 | no | — |
| 402 | C2×D4 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 403 | C2×D4 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 404 | C22×C4 | — | 2 | 4 | no | — |
| 405 | C22×C4 | — | 2 | 4 | no | — |
| 406 | C22×C4 | — | 2 | 2 | no | — |
| 407 | C22×C4 | — | 2 | 2 | no | — |
| 408 | C22×C4 | — | 20 | 1 | no | — |
| 409 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 410 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 411 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 412 | Q16 | — | 20 | 4 | no | — |
| 413 | SD16 | — | 20 | 4 | no | — |
| 414 | SD16 | — | 20 | 4 | no | — |
| 415 | SD16 | — | 40 | 2 | no | — |
| 416 | D8 | — | 20 | 4 | no | — |
| 417 | D8 | — | 40 | 2 | no | — |
| 418 | C2×C8 | — | 10 | 4 | no | — |
| 419 | C2×C8 | — | 10 | 2 | no | — |
| 420 | C2×C8 | — | 10 | 2 | no | — |
| 421 | C2×C8 | — | 10 | 2 | no | — |
| 422 | C4⋊C4 | — | 2 | 4 | no | — |
| 423 | C4⋊C4 | — | 2 | 4 | no | — |
| 424 | C4⋊C4 | — | 2 | 1 | no | — |
| 425 | C4⋊C4 | — | 2 | 1 | no | — |
| 426 | C4⋊C4 | — | 2 | 1 | no | — |
| 427 | C4⋊C4 | — | 2 | 1 | no | — |
| 428 | C4⋊C4 | — | 2 | 1 | no | — |
| 429 | C4⋊C4 | — | 2 | 1 | no | — |
| 430 | C4⋊C4 | — | 2 | 2 | no | — |
| 431 | C4⋊C4 | — | 2 | 2 | no | — |
| 432 | C4⋊C4 | — | 10 | 1 | no | — |
| 433 | C4⋊C4 | — | 10 | 1 | no | — |
| 434 | C4⋊C4 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 435 | C4⋊C4 | C2×C22⋊D5 | 1 | 2 | yes | — |
| 436 | C22⋊C4 | — | 2 | 4 | no | — |
| 437 | C22⋊C4 | — | 2 | 4 | no | — |
| 438 | C22⋊C4 | — | 2 | 2 | no | — |
| 439 | C22⋊C4 | — | 2 | 2 | no | — |
| 440 | C22⋊C4 | — | 2 | 2 | no | — |
| 441 | C22⋊C4 | — | 2 | 2 | no | — |
| 442 | C22⋊C4 | — | 2 | 2 | no | — |
| 443 | C22⋊C4 | — | 20 | 1 | no | — |
| 444 | C22⋊C4 | — | 20 | 1 | no | — |
| 445 | C42 | — | 2 | 2 | no | — |
| 446 | C42 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 447 | C42 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 448 | C42 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 449 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 450 | C2×C5 | — | 4 | 1 | no | — |
| 451 | C2×C5 | — | 8 | 2 | no | — |
| 452 | C2×C5 | — | 8 | 2 | no | — |
| 453 | C2×C5 | C2×#453 | 1 | 1 | yes | characteristic |
| 454 | C2×C5 | #3019 | 1 | 1 | yes | characteristic |
| 455 | C2×C5 | #3020 | 1 | 1 | yes | characteristic |
| 456 | D5 | — | 16 | 1 | no | — |
| 457 | C23 | — | 2 | 2 | no | — |
| 458 | C23 | — | 2 | 2 | no | — |
| 459 | C23 | — | 20 | 1 | no | — |
| 460 | C23 | #4099 | 1 | 1 | yes | characteristic |
| 461 | Q8 | — | 4 | 2 | no | — |
| 462 | Q8 | — | 4 | 2 | no | — |
| 463 | Q8 | — | 4 | 2 | no | — |
| 464 | Q8 | — | 4 | 2 | no | — |
| 465 | Q8 | — | 20 | 2 | no | — |
| 466 | D4 | — | 4 | 2 | no | — |
| 467 | D4 | — | 4 | 2 | no | — |
| 468 | D4 | — | 4 | 2 | no | — |
| 469 | D4 | — | 4 | 2 | no | — |
| 470 | D4 | — | 4 | 2 | no | — |
| 471 | D4 | — | 4 | 2 | no | — |
| 472 | D4 | — | 8 | 2 | no | — |
| 473 | D4 | — | 8 | 2 | no | — |
| 474 | D4 | — | 8 | 4 | no | — |
| 475 | D4 | — | 8 | 4 | no | — |
| 476 | D4 | — | 20 | 2 | no | — |
| 477 | D4 | — | 20 | 1 | no | — |
| 478 | D4 | — | 20 | 1 | no | — |
| 479 | D4 | — | 20 | 2 | no | — |
| 480 | D4 | — | 40 | 2 | no | — |
| 481 | C2×C4 | — | 2 | 2 | no | — |
| 482 | C2×C4 | — | 2 | 2 | no | — |
| 483 | C2×C4 | — | 2 | 2 | no | — |
| 484 | C2×C4 | — | 2 | 2 | no | — |
| 485 | C2×C4 | — | 2 | 2 | no | — |
| 486 | C2×C4 | — | 4 | 1 | no | — |
| 487 | C2×C4 | — | 4 | 1 | no | — |
| 488 | C2×C4 | — | 4 | 4 | no | — |
| 489 | C2×C4 | — | 4 | 4 | no | — |
| 490 | C2×C4 | — | 8 | 4 | no | — |
| 491 | C2×C4 | — | 8 | 4 | no | — |
| 492 | C2×C4 | — | 20 | 1 | no | — |
| 493 | C2×C4 | — | 40 | 2 | no | — |
| 494 | C2×C4 | #4099 | 1 | 1 | yes | characteristic |
| 495 | C2×C4 | #4099 | 1 | 1 | yes | characteristic |
| 496 | C2×C4 | #4099 | 1 | 1 | yes | characteristic |
| 497 | C2×C4 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 498 | C2×C4 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 499 | C2×C4 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 500 | C8 | — | 10 | 4 | no | — |
| 501 | C8 | — | 20 | 2 | no | — |
| 502 | C8 | — | 20 | 2 | no | — |
| 503 | C5 | #19053 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 504 | C22 | — | 2 | 1 | no | — |
| 505 | C22 | — | 2 | 1 | no | — |
| 506 | C22 | — | 2 | 1 | no | — |
| 507 | C22 | — | 4 | 2 | no | — |
| 508 | C22 | — | 4 | 2 | no | — |
| 509 | C22 | — | 4 | 2 | no | — |
| 510 | C22 | — | 4 | 2 | no | — |
| 511 | C22 | — | 4 | 2 | no | — |
| 512 | C22 | — | 4 | 2 | no | — |
| 513 | C22 | — | 40 | 1 | no | — |
| 514 | C22 | — | 40 | 1 | no | — |
| 515 | C22 | — | 40 | 1 | no | — |
| 516 | C22 | C2×#4099 | 1 | 1 | yes | characteristic |
| 517 | C4 | — | 2 | 1 | no | — |
| 518 | C4 | — | 2 | 1 | no | — |
| 519 | C4 | — | 2 | 1 | no | — |
| 520 | C4 | — | 2 | 1 | no | — |
| 521 | C4 | — | 2 | 1 | no | — |
| 522 | C4 | — | 4 | 2 | no | — |
| 523 | C4 | — | 4 | 2 | no | — |
| 524 | C4 | — | 4 | 2 | no | — |
| 525 | C4 | — | 4 | 2 | no | — |
| 526 | C4 | — | 40 | 1 | no | — |
| 527 | C4 | #65530 | 1 | 2 | yes | — |
| 528 | C2 | — | 4 | 1 | no | — |
| 529 | C2 | — | 8 | 2 | no | — |
| 530 | C2 | — | 8 | 2 | no | — |
| 531 | C2 | — | 80 | 1 | no | — |
| 532 | C2 | C2×#65530 | 1 | 1 | yes | characteristic |
| 533 | C2 | #10615835 | 1 | 1 | yes | characteristic |
| 534 | C2 | #10615847 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#4099 |
| commutator, cosocle | C42×C5 | C24 |
| Frattini | C42 | C23×D5 |
| Fitting | C5×#3548 | C2 |
| socle | C22×C5 | C2×#120 |
| hypercenter | #3548 | D5 |
| hypocenter | C5 | #19053 |
| LCS | G ▷ C42×C5 ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #3548 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3548 | C2 | semidirect |
| 2. #10615092 | C2 | semidirect |
| 3. #10615038 | C2 | semidirect |
| 4. #10615017 | C2 | semidirect |
| 5. #10602746 | C2 | semidirect |
| 6. #10602745 | C2 | semidirect |
| 7. #10602615 | C2 | semidirect |
| 8. #10602592 | C2 | semidirect |
| 9. #10602591 | C2 | semidirect |
| 121. #3548 | D5 | semidirect |
| 503. C5 | #19053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3548 | 2 |
| #10615092 | 2 |
| #10615038 | 2 |
| #10615017 | 2 |
| #10602746 | 2 |
| #10602745 | 2 |
| #10602615 | 2 |
| #10602592 | 2 |
| #10602591 | 2 |
| #19053 | 5 |