Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1116 conjugacy classes of subgroups.
The subgroup lattice has 554 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10618106 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×#2862 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10614940 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10614934 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10602583 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10600487 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10600486 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10600188 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C4×#3937 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×C5×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C5×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 12 | #66151 | — | 2 | 2 | no | — |
| 13 | C2×#4088 | C22 | 1 | 4 | yes | — |
| 14 | C2×#4088 | C22 | 1 | 2 | yes | — |
| 15 | #66068 | — | 2 | 1 | no | — |
| 16 | #66067 | — | 2 | 2 | no | — |
| 17 | #66066 | — | 2 | 1 | no | — |
| 18 | #66064 | — | 2 | 1 | no | — |
| 19 | #66062 | — | 2 | 1 | no | — |
| 20 | #66060 | — | 2 | 1 | no | — |
| 21 | #66059 | — | 2 | 1 | no | — |
| 22 | #65848 | — | 2 | 2 | no | — |
| 23 | #65844 | C22 | 1 | 2 | yes | — |
| 24 | #65838 | C22 | 1 | 2 | yes | — |
| 25 | #65811 | C22 | 1 | 1 | yes | characteristic |
| 26 | C4×#709 | C22 | 1 | 1 | yes | characteristic |
| 27 | C5×#391 | — | 2 | 2 | no | — |
| 28 | C5×#391 | C22 | 1 | 4 | yes | — |
| 29 | C5×#382 | — | 2 | 2 | no | — |
| 30 | C43×C5 | C22 | 1 | 1 | yes | characteristic |
| 31 | #65514 | C22 | 1 | 2 | yes | — |
| 32 | #65381 | — | 2 | 1 | no | — |
| 33 | #65379 | — | 2 | 1 | no | — |
| 34 | #65379 | — | 2 | 1 | no | — |
| 35 | #65375 | — | 2 | 2 | no | — |
| 36 | #65374 | — | 2 | 1 | no | — |
| 37 | #65372 | — | 2 | 1 | no | — |
| 38 | #65372 | — | 2 | 1 | no | — |
| 39 | C2×#3937 | C22 | 1 | 2 | yes | — |
| 40 | C2×#3937 | C22 | 1 | 4 | yes | — |
| 41 | #65213 | C22 | 1 | 1 | yes | characteristic |
| 42 | C4×#681 | C22 | 1 | 1 | yes | characteristic |
| 43 | #64750 | C22 | 1 | 4 | yes | — |
| 44 | #64743 | C22 | 1 | 2 | yes | — |
| 45 | #25615 | — | 5 | 1 | no | maximal, Sylow |
| 46 | C22×C5×Q8 | D4 | 1 | 2 | yes | — |
| 47 | C22×C5×Q8 | C23 | 1 | 2 | yes | — |
| 48 | C2×#713 | — | 2 | 2 | no | — |
| 49 | C2×#709 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×#709 | C23 | 1 | 2 | yes | — |
| 51 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 52 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 53 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 54 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 55 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 56 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 57 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 58 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 59 | C2×C5×C4⋊C4 | — | 2 | 1 | no | — |
| 60 | C2×C5×C4⋊C4 | — | 2 | 1 | no | — |
| 61 | C2×C5×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 62 | C2×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 63 | C2×C42×C5 | — | 2 | 1 | no | — |
| 64 | C2×C42×C5 | — | 2 | 1 | no | — |
| 65 | C2×C42×C5 | C23 | 1 | 2 | yes | — |
| 66 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 67 | #4093 | — | 2 | 2 | no | — |
| 68 | #4093 | — | 2 | 4 | no | — |
| 69 | #4092 | — | 2 | 2 | no | — |
| 70 | #4092 | — | 2 | 4 | no | — |
| 71 | Q8×Dic5 | — | 2 | 2 | no | — |
| 72 | C2×#689 | — | 2 | 4 | no | — |
| 73 | C2×#689 | — | 2 | 2 | no | — |
| 74 | #4088 | — | 2 | 8 | no | — |
| 75 | #4088 | — | 4 | 4 | no | — |
| 76 | #4088 | — | 4 | 4 | no | — |
| 77 | C2×#688 | — | 2 | 2 | no | — |
| 78 | C2×#688 | — | 2 | 4 | no | — |
| 79 | #4076 | — | 2 | 1 | no | — |
| 80 | #4076 | — | 2 | 1 | no | — |
| 81 | #4076 | — | 2 | 4 | no | — |
| 82 | C4×C22⋊D5 | — | 2 | 1 | no | — |
| 83 | C4×C22⋊D5 | — | 2 | 1 | no | — |
| 84 | C4×C22⋊D5 | — | 2 | 4 | no | — |
| 85 | #4072 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×#681 | C23 | 1 | 2 | yes | — |
| 87 | C2×#681 | C23 | 1 | 2 | yes | — |
| 88 | #4044 | — | 2 | 4 | no | — |
| 89 | #4043 | — | 2 | 2 | no | — |
| 90 | #4043 | — | 2 | 2 | no | — |
| 91 | #4041 | — | 2 | 2 | no | — |
| 92 | #4041 | — | 2 | 2 | no | — |
| 93 | #4041 | — | 2 | 2 | no | — |
| 94 | #4040 | — | 2 | 4 | no | — |
| 95 | #4039 | — | 2 | 2 | no | — |
| 96 | #4039 | — | 2 | 2 | no | — |
| 97 | #4038 | — | 2 | 2 | no | — |
| 98 | #4038 | — | 2 | 2 | no | — |
| 99 | D5×C4⋊C4 | — | 2 | 2 | no | — |
| 100 | #4036 | — | 2 | 2 | no | — |
| 101 | #4033 | — | 2 | 2 | no | — |
| 102 | #4021 | D4 | 1 | 2 | yes | — |
| 103 | #4020 | D4 | 1 | 1 | yes | characteristic |
| 104 | C4×D20 | — | 2 | 1 | no | — |
| 105 | C4×D20 | — | 2 | 1 | no | — |
| 106 | C4×D20 | D4 | 1 | 1 | yes | characteristic |
| 107 | C4×D20 | D4 | 1 | 1 | yes | characteristic |
| 108 | #4018 | — | 2 | 1 | no | — |
| 109 | C42×D5 | — | 2 | 1 | no | — |
| 110 | #4015 | D4 | 1 | 1 | yes | characteristic |
| 111 | C4×Dic10 | D4 | 1 | 1 | yes | characteristic |
| 112 | C4×Dic10 | D4 | 1 | 1 | yes | characteristic |
| 113 | C5×#95 | — | 2 | 8 | no | — |
| 114 | #3967 | — | 2 | 2 | no | — |
| 115 | #3967 | — | 2 | 2 | no | — |
| 116 | #3937 | — | 2 | 4 | no | — |
| 117 | #3937 | — | 4 | 4 | no | — |
| 118 | C4⋊#168 | — | 2 | 1 | no | — |
| 119 | C4⋊#168 | — | 2 | 1 | no | — |
| 120 | #3935 | — | 2 | 1 | no | — |
| 121 | C4×#168 | — | 2 | 1 | no | — |
| 122 | #3511 | — | 5 | 1 | no | — |
| 123 | #3152 | — | 5 | 1 | no | — |
| 124 | #3039 | — | 5 | 1 | no | — |
| 125 | #2862 | D5 | 1 | 1 | yes | characteristic, complemented |
| 126 | #2007 | — | 5 | 4 | no | — |
| 127 | #1997 | — | 5 | 1 | no | — |
| 128 | #1962 | — | 5 | 1 | no | — |
| 129 | #1882 | — | 5 | 4 | no | — |
| 130 | C4×#104 | — | 5 | 1 | no | — |
| 131 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 132 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 133 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 134 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 135 | C2×C5×Q8 | — | 2 | 4 | no | — |
| 136 | C2×C5×Q8 | — | 2 | 4 | no | — |
| 137 | C2×C5×Q8 | — | 4 | 4 | no | — |
| 138 | C22×C4×C5 | — | 2 | 2 | no | — |
| 139 | C22×C4×C5 | — | 2 | 2 | no | — |
| 140 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C22×C4×C5 | C2×D4 | 1 | 4 | yes | — |
| 143 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 144 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 145 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 146 | #713 | — | 8 | 4 | no | — |
| 147 | #709 | — | 2 | 2 | no | — |
| 148 | #709 | — | 2 | 4 | no | — |
| 149 | #709 | — | 2 | 4 | no | — |
| 150 | #709 | — | 2 | 2 | no | — |
| 151 | C2×D20 | — | 2 | 1 | no | — |
| 152 | C2×D20 | — | 2 | 1 | no | — |
| 153 | C2×D20 | — | 2 | 4 | no | — |
| 154 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×D20 | C2×D4 | 1 | 2 | yes | — |
| 156 | C2×C4×D5 | — | 2 | 1 | no | — |
| 157 | C2×C4×D5 | — | 2 | 1 | no | — |
| 158 | C2×C4×D5 | — | 2 | 1 | no | — |
| 159 | C2×C4×D5 | — | 2 | 2 | no | — |
| 160 | C2×C4×D5 | — | 2 | 4 | no | — |
| 161 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×Dic10 | C2×D4 | 1 | 2 | yes | — |
| 163 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 164 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 165 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 166 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 167 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 168 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 169 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 170 | C5×C4⋊C4 | — | 4 | 1 | no | — |
| 171 | C42×C5 | — | 2 | 4 | no | — |
| 172 | C42×C5 | — | 2 | 2 | no | — |
| 173 | C42×C5 | — | 2 | 2 | no | — |
| 174 | C42×C5 | — | 4 | 2 | no | — |
| 175 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 180 | #689 | — | 4 | 8 | no | — |
| 181 | #689 | — | 4 | 4 | no | — |
| 182 | #688 | — | 4 | 8 | no | — |
| 183 | #688 | — | 4 | 4 | no | — |
| 184 | #685 | — | 2 | 4 | no | — |
| 185 | #685 | — | 2 | 4 | no | — |
| 186 | #685 | — | 2 | 4 | no | — |
| 187 | #685 | — | 2 | 1 | no | — |
| 188 | #685 | — | 2 | 1 | no | — |
| 189 | #685 | — | 2 | 2 | no | — |
| 190 | #685 | — | 2 | 2 | no | — |
| 191 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 192 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 193 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 194 | C4⋊Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C4⋊Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 196 | #683 | — | 2 | 4 | no | — |
| 197 | #683 | — | 2 | 1 | no | — |
| 198 | #683 | — | 2 | 1 | no | — |
| 199 | C4×Dic5 | — | 2 | 4 | no | — |
| 200 | C4×Dic5 | — | 2 | 1 | no | — |
| 201 | C4×Dic5 | — | 2 | 1 | no | — |
| 202 | C4×Dic5 | — | 2 | 1 | no | — |
| 203 | #681 | — | 2 | 2 | no | — |
| 204 | #681 | — | 2 | 4 | no | — |
| 205 | #681 | #41 | 1 | 4 | yes | complemented |
| 206 | C2×#168 | — | 2 | 2 | no | — |
| 207 | C2×#168 | — | 2 | 2 | no | — |
| 208 | C2×#137 | — | 5 | 4 | no | — |
| 209 | C2×#137 | — | 5 | 2 | no | — |
| 210 | #556 | — | 10 | 1 | no | — |
| 211 | #555 | — | 10 | 1 | no | — |
| 212 | #554 | — | 10 | 1 | no | — |
| 213 | #553 | — | 10 | 2 | no | — |
| 214 | #548 | — | 10 | 2 | no | — |
| 215 | #547 | — | 10 | 1 | no | — |
| 216 | #542 | — | 10 | 2 | no | — |
| 217 | #537 | — | 5 | 2 | no | — |
| 218 | #533 | — | 10 | 1 | no | — |
| 219 | #532 | — | 5 | 1 | no | — |
| 220 | #532 | — | 10 | 1 | no | — |
| 221 | C2×C4⋊Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 222 | C2×C4⋊Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 223 | #520 | — | 5 | 2 | no | — |
| 224 | C4×#41 | — | 5 | 1 | no | — |
| 225 | #497 | — | 10 | 2 | no | — |
| 226 | #494 | — | 10 | 1 | no | — |
| 227 | #492 | — | 10 | 1 | no | — |
| 228 | #462 | — | 10 | 1 | no | — |
| 229 | #462 | — | 10 | 1 | no | — |
| 230 | #461 | — | 10 | 1 | no | — |
| 231 | #461 | — | 10 | 1 | no | — |
| 232 | #423 | — | 5 | 1 | no | — |
| 233 | C2×#104 | — | 5 | 2 | no | — |
| 234 | C2×#104 | — | 5 | 4 | no | — |
| 235 | #419 | — | 5 | 2 | no | — |
| 236 | C4×M16 | — | 5 | 1 | no | — |
| 237 | #391 | — | 2 | 2 | no | — |
| 238 | #391 | C2×D5 | 1 | 4 | yes | — |
| 239 | #382 | — | 2 | 2 | no | — |
| 240 | C43 | C2×D5 | 1 | 1 | yes | characteristic |
| 241 | #343 | — | 5 | 4 | no | — |
| 242 | #339 | — | 5 | 2 | no | — |
| 243 | C23×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 244 | C22×D5 | — | 2 | 1 | no | — |
| 245 | C22×D5 | — | 2 | 2 | no | — |
| 246 | C5×Q8 | — | 4 | 4 | no | — |
| 247 | C5×Q8 | — | 4 | 2 | no | — |
| 248 | C5×Q8 | — | 4 | 2 | no | — |
| 249 | C5×Q8 | — | 4 | 4 | no | — |
| 250 | C5×Q8 | — | 8 | 2 | no | — |
| 251 | C2×C4×C5 | — | 2 | 2 | no | — |
| 252 | C2×C4×C5 | — | 2 | 2 | no | — |
| 253 | C2×C4×C5 | — | 2 | 4 | no | — |
| 254 | C2×C4×C5 | — | 2 | 4 | no | — |
| 255 | C2×C4×C5 | — | 4 | 2 | no | — |
| 256 | C2×C4×C5 | — | 4 | 2 | no | — |
| 257 | C2×C4×C5 | — | 4 | 4 | no | — |
| 258 | C2×C4×C5 | — | 4 | 2 | no | — |
| 259 | C2×C4×C5 | — | 4 | 4 | no | — |
| 260 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 261 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 262 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 263 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 264 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 265 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 266 | C2×C4×C5 | C2×#41 | 1 | 2 | yes | — |
| 267 | C2×C4×C5 | H(5,𝔽2) | 1 | 2 | yes | — |
| 268 | C22⋊D5 | — | 4 | 2 | no | — |
| 269 | C22⋊D5 | — | 4 | 4 | no | — |
| 270 | C2×Dic5 | — | 2 | 1 | no | — |
| 271 | C2×Dic5 | — | 2 | 1 | no | — |
| 272 | C2×Dic5 | — | 2 | 2 | no | — |
| 273 | C2×Dic5 | — | 2 | 1 | no | — |
| 274 | D20 | — | 2 | 1 | no | — |
| 275 | D20 | — | 2 | 1 | no | — |
| 276 | D20 | — | 2 | 4 | no | — |
| 277 | D20 | — | 4 | 2 | no | — |
| 278 | D20 | — | 4 | 2 | no | — |
| 279 | D20 | — | 8 | 4 | no | — |
| 280 | C4×D5 | — | 4 | 2 | no | — |
| 281 | C4×D5 | — | 4 | 2 | no | — |
| 282 | C4×D5 | — | 4 | 2 | no | — |
| 283 | C4×D5 | — | 4 | 2 | no | — |
| 284 | C4×D5 | — | 4 | 2 | no | — |
| 285 | C4×D5 | — | 8 | 4 | no | — |
| 286 | Dic10 | — | 2 | 1 | no | — |
| 287 | Dic10 | — | 2 | 1 | no | — |
| 288 | Dic10 | — | 2 | 4 | no | — |
| 289 | #168 | — | 2 | 4 | no | — |
| 290 | #168 | — | 4 | 2 | no | — |
| 291 | C2×#41 | — | 5 | 1 | no | — |
| 292 | C2×#41 | — | 5 | 2 | no | — |
| 293 | C2×#41 | — | 10 | 2 | no | — |
| 294 | C22×Q8 | C22⋊D5 | 1 | 2 | yes | — |
| 295 | C22×Q8 | C22×D5 | 1 | 2 | yes | — |
| 296 | #137 | — | 10 | 8 | no | — |
| 297 | #137 | — | 20 | 4 | no | — |
| 298 | #137 | — | 20 | 4 | no | — |
| 299 | C2×Q16 | — | 10 | 2 | no | — |
| 300 | C2×Q16 | — | 10 | 4 | no | — |
| 301 | C2×SD16 | — | 10 | 2 | no | — |
| 302 | C2×SD16 | — | 10 | 4 | no | — |
| 303 | C2×M16 | — | 5 | 2 | no | — |
| 304 | C2×M16 | — | 5 | 2 | no | — |
| 305 | C4⋊Q8 | — | 2 | 1 | no | — |
| 306 | C4⋊Q8 | — | 2 | 1 | no | — |
| 307 | C4⋊Q8 | — | 2 | 1 | no | — |
| 308 | C4⋊Q8 | — | 2 | 1 | no | — |
| 309 | C4⋊Q8 | — | 2 | 1 | no | — |
| 310 | C4⋊Q8 | — | 2 | 1 | no | — |
| 311 | C4⋊Q8 | — | 2 | 1 | no | — |
| 312 | C4⋊Q8 | — | 2 | 1 | no | — |
| 313 | C4⋊Q8 | — | 5 | 1 | no | — |
| 314 | #127 | — | 5 | 1 | no | — |
| 315 | #126 | — | 10 | 4 | no | — |
| 316 | #125 | — | 10 | 2 | no | — |
| 317 | #124 | — | 5 | 2 | no | — |
| 318 | #124 | — | 10 | 2 | no | — |
| 319 | #124 | — | 10 | 4 | no | — |
| 320 | #123 | — | 10 | 4 | no | — |
| 321 | C22⋊Q8 | — | 10 | 2 | no | — |
| 322 | C22⋊Q8 | — | 10 | 2 | no | — |
| 323 | C22⋊Q8 | — | 10 | 2 | no | — |
| 324 | C22⋊Q8 | — | 10 | 4 | no | — |
| 325 | #121 | — | 10 | 2 | no | — |
| 326 | #121 | — | 10 | 2 | no | — |
| 327 | #121 | — | 10 | 2 | no | — |
| 328 | #121 | — | 10 | 1 | no | — |
| 329 | #121 | — | 10 | 1 | no | — |
| 330 | #121 | — | 10 | 4 | no | — |
| 331 | C4×Q8 | — | 5 | 1 | no | — |
| 332 | C4×Q8 | — | 5 | 1 | no | — |
| 333 | C4×Q8 | — | 10 | 2 | no | — |
| 334 | C4×Q8 | — | 10 | 2 | no | — |
| 335 | C4×D4 | — | 5 | 1 | no | — |
| 336 | C4×D4 | — | 5 | 1 | no | — |
| 337 | C4×D4 | — | 10 | 2 | no | — |
| 338 | C4×D4 | — | 10 | 2 | no | — |
| 339 | C4×D4 | — | 10 | 1 | no | — |
| 340 | C4×D4 | — | 10 | 1 | no | — |
| 341 | C4×D4 | — | 10 | 4 | no | — |
| 342 | C4×D4 | — | 10 | 1 | no | — |
| 343 | C4×D4 | — | 10 | 1 | no | — |
| 344 | #117 | — | 5 | 1 | no | — |
| 345 | #117 | — | 10 | 2 | no | — |
| 346 | #117 | — | 10 | 2 | no | — |
| 347 | #117 | — | 10 | 1 | no | — |
| 348 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 349 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 350 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 351 | C2×C4⋊C4 | C22⋊D5 | 1 | 2 | yes | — |
| 352 | C2×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 353 | C2×C42 | — | 2 | 1 | no | — |
| 354 | C2×C42 | — | 2 | 1 | no | — |
| 355 | C2×C42 | — | 10 | 1 | no | — |
| 356 | C2×C42 | C22×D5 | 1 | 2 | yes | — |
| 357 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 358 | C4⋊C8 | — | 10 | 1 | no | — |
| 359 | C4⋊C8 | — | 10 | 1 | no | — |
| 360 | #104 | — | 10 | 4 | no | — |
| 361 | #104 | — | 20 | 4 | no | — |
| 362 | #103 | — | 10 | 2 | no | — |
| 363 | #103 | — | 10 | 2 | no | — |
| 364 | #97 | — | 10 | 1 | no | — |
| 365 | C4×C8 | — | 10 | 1 | no | — |
| 366 | #95 | — | 2 | 8 | no | — |
| 367 | C22×C5 | — | 2 | 1 | no | — |
| 368 | C22×C5 | — | 2 | 1 | no | — |
| 369 | C22×C5 | C2×#120 | 1 | 1 | yes | characteristic |
| 370 | C22×C5 | #550 | 1 | 2 | yes | — |
| 371 | C2×D5 | — | 4 | 2 | no | — |
| 372 | C2×D5 | — | 4 | 1 | no | — |
| 373 | C2×D5 | — | 4 | 1 | no | — |
| 374 | C2×D5 | — | 4 | 2 | no | — |
| 375 | C2×D5 | — | 4 | 1 | no | — |
| 376 | C2×D5 | — | 4 | 2 | no | — |
| 377 | C4×C5 | — | 2 | 1 | no | — |
| 378 | C4×C5 | — | 2 | 1 | no | — |
| 379 | C4×C5 | — | 4 | 4 | no | — |
| 380 | C4×C5 | — | 4 | 4 | no | — |
| 381 | C4×C5 | — | 8 | 2 | no | — |
| 382 | C4×C5 | #455 | 1 | 2 | yes | — |
| 383 | C4×C5 | #456 | 1 | 2 | yes | — |
| 384 | C4×C5 | #532 | 1 | 1 | yes | characteristic |
| 385 | C4×C5 | #535 | 1 | 1 | yes | characteristic |
| 386 | C4×C5 | #546 | 1 | 2 | yes | — |
| 387 | Dic5 | — | 4 | 1 | no | — |
| 388 | Dic5 | — | 4 | 2 | no | — |
| 389 | Dic5 | — | 4 | 1 | no | — |
| 390 | Dic5 | — | 4 | 1 | no | — |
| 391 | #41 | — | 10 | 2 | no | — |
| 392 | #41 | — | 10 | 4 | no | — |
| 393 | #41 | — | 10 | 4 | no | — |
| 394 | #41 | — | 10 | 2 | no | — |
| 395 | #41 | — | 40 | 4 | no | — |
| 396 | C2×Q8 | — | 2 | 2 | no | — |
| 397 | C2×Q8 | — | 2 | 2 | no | — |
| 398 | C2×Q8 | — | 2 | 2 | no | — |
| 399 | C2×Q8 | — | 2 | 2 | no | — |
| 400 | C2×Q8 | — | 2 | 4 | no | — |
| 401 | C2×Q8 | — | 2 | 4 | no | — |
| 402 | C2×Q8 | — | 4 | 4 | no | — |
| 403 | C2×Q8 | — | 5 | 1 | no | — |
| 404 | C2×Q8 | — | 5 | 2 | no | — |
| 405 | C2×D4 | — | 5 | 1 | no | — |
| 406 | C2×D4 | — | 5 | 2 | no | — |
| 407 | C2×D4 | — | 10 | 4 | no | — |
| 408 | C2×D4 | — | 10 | 1 | no | — |
| 409 | C2×D4 | — | 10 | 2 | no | — |
| 410 | C2×D4 | — | 10 | 1 | no | — |
| 411 | C2×D4 | — | 10 | 1 | no | — |
| 412 | C22×C4 | — | 2 | 2 | no | — |
| 413 | C22×C4 | — | 2 | 2 | no | — |
| 414 | C22×C4 | — | 10 | 4 | no | — |
| 415 | C22×C4 | — | 10 | 1 | no | — |
| 416 | C22×C4 | — | 10 | 2 | no | — |
| 417 | C22×C4 | — | 10 | 1 | no | — |
| 418 | C22×C4 | — | 10 | 1 | no | — |
| 419 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 420 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 421 | C22×C4 | C2×C22⋊D5 | 1 | 4 | yes | — |
| 422 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 423 | Q16 | — | 20 | 8 | no | — |
| 424 | Q16 | — | 20 | 4 | no | — |
| 425 | SD16 | — | 20 | 8 | no | — |
| 426 | SD16 | — | 20 | 4 | no | — |
| 427 | M16 | — | 5 | 4 | no | — |
| 428 | M16 | — | 10 | 2 | no | — |
| 429 | M16 | — | 10 | 4 | no | — |
| 430 | C2×C8 | — | 10 | 2 | no | — |
| 431 | C2×C8 | — | 10 | 2 | no | — |
| 432 | C4⋊C4 | — | 2 | 2 | no | — |
| 433 | C4⋊C4 | — | 2 | 2 | no | — |
| 434 | C4⋊C4 | — | 2 | 2 | no | — |
| 435 | C4⋊C4 | — | 2 | 2 | no | — |
| 436 | C4⋊C4 | — | 4 | 1 | no | — |
| 437 | C4⋊C4 | — | 4 | 1 | no | — |
| 438 | C4⋊C4 | — | 4 | 1 | no | — |
| 439 | C4⋊C4 | — | 4 | 1 | no | — |
| 440 | C4⋊C4 | — | 5 | 1 | no | — |
| 441 | C4⋊C4 | — | 5 | 1 | no | — |
| 442 | C4⋊C4 | — | 10 | 4 | no | — |
| 443 | C4⋊C4 | — | 10 | 4 | no | — |
| 444 | C4⋊C4 | — | 10 | 1 | no | — |
| 445 | C4⋊C4 | — | 10 | 1 | no | — |
| 446 | C4⋊C4 | — | 10 | 1 | no | — |
| 447 | C4⋊C4 | — | 10 | 1 | no | — |
| 448 | C22⋊C4 | — | 10 | 4 | no | — |
| 449 | C22⋊C4 | — | 10 | 4 | no | — |
| 450 | C22⋊C4 | — | 10 | 4 | no | — |
| 451 | C22⋊C4 | — | 10 | 1 | no | — |
| 452 | C22⋊C4 | — | 10 | 1 | no | — |
| 453 | C22⋊C4 | — | 10 | 1 | no | — |
| 454 | C22⋊C4 | — | 10 | 2 | no | — |
| 455 | C22⋊C4 | — | 10 | 2 | no | — |
| 456 | C42 | — | 2 | 4 | no | — |
| 457 | C42 | — | 2 | 2 | no | — |
| 458 | C42 | — | 2 | 2 | no | — |
| 459 | C42 | — | 4 | 2 | no | — |
| 460 | C42 | — | 10 | 4 | no | — |
| 461 | C42 | — | 10 | 1 | no | — |
| 462 | C42 | — | 10 | 1 | no | — |
| 463 | C42 | — | 10 | 1 | no | — |
| 464 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 465 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 466 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 467 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 468 | C2×C5 | — | 2 | 2 | no | — |
| 469 | C2×C5 | #2431 | 1 | 1 | yes | characteristic |
| 470 | C2×C5 | C2×#455 | 1 | 1 | yes | characteristic |
| 471 | C2×C5 | C2×#456 | 1 | 1 | yes | characteristic |
| 472 | D5 | — | 8 | 1 | no | — |
| 473 | D5 | — | 8 | 2 | no | — |
| 474 | C23 | — | 10 | 1 | no | — |
| 475 | C23 | — | 10 | 2 | no | — |
| 476 | C23 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 477 | Q8 | — | 4 | 4 | no | — |
| 478 | Q8 | — | 4 | 2 | no | — |
| 479 | Q8 | — | 4 | 2 | no | — |
| 480 | Q8 | — | 4 | 4 | no | — |
| 481 | Q8 | — | 8 | 2 | no | — |
| 482 | Q8 | — | 10 | 1 | no | — |
| 483 | Q8 | — | 10 | 1 | no | — |
| 484 | Q8 | — | 10 | 4 | no | — |
| 485 | D4 | — | 10 | 1 | no | — |
| 486 | D4 | — | 10 | 1 | no | — |
| 487 | D4 | — | 10 | 4 | no | — |
| 488 | D4 | — | 20 | 2 | no | — |
| 489 | D4 | — | 20 | 4 | no | — |
| 490 | D4 | — | 20 | 2 | no | — |
| 491 | D4 | — | 20 | 2 | no | — |
| 492 | D4 | — | 40 | 4 | no | — |
| 493 | C2×C4 | — | 2 | 2 | no | — |
| 494 | C2×C4 | — | 2 | 2 | no | — |
| 495 | C2×C4 | — | 2 | 4 | no | — |
| 496 | C2×C4 | — | 2 | 4 | no | — |
| 497 | C2×C4 | — | 4 | 2 | no | — |
| 498 | C2×C4 | — | 4 | 2 | no | — |
| 499 | C2×C4 | — | 4 | 4 | no | — |
| 500 | C2×C4 | — | 4 | 2 | no | — |
| 501 | C2×C4 | — | 4 | 4 | no | — |
| 502 | C2×C4 | — | 10 | 1 | no | — |
| 503 | C2×C4 | — | 10 | 2 | no | — |
| 504 | C2×C4 | — | 10 | 1 | no | — |
| 505 | C2×C4 | — | 10 | 1 | no | — |
| 506 | C2×C4 | — | 20 | 2 | no | — |
| 507 | C2×C4 | — | 20 | 2 | no | — |
| 508 | C2×C4 | — | 20 | 2 | no | — |
| 509 | C2×C4 | — | 20 | 2 | no | — |
| 510 | C2×C4 | — | 20 | 2 | no | — |
| 511 | C2×C4 | — | 40 | 4 | no | — |
| 512 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 513 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 514 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 515 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 516 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 517 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 518 | C2×C4 | D5×#41 | 1 | 2 | yes | — |
| 519 | C2×C4 | #4149 | 1 | 2 | yes | — |
| 520 | C8 | — | 10 | 4 | no | — |
| 521 | C8 | — | 20 | 2 | no | — |
| 522 | C5 | #25615 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 523 | C22 | — | 2 | 1 | no | — |
| 524 | C22 | — | 2 | 1 | no | — |
| 525 | C22 | — | 20 | 1 | no | — |
| 526 | C22 | — | 20 | 2 | no | — |
| 527 | C22 | — | 20 | 2 | no | — |
| 528 | C22 | — | 20 | 1 | no | — |
| 529 | C22 | — | 20 | 1 | no | — |
| 530 | C22 | — | 20 | 2 | no | — |
| 531 | C22 | C2×#4083 | 1 | 1 | yes | characteristic |
| 532 | C22 | #66168 | 1 | 2 | yes | — |
| 533 | C4 | — | 2 | 1 | no | — |
| 534 | C4 | — | 2 | 1 | no | — |
| 535 | C4 | — | 4 | 4 | no | — |
| 536 | C4 | — | 4 | 4 | no | — |
| 537 | C4 | — | 8 | 2 | no | — |
| 538 | C4 | — | 20 | 1 | no | — |
| 539 | C4 | — | 20 | 2 | no | — |
| 540 | C4 | — | 20 | 1 | no | — |
| 541 | C4 | — | 20 | 1 | no | — |
| 542 | C4 | #65350 | 1 | 2 | yes | — |
| 543 | C4 | #65384 | 1 | 2 | yes | — |
| 544 | C4 | #66002 | 1 | 1 | yes | characteristic |
| 545 | C4 | #66008 | 1 | 1 | yes | characteristic |
| 546 | C4 | #66010 | 1 | 2 | yes | — |
| 547 | C2 | — | 2 | 2 | no | — |
| 548 | C2 | — | 40 | 1 | no | — |
| 549 | C2 | — | 40 | 2 | no | — |
| 550 | C2 | C2×#65350 | 1 | 1 | yes | characteristic |
| 551 | C2 | #10614689 | 1 | 1 | yes | characteristic |
| 552 | C2 | C2×#65384 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2862 | C2 | semidirect |
| 3. #10614940 | C2 | semidirect |
| 4. #10614934 | C2 | semidirect |
| 5. #10602583 | C2 | semidirect |
| 6. #10600487 | C2 | semidirect |
| 7. #10600486 | C2 | semidirect |
| 8. #10600188 | C2 | semidirect |
| 9. C4×#3937 | C2 | semidirect |
| 125. #2862 | D5 | semidirect |
| 205. #681 | #41 | semidirect |
| 522. C5 | #25615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10618106 | 2 |
| C5×#2862 | 2 |
| #10614940 | 2 |
| #10614934 | 2 |
| #10602583 | 2 |
| #10600487 | 2 |
| #10600486 | 2 |
| #10600188 | 2 |
| C4×#3937 | 2 |
| #25615 | 5 |