Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1886 conjugacy classes of subgroups.
The subgroup lattice has 692 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 | #10618105 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C5×#487 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10614938 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10614934 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10613327 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10613326 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10613325 | C2 | 1 | 8 | yes | maximal, complemented |
| 9 | #10613324 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10613323 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10610531 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #10610505 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #10610194 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C4×#4047 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C2×C5×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C5×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 17 | #66151 | — | 2 | 2 | no | — |
| 18 | #66150 | C22 | 1 | 2 | yes | — |
| 19 | #66146 | C22 | 1 | 2 | yes | — |
| 20 | C2×#4088 | C22 | 1 | 4 | yes | — |
| 21 | C2×#4047 | C22 | 1 | 2 | yes | — |
| 22 | #66068 | — | 2 | 1 | no | — |
| 23 | #66067 | C22 | 1 | 4 | yes | — |
| 24 | #66066 | — | 2 | 1 | no | — |
| 25 | #66066 | — | 2 | 1 | no | — |
| 26 | #66066 | — | 2 | 1 | no | — |
| 27 | #66065 | C22 | 1 | 4 | yes | — |
| 28 | #66064 | — | 2 | 1 | no | — |
| 29 | #66062 | C22 | 1 | 2 | yes | — |
| 30 | #66062 | C22 | 1 | 2 | yes | — |
| 31 | #66062 | C22 | 1 | 2 | yes | — |
| 32 | #66060 | — | 2 | 1 | no | — |
| 33 | #66059 | C22 | 1 | 2 | yes | — |
| 34 | #66055 | — | 2 | 1 | no | — |
| 35 | #66055 | — | 2 | 1 | no | — |
| 36 | #65848 | — | 2 | 2 | no | — |
| 37 | #65847 | — | 2 | 2 | no | — |
| 38 | #65847 | — | 2 | 2 | no | — |
| 39 | #65844 | C22 | 1 | 2 | yes | — |
| 40 | #65838 | C22 | 1 | 2 | yes | — |
| 41 | #65811 | C22 | 1 | 1 | yes | characteristic |
| 42 | C4×#709 | C22 | 1 | 1 | yes | characteristic |
| 43 | #65804 | C22 | 1 | 1 | yes | characteristic |
| 44 | C5×#487 | C22 | 1 | 2 | yes | — |
| 45 | C5×#487 | C22 | 1 | 4 | yes | — |
| 46 | C5×#487 | C22 | 1 | 2 | yes | — |
| 47 | C2×C5×#103 | C22 | 1 | 4 | yes | — |
| 48 | C2×C4×C5×C8 | C22 | 1 | 1 | yes | characteristic |
| 49 | #65402 | C22 | 1 | 4 | yes | — |
| 50 | #65390 | C22 | 1 | 2 | yes | — |
| 51 | #65381 | C22 | 1 | 2 | yes | — |
| 52 | #65375 | C22 | 1 | 4 | yes | — |
| 53 | #65374 | C22 | 1 | 2 | yes | — |
| 54 | #65369 | C22 | 1 | 4 | yes | — |
| 55 | #65368 | C22 | 1 | 2 | yes | — |
| 56 | #65367 | C22 | 1 | 2 | yes | — |
| 57 | #65253 | C22 | 1 | 4 | yes | — |
| 58 | C4×#681 | C22 | 1 | 1 | yes | characteristic |
| 59 | #65106 | C22 | 1 | 8 | yes | — |
| 60 | #65105 | C22 | 1 | 8 | yes | — |
| 61 | #65102 | C22 | 1 | 8 | yes | — |
| 62 | #65101 | C22 | 1 | 8 | yes | — |
| 63 | #65096 | C22 | 1 | 8 | yes | — |
| 64 | #65079 | C22 | 1 | 8 | yes | — |
| 65 | #65078 | C22 | 1 | 8 | yes | — |
| 66 | #65077 | C22 | 1 | 8 | yes | — |
| 67 | #64986 | C22 | 1 | 4 | yes | — |
| 68 | #64983 | C22 | 1 | 1 | yes | characteristic |
| 69 | #64983 | C22 | 1 | 1 | yes | characteristic |
| 70 | #64978 | C22 | 1 | 4 | yes | — |
| 71 | C4×#676 | C22 | 1 | 2 | yes | — |
| 72 | C4×C8×D5 | C22 | 1 | 2 | yes | — |
| 73 | #64970 | C22 | 1 | 1 | yes | characteristic |
| 74 | #64970 | C22 | 1 | 1 | yes | characteristic |
| 75 | #60723 | — | 5 | 1 | no | maximal, Sylow |
| 76 | C22×C5×Q8 | — | 2 | 1 | no | — |
| 77 | C22×C5×Q8 | C23 | 1 | 2 | yes | — |
| 78 | C2×#713 | — | 2 | 2 | no | — |
| 79 | C2×#709 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×#709 | C23 | 1 | 2 | yes | — |
| 81 | C22×C5×C8 | C23 | 1 | 2 | yes | — |
| 82 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 83 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 84 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 85 | C5×C4⋊Q8 | — | 2 | 1 | no | — |
| 86 | C5×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 87 | C5×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 88 | C5×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 89 | C5×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 90 | C2×C5×C4⋊C4 | — | 2 | 1 | no | — |
| 91 | C2×C5×C4⋊C4 | — | 2 | 1 | no | — |
| 92 | C2×C5×C4⋊C4 | — | 2 | 1 | no | — |
| 93 | C2×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 94 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 95 | #4093 | — | 2 | 2 | no | — |
| 96 | #4093 | — | 2 | 4 | no | — |
| 97 | #4093 | — | 2 | 2 | no | — |
| 98 | #4092 | — | 2 | 2 | no | — |
| 99 | #4092 | — | 2 | 4 | no | — |
| 100 | #4092 | C23 | 1 | 4 | yes | — |
| 101 | #4092 | C23 | 1 | 4 | yes | — |
| 102 | Q8×Dic5 | — | 2 | 2 | no | — |
| 103 | Q8×Dic5 | — | 2 | 2 | no | — |
| 104 | Q8×Dic5 | — | 2 | 2 | no | — |
| 105 | Q8×Dic5 | C23 | 1 | 4 | yes | — |
| 106 | Q8×Dic5 | C23 | 1 | 4 | yes | — |
| 107 | #4090 | — | 2 | 2 | no | — |
| 108 | C2×#689 | C23 | 1 | 8 | yes | — |
| 109 | #4088 | — | 2 | 16 | no | — |
| 110 | C2×#688 | C23 | 1 | 8 | yes | — |
| 111 | #4076 | — | 2 | 1 | no | — |
| 112 | #4076 | — | 2 | 1 | no | — |
| 113 | #4076 | — | 2 | 4 | no | — |
| 114 | #4075 | — | 2 | 4 | no | — |
| 115 | C4×C22⋊D5 | — | 2 | 4 | no | — |
| 116 | C4×C22⋊D5 | D4 | 1 | 2 | yes | — |
| 117 | C4×C22⋊D5 | D4 | 1 | 2 | yes | — |
| 118 | #4072 | — | 2 | 4 | no | — |
| 119 | #4072 | C23 | 1 | 2 | yes | — |
| 120 | #4072 | C23 | 1 | 1 | yes | characteristic |
| 121 | #4070 | — | 2 | 1 | no | — |
| 122 | #4070 | — | 2 | 1 | no | — |
| 123 | C2×#681 | C23 | 1 | 2 | yes | — |
| 124 | #4047 | — | 2 | 8 | no | — |
| 125 | C2×#676 | C23 | 1 | 4 | yes | — |
| 126 | C2×C8×D5 | C23 | 1 | 4 | yes | — |
| 127 | #4044 | — | 2 | 4 | no | — |
| 128 | #4044 | — | 2 | 4 | no | — |
| 129 | #4044 | — | 2 | 4 | no | — |
| 130 | #4043 | — | 2 | 2 | no | — |
| 131 | #4043 | — | 2 | 2 | no | — |
| 132 | #4043 | — | 2 | 2 | no | — |
| 133 | #4043 | C23 | 1 | 4 | yes | — |
| 134 | #4041 | — | 2 | 2 | no | — |
| 135 | #4041 | — | 2 | 2 | no | — |
| 136 | #4041 | C23 | 1 | 4 | yes | — |
| 137 | #4040 | — | 2 | 4 | no | — |
| 138 | #4039 | — | 2 | 2 | no | — |
| 139 | #4039 | C23 | 1 | 4 | yes | — |
| 140 | #4038 | — | 2 | 2 | no | — |
| 141 | #4038 | — | 2 | 2 | no | — |
| 142 | #4038 | — | 2 | 2 | no | — |
| 143 | #4038 | — | 2 | 2 | no | — |
| 144 | D5×C4⋊C4 | — | 2 | 2 | no | — |
| 145 | #4036 | — | 2 | 2 | no | — |
| 146 | #4036 | — | 2 | 2 | no | — |
| 147 | #4036 | — | 2 | 2 | no | — |
| 148 | #4035 | — | 2 | 4 | no | — |
| 149 | #4035 | — | 2 | 4 | no | — |
| 150 | #4033 | — | 2 | 2 | no | — |
| 151 | #4033 | — | 2 | 2 | no | — |
| 152 | #4033 | C23 | 1 | 4 | yes | — |
| 153 | #4021 | C23 | 1 | 2 | yes | — |
| 154 | #4020 | C23 | 1 | 1 | yes | characteristic |
| 155 | C4×D20 | — | 2 | 1 | no | — |
| 156 | C4×D20 | — | 2 | 1 | no | — |
| 157 | C4×D20 | D4 | 1 | 1 | yes | characteristic |
| 158 | C4×D20 | D4 | 1 | 1 | yes | characteristic |
| 159 | #4018 | C23 | 1 | 2 | yes | — |
| 160 | C42×D5 | C23 | 1 | 2 | yes | — |
| 161 | #4016 | C23 | 1 | 2 | yes | — |
| 162 | #4015 | C23 | 1 | 1 | yes | characteristic |
| 163 | #4015 | C23 | 1 | 1 | yes | characteristic |
| 164 | #4015 | C23 | 1 | 1 | yes | characteristic |
| 165 | C4×Dic10 | — | 2 | 1 | no | — |
| 166 | C4×Dic10 | — | 2 | 1 | no | — |
| 167 | C4×Dic10 | D4 | 1 | 1 | yes | characteristic |
| 168 | C4×Dic10 | D4 | 1 | 1 | yes | characteristic |
| 169 | C5×#103 | C23 | 1 | 8 | yes | — |
| 170 | C5×#103 | C23 | 1 | 8 | yes | — |
| 171 | C4×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 172 | C4×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 173 | C4×C5×C8 | C23 | 1 | 2 | yes | — |
| 174 | #3953 | C23 | 1 | 4 | yes | — |
| 175 | #3953 | C23 | 1 | 4 | yes | — |
| 176 | #3948 | C23 | 1 | 4 | yes | — |
| 177 | #3948 | C23 | 1 | 4 | yes | — |
| 178 | #3947 | C23 | 1 | 4 | yes | — |
| 179 | C8×Dic5 | C23 | 1 | 4 | yes | — |
| 180 | #3940 | C23 | 1 | 8 | yes | — |
| 181 | #3939 | C23 | 1 | 8 | yes | — |
| 182 | #3935 | C23 | 1 | 2 | yes | — |
| 183 | C4×#168 | C23 | 1 | 2 | yes | — |
| 184 | #3511 | — | 5 | 1 | no | — |
| 185 | #3509 | — | 5 | 1 | no | — |
| 186 | #3185 | — | 5 | 2 | no | — |
| 187 | #3182 | — | 5 | 2 | no | — |
| 188 | #3178 | — | 5 | 8 | no | — |
| 189 | #3170 | — | 5 | 2 | no | — |
| 190 | #3167 | — | 5 | 2 | no | — |
| 191 | #3165 | — | 5 | 1 | no | — |
| 192 | #3152 | — | 5 | 1 | no | — |
| 193 | #3131 | — | 5 | 1 | no | — |
| 194 | C2×#487 | D5 | 1 | 1 | yes | characteristic, complemented |
| 195 | #3063 | — | 5 | 4 | no | — |
| 196 | #2947 | — | 5 | 4 | no | — |
| 197 | C4×#131 | — | 5 | 1 | no | — |
| 198 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 199 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 200 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 201 | C2×C5×Q8 | — | 2 | 8 | no | — |
| 202 | C2×C5×Q8 | — | 8 | 2 | no | — |
| 203 | C2×C5×Q8 | C24 | 1 | 4 | yes | — |
| 204 | C22×C4×C5 | — | 2 | 2 | no | — |
| 205 | C22×C4×C5 | — | 2 | 2 | no | — |
| 206 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 209 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 210 | C2×C22⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 211 | #713 | — | 8 | 4 | no | — |
| 212 | #709 | — | 2 | 4 | no | — |
| 213 | #709 | — | 2 | 8 | no | — |
| 214 | C2×D20 | — | 2 | 1 | no | — |
| 215 | C2×D20 | — | 2 | 1 | no | — |
| 216 | C2×D20 | — | 2 | 4 | no | — |
| 217 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 218 | C2×D20 | C24 | 1 | 2 | yes | — |
| 219 | C2×C4×D5 | — | 2 | 2 | no | — |
| 220 | C2×C4×D5 | — | 2 | 4 | no | — |
| 221 | C2×C4×D5 | C2×D4 | 1 | 2 | yes | — |
| 222 | C2×C4×D5 | C2×D4 | 1 | 2 | yes | — |
| 223 | C2×C4×D5 | C24 | 1 | 2 | yes | — |
| 224 | C2×Dic10 | — | 2 | 1 | no | — |
| 225 | C2×Dic10 | — | 2 | 1 | no | — |
| 226 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | C2×Dic10 | C24 | 1 | 2 | yes | — |
| 228 | C2×C5×C8 | — | 2 | 4 | no | — |
| 229 | C2×C5×C8 | C24 | 1 | 2 | yes | — |
| 230 | C2×C5×C8 | C24 | 1 | 2 | yes | — |
| 231 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 232 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 233 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 234 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 235 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 236 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 237 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 238 | C5×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 239 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 240 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 242 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 243 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 244 | C22⋊Dic5 | C2×D4 | 1 | 2 | yes | — |
| 245 | #689 | — | 2 | 16 | no | — |
| 246 | #688 | — | 2 | 16 | no | — |
| 247 | #685 | — | 2 | 4 | no | — |
| 248 | #685 | — | 2 | 4 | no | — |
| 249 | #685 | — | 2 | 4 | no | — |
| 250 | #685 | — | 2 | 2 | no | — |
| 251 | #685 | — | 2 | 2 | no | — |
| 252 | #685 | — | 2 | 4 | no | — |
| 253 | #685 | — | 2 | 4 | no | — |
| 254 | #685 | C2×D4 | 1 | 2 | yes | — |
| 255 | #685 | C2×D4 | 1 | 2 | yes | — |
| 256 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 257 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 258 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 259 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 260 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 261 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 262 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 263 | C4⋊Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 264 | C4⋊Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 265 | C4⋊Dic5 | C24 | 1 | 2 | yes | — |
| 266 | C4⋊Dic5 | C24 | 1 | 2 | yes | — |
| 267 | #683 | — | 2 | 2 | no | — |
| 268 | #683 | — | 2 | 2 | no | — |
| 269 | #683 | — | 2 | 4 | no | — |
| 270 | #683 | — | 2 | 4 | no | — |
| 271 | #683 | — | 2 | 4 | no | — |
| 272 | #683 | C2×D4 | 1 | 2 | yes | — |
| 273 | #683 | C2×D4 | 1 | 2 | yes | — |
| 274 | C4×Dic5 | — | 2 | 2 | no | — |
| 275 | C4×Dic5 | — | 2 | 4 | no | — |
| 276 | C4×Dic5 | — | 2 | 4 | no | — |
| 277 | C4×Dic5 | — | 2 | 4 | no | — |
| 278 | C4×Dic5 | C2×D4 | 1 | 2 | yes | — |
| 279 | C4×Dic5 | C2×D4 | 1 | 2 | yes | — |
| 280 | C4×Dic5 | C24 | 1 | 2 | yes | — |
| 281 | #681 | #41 | 1 | 8 | yes | complemented |
| 282 | C2×#168 | C24 | 1 | 4 | yes | — |
| 283 | #676 | — | 2 | 8 | no | — |
| 284 | C8×D5 | — | 2 | 8 | no | — |
| 285 | C2×#137 | — | 5 | 4 | no | — |
| 286 | C2×#131 | — | 5 | 2 | no | — |
| 287 | #557 | — | 10 | 1 | no | — |
| 288 | #557 | — | 10 | 1 | no | — |
| 289 | #556 | — | 10 | 1 | no | — |
| 290 | #556 | — | 10 | 1 | no | — |
| 291 | #556 | — | 10 | 1 | no | — |
| 292 | #555 | — | 10 | 1 | no | — |
| 293 | #554 | — | 10 | 1 | no | — |
| 294 | #553 | — | 10 | 2 | no | — |
| 295 | #552 | — | 10 | 2 | no | — |
| 296 | #552 | — | 10 | 2 | no | — |
| 297 | #548 | — | 10 | 2 | no | — |
| 298 | #547 | — | 10 | 1 | no | — |
| 299 | #542 | — | 5 | 4 | no | — |
| 300 | #541 | — | 5 | 4 | no | — |
| 301 | #537 | — | 5 | 2 | no | — |
| 302 | #536 | — | 5 | 2 | no | — |
| 303 | #533 | — | 5 | 2 | no | — |
| 304 | #533 | — | 5 | 2 | no | — |
| 305 | #533 | — | 5 | 2 | no | — |
| 306 | #533 | — | 5 | 1 | no | — |
| 307 | #532 | — | 5 | 2 | no | — |
| 308 | #532 | — | 5 | 1 | no | — |
| 309 | C2×C4⋊Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 310 | C2×C4⋊Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 311 | #520 | — | 5 | 2 | no | — |
| 312 | #519 | — | 5 | 2 | no | — |
| 313 | C4×#41 | — | 5 | 1 | no | — |
| 314 | #501 | — | 5 | 4 | no | — |
| 315 | #500 | — | 5 | 2 | no | — |
| 316 | #498 | — | 5 | 2 | no | — |
| 317 | #497 | — | 5 | 4 | no | — |
| 318 | #494 | — | 5 | 2 | no | — |
| 319 | #492 | — | 5 | 2 | no | — |
| 320 | #488 | — | 5 | 4 | no | — |
| 321 | #487 | — | 5 | 1 | no | — |
| 322 | #487 | — | 5 | 1 | no | — |
| 323 | #487 | C2×D5 | 1 | 2 | yes | — |
| 324 | #487 | C2×D5 | 1 | 4 | yes | — |
| 325 | #487 | C2×D5 | 1 | 2 | yes | — |
| 326 | #486 | — | 5 | 1 | no | — |
| 327 | #486 | — | 5 | 1 | no | — |
| 328 | #470 | — | 5 | 8 | no | — |
| 329 | #468 | — | 5 | 8 | no | — |
| 330 | #467 | — | 5 | 8 | no | — |
| 331 | #465 | — | 5 | 8 | no | — |
| 332 | #441 | — | 5 | 8 | no | — |
| 333 | #440 | — | 5 | 8 | no | — |
| 334 | C4×Q16 | — | 5 | 8 | no | — |
| 335 | C4×SD16 | — | 5 | 8 | no | — |
| 336 | #428 | — | 5 | 4 | no | — |
| 337 | #416 | — | 5 | 4 | no | — |
| 338 | C2×#103 | C2×D5 | 1 | 4 | yes | — |
| 339 | #405 | — | 5 | 2 | no | — |
| 340 | #405 | — | 5 | 4 | no | — |
| 341 | C4×M16 | — | 5 | 1 | no | — |
| 342 | C4×M16 | — | 5 | 2 | no | — |
| 343 | C2×C4×C8 | — | 5 | 2 | no | — |
| 344 | C2×C4×C8 | C2×D5 | 1 | 1 | yes | characteristic |
| 345 | C23×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 346 | C22×D5 | — | 2 | 2 | no | — |
| 347 | C22×D5 | C22×D4 | 1 | 2 | yes | — |
| 348 | C5×Q8 | — | 2 | 8 | no | — |
| 349 | C5×Q8 | — | 4 | 4 | no | — |
| 350 | C5×Q8 | — | 4 | 4 | no | — |
| 351 | C5×Q8 | — | 8 | 2 | no | — |
| 352 | C2×C4×C5 | — | 2 | 2 | no | — |
| 353 | C2×C4×C5 | — | 2 | 2 | no | — |
| 354 | C2×C4×C5 | — | 2 | 4 | no | — |
| 355 | C2×C4×C5 | — | 2 | 4 | no | — |
| 356 | C2×C4×C5 | — | 4 | 4 | no | — |
| 357 | C2×C4×C5 | — | 8 | 2 | no | — |
| 358 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 359 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 360 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 361 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 362 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 363 | C2×C4×C5 | C2×#41 | 1 | 4 | yes | — |
| 364 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 365 | C22⋊D5 | — | 2 | 4 | no | — |
| 366 | C22⋊D5 | — | 4 | 4 | no | — |
| 367 | C2×Dic5 | — | 2 | 2 | no | — |
| 368 | C2×Dic5 | — | 2 | 2 | no | — |
| 369 | C2×Dic5 | — | 2 | 2 | no | — |
| 370 | C2×Dic5 | C22×D4 | 1 | 2 | yes | — |
| 371 | C2×Dic5 | C22×D4 | 1 | 2 | yes | — |
| 372 | C2×Dic5 | C22×D4 | 1 | 2 | yes | — |
| 373 | D20 | — | 2 | 2 | no | — |
| 374 | D20 | — | 2 | 4 | no | — |
| 375 | D20 | — | 4 | 2 | no | — |
| 376 | D20 | — | 4 | 2 | no | — |
| 377 | D20 | — | 8 | 4 | no | — |
| 378 | C4×D5 | — | 2 | 4 | no | — |
| 379 | C4×D5 | — | 2 | 4 | no | — |
| 380 | C4×D5 | — | 2 | 4 | no | — |
| 381 | C4×D5 | — | 4 | 4 | no | — |
| 382 | C4×D5 | — | 8 | 4 | no | — |
| 383 | Dic10 | — | 2 | 2 | no | — |
| 384 | Dic10 | — | 2 | 4 | no | — |
| 385 | Dic10 | — | 4 | 2 | no | — |
| 386 | Dic10 | — | 4 | 2 | no | — |
| 387 | C5×C8 | — | 2 | 2 | no | — |
| 388 | C5×C8 | — | 2 | 2 | no | — |
| 389 | #168 | C2×#41 | 1 | 8 | yes | — |
| 390 | C2×#41 | — | 5 | 1 | no | — |
| 391 | C2×#41 | — | 5 | 2 | no | — |
| 392 | C2×#41 | — | 10 | 2 | no | — |
| 393 | C22×Q8 | — | 2 | 1 | no | — |
| 394 | C22×Q8 | C22×D5 | 1 | 2 | yes | — |
| 395 | #137 | — | 10 | 16 | no | — |
| 396 | C2×Q16 | — | 5 | 8 | no | — |
| 397 | C2×SD16 | — | 5 | 8 | no | — |
| 398 | #131 | — | 10 | 8 | no | — |
| 399 | C2×M16 | — | 5 | 2 | no | — |
| 400 | C2×M16 | — | 5 | 4 | no | — |
| 401 | C22×C8 | — | 5 | 4 | no | — |
| 402 | C22×C8 | C22×D5 | 1 | 2 | yes | — |
| 403 | C4⋊Q8 | — | 2 | 1 | no | — |
| 404 | C4⋊Q8 | — | 2 | 1 | no | — |
| 405 | C4⋊Q8 | — | 2 | 1 | no | — |
| 406 | C4⋊Q8 | — | 2 | 1 | no | — |
| 407 | C4⋊Q8 | — | 5 | 1 | no | — |
| 408 | C4⋊Q8 | — | 5 | 1 | no | — |
| 409 | C4⋊Q8 | — | 5 | 1 | no | — |
| 410 | C4⋊Q8 | — | 10 | 2 | no | — |
| 411 | C4⋊Q8 | C22×D5 | 1 | 2 | yes | — |
| 412 | C4⋊Q8 | C22×D5 | 1 | 2 | yes | — |
| 413 | C4⋊Q8 | C22×D5 | 1 | 2 | yes | — |
| 414 | C4⋊Q8 | C22×D5 | 1 | 2 | yes | — |
| 415 | #127 | — | 5 | 1 | no | — |
| 416 | #126 | — | 10 | 4 | no | — |
| 417 | #126 | — | 10 | 4 | no | — |
| 418 | #126 | — | 10 | 4 | no | — |
| 419 | #125 | — | 5 | 2 | no | — |
| 420 | #125 | — | 10 | 2 | no | — |
| 421 | #125 | — | 10 | 2 | no | — |
| 422 | #125 | — | 10 | 2 | no | — |
| 423 | #125 | — | 10 | 4 | no | — |
| 424 | #125 | — | 10 | 4 | no | — |
| 425 | #124 | — | 5 | 2 | no | — |
| 426 | #124 | — | 10 | 2 | no | — |
| 427 | #124 | — | 10 | 4 | no | — |
| 428 | #124 | — | 10 | 2 | no | — |
| 429 | #123 | — | 10 | 4 | no | — |
| 430 | #123 | — | 10 | 4 | no | — |
| 431 | C22⋊Q8 | — | 5 | 4 | no | — |
| 432 | C22⋊Q8 | — | 5 | 4 | no | — |
| 433 | C22⋊Q8 | — | 5 | 4 | no | — |
| 434 | C22⋊Q8 | — | 10 | 2 | no | — |
| 435 | C22⋊Q8 | — | 10 | 2 | no | — |
| 436 | C22⋊Q8 | — | 10 | 2 | no | — |
| 437 | C22⋊Q8 | — | 10 | 4 | no | — |
| 438 | C22⋊Q8 | — | 10 | 2 | no | — |
| 439 | C22⋊Q8 | — | 10 | 1 | no | — |
| 440 | C22⋊Q8 | — | 10 | 1 | no | — |
| 441 | #121 | — | 5 | 4 | no | — |
| 442 | #121 | — | 10 | 2 | no | — |
| 443 | #121 | — | 10 | 2 | no | — |
| 444 | #121 | — | 10 | 4 | no | — |
| 445 | #121 | — | 10 | 1 | no | — |
| 446 | #121 | — | 10 | 1 | no | — |
| 447 | C4×Q8 | — | 5 | 1 | no | — |
| 448 | C4×Q8 | — | 5 | 1 | no | — |
| 449 | C4×Q8 | — | 5 | 4 | no | — |
| 450 | C4×Q8 | — | 5 | 4 | no | — |
| 451 | C4×Q8 | — | 5 | 4 | no | — |
| 452 | C4×Q8 | — | 10 | 2 | no | — |
| 453 | C4×Q8 | — | 10 | 2 | no | — |
| 454 | C4×Q8 | — | 10 | 2 | no | — |
| 455 | C4×Q8 | — | 10 | 2 | no | — |
| 456 | C4×Q8 | — | 10 | 2 | no | — |
| 457 | C4×Q8 | — | 10 | 1 | no | — |
| 458 | C4×Q8 | — | 10 | 1 | no | — |
| 459 | C4×D4 | — | 5 | 2 | no | — |
| 460 | C4×D4 | — | 5 | 2 | no | — |
| 461 | C4×D4 | — | 5 | 4 | no | — |
| 462 | C4×D4 | — | 5 | 1 | no | — |
| 463 | C4×D4 | — | 5 | 1 | no | — |
| 464 | C4×D4 | — | 10 | 2 | no | — |
| 465 | C4×D4 | — | 10 | 4 | no | — |
| 466 | C4×D4 | — | 10 | 1 | no | — |
| 467 | C4×D4 | — | 10 | 1 | no | — |
| 468 | #117 | — | 5 | 1 | no | — |
| 469 | #117 | — | 5 | 2 | no | — |
| 470 | #117 | — | 5 | 2 | no | — |
| 471 | #117 | — | 10 | 4 | no | — |
| 472 | #117 | — | 10 | 2 | no | — |
| 473 | #117 | — | 10 | 2 | no | — |
| 474 | #117 | — | 10 | 2 | no | — |
| 475 | #117 | — | 10 | 2 | no | — |
| 476 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 477 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 478 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 479 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 480 | C2×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 481 | C2×C42 | — | 5 | 2 | no | — |
| 482 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 483 | #107 | — | 5 | 8 | no | — |
| 484 | #106 | — | 5 | 8 | no | — |
| 485 | #103 | — | 5 | 4 | no | — |
| 486 | #103 | — | 5 | 4 | no | — |
| 487 | #103 | C22×D5 | 1 | 8 | yes | — |
| 488 | #103 | C22×D5 | 1 | 8 | yes | — |
| 489 | #102 | — | 5 | 4 | no | — |
| 490 | #102 | — | 5 | 4 | no | — |
| 491 | #97 | — | 5 | 4 | no | — |
| 492 | #97 | — | 5 | 2 | no | — |
| 493 | C4×C8 | — | 5 | 4 | no | — |
| 494 | C4×C8 | — | 5 | 2 | no | — |
| 495 | C4×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 496 | C4×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 497 | C4×C8 | C22×D5 | 1 | 2 | yes | — |
| 498 | C22×C5 | — | 2 | 1 | no | — |
| 499 | C22×C5 | — | 2 | 1 | no | — |
| 500 | C22×C5 | #532 | 1 | 2 | yes | — |
| 501 | C22×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 502 | C2×D5 | — | 2 | 2 | no | — |
| 503 | C2×D5 | — | 2 | 2 | no | — |
| 504 | C2×D5 | — | 2 | 2 | no | — |
| 505 | C2×D5 | — | 4 | 2 | no | — |
| 506 | C2×D5 | — | 4 | 2 | no | — |
| 507 | C2×D5 | — | 4 | 2 | no | — |
| 508 | C4×C5 | — | 2 | 1 | no | — |
| 509 | C4×C5 | — | 2 | 1 | no | — |
| 510 | C4×C5 | — | 4 | 4 | no | — |
| 511 | C4×C5 | — | 4 | 4 | no | — |
| 512 | C4×C5 | #532 | 1 | 2 | yes | — |
| 513 | C4×C5 | #577 | 1 | 2 | yes | — |
| 514 | C4×C5 | #578 | 1 | 2 | yes | — |
| 515 | C4×C5 | C22×#41 | 1 | 2 | yes | — |
| 516 | Dic5 | — | 2 | 2 | no | — |
| 517 | Dic5 | — | 2 | 2 | no | — |
| 518 | Dic5 | — | 2 | 2 | no | — |
| 519 | Dic5 | — | 4 | 2 | no | — |
| 520 | Dic5 | — | 4 | 2 | no | — |
| 521 | Dic5 | — | 4 | 2 | no | — |
| 522 | #41 | — | 10 | 4 | no | — |
| 523 | #41 | — | 10 | 8 | no | — |
| 524 | #41 | — | 40 | 4 | no | — |
| 525 | C2×Q8 | — | 2 | 2 | no | — |
| 526 | C2×Q8 | — | 2 | 2 | no | — |
| 527 | C2×Q8 | — | 2 | 2 | no | — |
| 528 | C2×Q8 | — | 2 | 8 | no | — |
| 529 | C2×Q8 | — | 5 | 1 | no | — |
| 530 | C2×Q8 | — | 5 | 2 | no | — |
| 531 | C2×Q8 | — | 8 | 2 | no | — |
| 532 | C2×Q8 | — | 10 | 1 | no | — |
| 533 | C2×Q8 | — | 10 | 1 | no | — |
| 534 | C2×Q8 | C23×D5 | 1 | 4 | yes | — |
| 535 | C2×D4 | — | 5 | 2 | no | — |
| 536 | C2×D4 | — | 5 | 1 | no | — |
| 537 | C2×D4 | — | 5 | 2 | no | — |
| 538 | C2×D4 | — | 10 | 4 | no | — |
| 539 | C2×D4 | — | 10 | 2 | no | — |
| 540 | C2×D4 | — | 10 | 1 | no | — |
| 541 | C2×D4 | — | 10 | 1 | no | — |
| 542 | C22×C4 | — | 2 | 2 | no | — |
| 543 | C22×C4 | — | 2 | 2 | no | — |
| 544 | C22×C4 | — | 5 | 2 | no | — |
| 545 | C22×C4 | — | 5 | 2 | no | — |
| 546 | C22×C4 | — | 5 | 2 | no | — |
| 547 | C22×C4 | — | 10 | 4 | no | — |
| 548 | C22×C4 | — | 10 | 2 | no | — |
| 549 | C22×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 550 | C22×C4 | D4×D5 | 1 | 1 | yes | characteristic |
| 551 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 552 | Q16 | — | 10 | 16 | no | — |
| 553 | SD16 | — | 10 | 16 | no | — |
| 554 | M16 | — | 5 | 8 | no | — |
| 555 | M16 | — | 10 | 8 | no | — |
| 556 | C2×C8 | — | 2 | 4 | no | — |
| 557 | C2×C8 | — | 5 | 4 | no | — |
| 558 | C2×C8 | — | 10 | 8 | no | — |
| 559 | C2×C8 | C23×D5 | 1 | 2 | yes | — |
| 560 | C2×C8 | C23×D5 | 1 | 2 | yes | — |
| 561 | C4⋊C4 | — | 2 | 2 | no | — |
| 562 | C4⋊C4 | — | 2 | 2 | no | — |
| 563 | C4⋊C4 | — | 2 | 2 | no | — |
| 564 | C4⋊C4 | — | 2 | 2 | no | — |
| 565 | C4⋊C4 | — | 2 | 2 | no | — |
| 566 | C4⋊C4 | — | 2 | 2 | no | — |
| 567 | C4⋊C4 | — | 2 | 2 | no | — |
| 568 | C4⋊C4 | — | 5 | 1 | no | — |
| 569 | C4⋊C4 | — | 5 | 1 | no | — |
| 570 | C4⋊C4 | — | 5 | 2 | no | — |
| 571 | C4⋊C4 | — | 5 | 2 | no | — |
| 572 | C4⋊C4 | — | 5 | 2 | no | — |
| 573 | C4⋊C4 | — | 5 | 2 | no | — |
| 574 | C4⋊C4 | — | 10 | 4 | no | — |
| 575 | C4⋊C4 | — | 10 | 4 | no | — |
| 576 | C4⋊C4 | — | 10 | 4 | no | — |
| 577 | C4⋊C4 | — | 10 | 4 | no | — |
| 578 | C4⋊C4 | — | 10 | 4 | no | — |
| 579 | C4⋊C4 | — | 10 | 4 | no | — |
| 580 | C4⋊C4 | — | 10 | 1 | no | — |
| 581 | C4⋊C4 | — | 10 | 1 | no | — |
| 582 | C4⋊C4 | — | 10 | 1 | no | — |
| 583 | C4⋊C4 | — | 10 | 1 | no | — |
| 584 | C4⋊C4 | — | 10 | 2 | no | — |
| 585 | C4⋊C4 | — | 10 | 2 | no | — |
| 586 | C4⋊C4 | C23×D5 | 1 | 4 | yes | — |
| 587 | C22⋊C4 | — | 5 | 2 | no | — |
| 588 | C22⋊C4 | — | 5 | 2 | no | — |
| 589 | C22⋊C4 | — | 5 | 2 | no | — |
| 590 | C22⋊C4 | — | 10 | 4 | no | — |
| 591 | C22⋊C4 | — | 10 | 4 | no | — |
| 592 | C22⋊C4 | — | 10 | 4 | no | — |
| 593 | C22⋊C4 | — | 10 | 4 | no | — |
| 594 | C22⋊C4 | — | 10 | 4 | no | — |
| 595 | C22⋊C4 | — | 10 | 2 | no | — |
| 596 | C22⋊C4 | — | 10 | 2 | no | — |
| 597 | C22⋊C4 | — | 10 | 2 | no | — |
| 598 | C42 | — | 5 | 2 | no | — |
| 599 | C42 | — | 5 | 2 | no | — |
| 600 | C42 | — | 5 | 2 | no | — |
| 601 | C42 | — | 10 | 4 | no | — |
| 602 | C42 | — | 10 | 4 | no | — |
| 603 | C42 | — | 10 | 4 | no | — |
| 604 | C42 | — | 10 | 2 | no | — |
| 605 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 606 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 607 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 608 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 609 | C2×C5 | — | 2 | 2 | no | — |
| 610 | C2×C5 | C2×#532 | 1 | 1 | yes | characteristic |
| 611 | C2×C5 | C2×#577 | 1 | 1 | yes | characteristic |
| 612 | C2×C5 | C2×#578 | 1 | 1 | yes | characteristic |
| 613 | D5 | — | 4 | 2 | no | — |
| 614 | D5 | — | 8 | 2 | no | — |
| 615 | C23 | — | 5 | 2 | no | — |
| 616 | C23 | — | 10 | 2 | no | — |
| 617 | C23 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 618 | Q8 | — | 2 | 8 | no | — |
| 619 | Q8 | — | 4 | 4 | no | — |
| 620 | Q8 | — | 4 | 4 | no | — |
| 621 | Q8 | — | 8 | 2 | no | — |
| 622 | Q8 | — | 10 | 2 | no | — |
| 623 | Q8 | — | 10 | 4 | no | — |
| 624 | Q8 | — | 20 | 2 | no | — |
| 625 | Q8 | — | 20 | 2 | no | — |
| 626 | D4 | — | 10 | 4 | no | — |
| 627 | D4 | — | 10 | 2 | no | — |
| 628 | D4 | — | 10 | 4 | no | — |
| 629 | D4 | — | 20 | 4 | no | — |
| 630 | D4 | — | 20 | 2 | no | — |
| 631 | D4 | — | 20 | 2 | no | — |
| 632 | D4 | — | 40 | 4 | no | — |
| 633 | C2×C4 | — | 2 | 2 | no | — |
| 634 | C2×C4 | — | 2 | 2 | no | — |
| 635 | C2×C4 | — | 2 | 4 | no | — |
| 636 | C2×C4 | — | 2 | 4 | no | — |
| 637 | C2×C4 | — | 4 | 4 | no | — |
| 638 | C2×C4 | — | 5 | 2 | no | — |
| 639 | C2×C4 | — | 5 | 2 | no | — |
| 640 | C2×C4 | — | 5 | 2 | no | — |
| 641 | C2×C4 | — | 8 | 2 | no | — |
| 642 | C2×C4 | — | 10 | 4 | no | — |
| 643 | C2×C4 | — | 10 | 4 | no | — |
| 644 | C2×C4 | — | 10 | 4 | no | — |
| 645 | C2×C4 | — | 10 | 2 | no | — |
| 646 | C2×C4 | — | 10 | 2 | no | — |
| 647 | C2×C4 | — | 10 | 2 | no | — |
| 648 | C2×C4 | — | 20 | 4 | no | — |
| 649 | C2×C4 | — | 40 | 4 | no | — |
| 650 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 651 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 652 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 653 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 654 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 655 | C2×C4 | D5×#41 | 1 | 4 | yes | — |
| 656 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 657 | C8 | — | 2 | 2 | no | — |
| 658 | C8 | — | 2 | 2 | no | — |
| 659 | C8 | — | 5 | 8 | no | — |
| 660 | C5 | #60723 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 661 | C22 | — | 2 | 1 | no | — |
| 662 | C22 | — | 2 | 1 | no | — |
| 663 | C22 | — | 10 | 2 | no | — |
| 664 | C22 | — | 10 | 2 | no | — |
| 665 | C22 | — | 10 | 2 | no | — |
| 666 | C22 | — | 20 | 2 | no | — |
| 667 | C22 | — | 20 | 2 | no | — |
| 668 | C22 | — | 20 | 2 | no | — |
| 669 | C22 | #66002 | 1 | 2 | yes | — |
| 670 | C22 | C22×D4×D5 | 1 | 1 | yes | characteristic |
| 671 | C4 | — | 2 | 1 | no | — |
| 672 | C4 | — | 2 | 1 | no | — |
| 673 | C4 | — | 4 | 4 | no | — |
| 674 | C4 | — | 4 | 4 | no | — |
| 675 | C4 | — | 10 | 2 | no | — |
| 676 | C4 | — | 10 | 2 | no | — |
| 677 | C4 | — | 10 | 2 | no | — |
| 678 | C4 | — | 20 | 2 | no | — |
| 679 | C4 | — | 20 | 2 | no | — |
| 680 | C4 | — | 20 | 2 | no | — |
| 681 | C4 | #66002 | 1 | 2 | yes | — |
| 682 | C4 | #66096 | 1 | 2 | yes | — |
| 683 | C4 | #66100 | 1 | 2 | yes | — |
| 684 | C4 | C2×D5×#41 | 1 | 2 | yes | — |
| 685 | C2 | — | 2 | 2 | no | — |
| 686 | C2 | — | 20 | 2 | no | — |
| 687 | C2 | — | 40 | 2 | no | — |
| 688 | C2 | C2×#66002 | 1 | 1 | yes | characteristic |
| 689 | C2 | C2×#66096 | 1 | 1 | yes | characteristic |
| 690 | C2 | C2×#66100 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10618105 | C2 | semidirect |
| 3. C2×C5×#487 | C2 | semidirect |
| 4. #10614938 | C2 | semidirect |
| 5. #10614934 | C2 | semidirect |
| 6. #10613327 | C2 | semidirect |
| 7. #10613326 | C2 | semidirect |
| 8. #10613325 | C2 | semidirect |
| 9. #10613324 | C2 | semidirect |
| 10. #10613323 | C2 | semidirect |
| 11. #10610531 | C2 | semidirect |
| 12. #10610505 | C2 | semidirect |
| 13. #10610194 | C2 | semidirect |
| 14. C4×#4047 | C2 | semidirect |
| 194. C2×#487 | D5 | semidirect |
| 281. #681 | #41 | semidirect |
| 660. C5 | #60723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10618106 | 2 |
| #10618105 | 2 |
| C2×C5×#487 | 2 |
| #10614938 | 2 |
| #10614934 | 2 |
| #10613327 | 2 |
| #10613326 | 2 |
| #10613325 | 2 |
| #10613324 | 2 |
| #10613323 | 2 |
| #10610531 | 2 |
| #10610505 | 2 |
| #10610194 | 2 |
| C4×#4047 | 2 |
| #60723 | 5 |