Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1950 conjugacy classes of subgroups.
The subgroup lattice has 496 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10618162 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10618105 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#3139 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10615070 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#65374 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10613460 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #10613326 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10613323 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10610694 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #10610678 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #10610257 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C4×#4053 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C5×#533 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C5×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 15 | #66150 | C22 | 1 | 2 | yes | — |
| 16 | #66146 | C22 | 1 | 2 | yes | — |
| 17 | C22×#688 | C22 | 1 | 4 | yes | — |
| 18 | C2×#4053 | C22 | 1 | 2 | yes | — |
| 19 | #66066 | — | 2 | 2 | no | — |
| 20 | #66065 | C22 | 1 | 4 | yes | complemented |
| 21 | #66062 | C22 | 1 | 4 | yes | complemented |
| 22 | #66059 | C22 | 1 | 4 | yes | — |
| 23 | #66055 | — | 2 | 2 | no | — |
| 24 | #66032 | C22 | 1 | 4 | yes | — |
| 25 | #65964 | — | 2 | 4 | no | — |
| 26 | #65919 | — | 2 | 2 | no | — |
| 27 | #65911 | — | 2 | 2 | no | — |
| 28 | #65859 | C22 | 1 | 2 | yes | — |
| 29 | #65855 | C22 | 1 | 2 | yes | — |
| 30 | #65847 | — | 2 | 4 | no | — |
| 31 | C2×#4020 | C22 | 1 | 1 | yes | characteristic |
| 32 | C4×#709 | C22 | 1 | 1 | yes | characteristic |
| 33 | #65804 | C22 | 1 | 1 | yes | characteristic |
| 34 | C5×#491 | C22 | 1 | 4 | yes | complemented |
| 35 | C5×#487 | C22 | 1 | 4 | yes | complemented |
| 36 | C5×#419 | C22 | 1 | 4 | yes | — |
| 37 | C4×C5×M16 | C22 | 1 | 1 | yes | characteristic |
| 38 | #65420 | C22 | 1 | 4 | yes | — |
| 39 | #65411 | C22 | 1 | 2 | yes | — |
| 40 | #65374 | C22 | 1 | 2 | yes | — |
| 41 | #65374 | C22 | 1 | 2 | yes | — |
| 42 | #65374 | C22 | 1 | 4 | yes | — |
| 43 | #65368 | C22 | 1 | 2 | yes | complemented |
| 44 | #65367 | C22 | 1 | 2 | yes | complemented |
| 45 | #65353 | C22 | 1 | 4 | yes | complemented |
| 46 | #65287 | C22 | 1 | 4 | yes | — |
| 47 | C2×C4×#168 | C22 | 1 | 1 | yes | characteristic |
| 48 | #65106 | C22 | 1 | 16 | yes | complemented |
| 49 | #65101 | C22 | 1 | 16 | yes | complemented |
| 50 | #65096 | C22 | 1 | 16 | yes | complemented |
| 51 | #65077 | C22 | 1 | 16 | yes | complemented |
| 52 | #65002 | C22 | 1 | 4 | yes | — |
| 53 | #64997 | C22 | 1 | 4 | yes | complemented |
| 54 | #64983 | C22 | 1 | 4 | yes | — |
| 55 | C4×#676 | C22 | 1 | 2 | yes | complemented |
| 56 | C4×C8×D5 | C22 | 1 | 2 | yes | complemented |
| 57 | #60712 | — | 5 | 1 | no | maximal, Sylow |
| 58 | C22×C5×Q8 | C23 | 1 | 2 | yes | — |
| 59 | C2×#713 | — | 2 | 4 | no | — |
| 60 | C2×#709 | C23 | 1 | 1 | yes | characteristic |
| 61 | C22×D20 | — | 2 | 2 | no | — |
| 62 | C22×D20 | C23 | 1 | 2 | yes | — |
| 63 | C2×C5×M16 | C23 | 1 | 2 | yes | — |
| 64 | C5×C4⋊Q8 | — | 2 | 2 | no | — |
| 65 | C5×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 66 | C5×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 67 | C5×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 68 | C5×#125 | C23 | 1 | 2 | yes | — |
| 69 | C5×C22⋊Q8 | — | 2 | 2 | no | — |
| 70 | C4×C5×Q8 | — | 2 | 2 | no | — |
| 71 | C5×#117 | C23 | 1 | 2 | yes | — |
| 72 | C2×C5×C4⋊C4 | — | 2 | 2 | no | — |
| 73 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 74 | #4093 | — | 2 | 2 | no | — |
| 75 | #4093 | — | 2 | 4 | no | — |
| 76 | #4092 | C23 | 1 | 8 | yes | — |
| 77 | Q8×Dic5 | — | 2 | 4 | no | — |
| 78 | Q8×Dic5 | C23 | 1 | 8 | yes | — |
| 79 | #4090 | — | 2 | 2 | no | — |
| 80 | C2×#688 | — | 2 | 16 | no | — |
| 81 | C2×#688 | C23 | 1 | 8 | yes | — |
| 82 | C2×#688 | C23 | 1 | 8 | yes | — |
| 83 | #4075 | — | 2 | 4 | no | — |
| 84 | C4×C22⋊D5 | D4 | 1 | 4 | yes | — |
| 85 | #4072 | — | 2 | 4 | no | — |
| 86 | #4072 | C23 | 1 | 2 | yes | — |
| 87 | #4072 | C23 | 1 | 1 | yes | characteristic |
| 88 | #4070 | — | 2 | 2 | no | — |
| 89 | C22×#168 | C23 | 1 | 2 | yes | — |
| 90 | #4053 | — | 2 | 8 | no | — |
| 91 | C2×#676 | C23 | 1 | 4 | yes | — |
| 92 | C2×C8×D5 | C23 | 1 | 4 | yes | — |
| 93 | #4044 | — | 2 | 8 | no | — |
| 94 | #4043 | — | 2 | 4 | no | — |
| 95 | #4041 | — | 2 | 4 | no | — |
| 96 | #4041 | — | 2 | 8 | no | — |
| 97 | #4041 | C23 | 1 | 8 | yes | — |
| 98 | #4040 | — | 2 | 8 | no | — |
| 99 | #4039 | — | 2 | 4 | no | — |
| 100 | #4039 | C23 | 1 | 8 | yes | — |
| 101 | #4038 | — | 2 | 4 | no | — |
| 102 | #4036 | — | 2 | 4 | no | — |
| 103 | #4035 | — | 2 | 8 | no | — |
| 104 | #4033 | — | 2 | 4 | no | — |
| 105 | #4028 | — | 2 | 4 | no | — |
| 106 | D5×C22⋊C4 | — | 2 | 4 | no | — |
| 107 | #4021 | — | 2 | 2 | no | — |
| 108 | #4020 | — | 2 | 2 | no | — |
| 109 | #4020 | — | 2 | 2 | no | — |
| 110 | #4020 | C23 | 1 | 2 | yes | — |
| 111 | #4020 | C23 | 1 | 2 | yes | — |
| 112 | C4×D20 | — | 2 | 4 | no | — |
| 113 | C4×D20 | D4 | 1 | 2 | yes | — |
| 114 | #4018 | C23 | 1 | 2 | yes | — |
| 115 | C42×D5 | C23 | 1 | 2 | yes | — |
| 116 | #4016 | C23 | 1 | 2 | yes | — |
| 117 | #4015 | C23 | 1 | 2 | yes | — |
| 118 | C4×Dic10 | — | 2 | 2 | no | — |
| 119 | C4×Dic10 | D4 | 1 | 2 | yes | — |
| 120 | C5×#103 | C23 | 1 | 16 | yes | — |
| 121 | C5×#97 | C23 | 1 | 2 | yes | — |
| 122 | C4×C5×C8 | C23 | 1 | 2 | yes | — |
| 123 | #3953 | C23 | 1 | 16 | yes | — |
| 124 | #3947 | C23 | 1 | 4 | yes | — |
| 125 | C8×Dic5 | C23 | 1 | 4 | yes | — |
| 126 | #3940 | C23 | 1 | 8 | yes | — |
| 127 | #3939 | C23 | 1 | 8 | yes | — |
| 128 | C4×#168 | C23 | 1 | 2 | yes | — |
| 129 | C4×#168 | C23 | 1 | 1 | yes | characteristic |
| 130 | C4×#168 | C23 | 1 | 1 | yes | characteristic |
| 131 | #3509 | — | 5 | 1 | no | — |
| 132 | #3508 | — | 5 | 1 | no | — |
| 133 | #3182 | — | 5 | 4 | no | — |
| 134 | #3174 | — | 5 | 8 | no | — |
| 135 | #3167 | — | 5 | 4 | no | — |
| 136 | #3160 | — | 5 | 1 | no | — |
| 137 | C2×#492 | — | 5 | 1 | no | — |
| 138 | #3139 | D5 | 1 | 1 | yes | characteristic, complemented |
| 139 | #3138 | — | 5 | 1 | no | — |
| 140 | #3057 | — | 5 | 4 | no | — |
| 141 | #2949 | — | 5 | 4 | no | — |
| 142 | C4×#131 | — | 5 | 1 | no | — |
| 143 | C23×D5 | — | 2 | 2 | no | — |
| 144 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 145 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 146 | C2×C5×Q8 | — | 2 | 8 | no | — |
| 147 | C2×C5×Q8 | C24 | 1 | 4 | yes | — |
| 148 | C22×C4×C5 | — | 2 | 2 | no | — |
| 149 | C22×C4×C5 | C2×D4 | 1 | 2 | yes | — |
| 150 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 151 | C2×C22⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 152 | #713 | — | 8 | 8 | no | — |
| 153 | #709 | — | 2 | 4 | no | — |
| 154 | C2×D20 | — | 2 | 8 | no | — |
| 155 | C2×D20 | — | 2 | 4 | no | — |
| 156 | C2×D20 | — | 2 | 2 | no | — |
| 157 | C2×D20 | — | 2 | 8 | no | — |
| 158 | C2×D20 | — | 2 | 4 | no | — |
| 159 | C2×D20 | — | 8 | 4 | no | — |
| 160 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C2×D20 | C24 | 1 | 4 | yes | — |
| 162 | C2×C4×D5 | — | 2 | 8 | no | — |
| 163 | C2×C4×D5 | C2×D4 | 1 | 4 | yes | — |
| 164 | C2×C4×D5 | C24 | 1 | 2 | yes | — |
| 165 | C2×Dic10 | — | 2 | 2 | no | — |
| 166 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C5×M16 | — | 2 | 4 | no | — |
| 168 | C2×C5×C8 | C24 | 1 | 4 | yes | — |
| 169 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 170 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 171 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 172 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 173 | C5×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 174 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 175 | C42×C5 | — | 2 | 2 | no | — |
| 176 | C42×C5 | C2×D4 | 1 | 2 | yes | — |
| 177 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 178 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 179 | C22⋊Dic5 | — | 2 | 2 | no | — |
| 180 | C22⋊Dic5 | C2×D4 | 1 | 2 | yes | — |
| 181 | #688 | — | 2 | 16 | no | — |
| 182 | #688 | — | 2 | 16 | no | — |
| 183 | #685 | — | 2 | 8 | no | — |
| 184 | #685 | — | 2 | 8 | no | — |
| 185 | #685 | — | 2 | 8 | no | — |
| 186 | #685 | C2×D4 | 1 | 4 | yes | — |
| 187 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 188 | C4⋊Dic5 | — | 2 | 8 | no | — |
| 189 | C4⋊Dic5 | C2×D4 | 1 | 2 | yes | — |
| 190 | C4⋊Dic5 | C24 | 1 | 4 | yes | — |
| 191 | #683 | — | 2 | 4 | no | — |
| 192 | #683 | — | 2 | 8 | no | — |
| 193 | #683 | C2×D4 | 1 | 4 | yes | — |
| 194 | C4×Dic5 | — | 2 | 2 | no | — |
| 195 | C4×Dic5 | — | 2 | 8 | no | — |
| 196 | C4×Dic5 | C2×D4 | 1 | 4 | yes | — |
| 197 | C4×Dic5 | C24 | 1 | 2 | yes | — |
| 198 | C2×#168 | #41 | 1 | 8 | yes | complemented |
| 199 | C2×#168 | C24 | 1 | 2 | yes | — |
| 200 | C2×#168 | C24 | 1 | 2 | yes | — |
| 201 | #676 | — | 2 | 8 | no | — |
| 202 | C8×D5 | — | 2 | 8 | no | — |
| 203 | C22×SD16 | — | 5 | 4 | no | — |
| 204 | C2×#131 | — | 5 | 2 | no | — |
| 205 | #559 | — | 10 | 2 | no | — |
| 206 | #557 | — | 10 | 2 | no | — |
| 207 | #556 | — | 10 | 2 | no | — |
| 208 | #552 | — | 10 | 4 | no | — |
| 209 | #550 | — | 10 | 2 | no | — |
| 210 | #546 | — | 10 | 4 | no | — |
| 211 | #541 | — | 5 | 4 | no | — |
| 212 | #540 | — | 5 | 4 | no | — |
| 213 | #536 | — | 5 | 2 | no | — |
| 214 | #535 | — | 5 | 2 | no | — |
| 215 | #533 | — | 5 | 4 | no | — |
| 216 | #533 | — | 5 | 1 | no | — |
| 217 | #533 | C2×D5 | 1 | 1 | yes | characteristic |
| 218 | #532 | — | 5 | 4 | no | — |
| 219 | C2×C4⋊Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 220 | C2×#127 | — | 5 | 1 | no | — |
| 221 | #519 | — | 5 | 2 | no | — |
| 222 | #518 | — | 5 | 2 | no | — |
| 223 | C4×#41 | — | 5 | 1 | no | — |
| 224 | #500 | — | 5 | 2 | no | — |
| 225 | #499 | — | 5 | 4 | no | — |
| 226 | #498 | — | 5 | 2 | no | — |
| 227 | #492 | — | 5 | 2 | no | — |
| 228 | #492 | — | 5 | 4 | no | — |
| 229 | #492 | — | 5 | 2 | no | — |
| 230 | #491 | C2×D5 | 1 | 4 | yes | complemented |
| 231 | #490 | — | 5 | 4 | no | — |
| 232 | #487 | C2×D5 | 1 | 4 | yes | complemented |
| 233 | #486 | — | 5 | 4 | no | — |
| 234 | #468 | — | 5 | 16 | no | — |
| 235 | #465 | — | 5 | 16 | no | — |
| 236 | #440 | — | 5 | 16 | no | — |
| 237 | C4×SD16 | — | 5 | 16 | no | — |
| 238 | #427 | — | 5 | 4 | no | — |
| 239 | #419 | C2×D5 | 1 | 4 | yes | — |
| 240 | #418 | — | 5 | 4 | no | — |
| 241 | #405 | — | 5 | 2 | no | — |
| 242 | #405 | — | 5 | 4 | no | — |
| 243 | C4×M16 | — | 5 | 2 | no | — |
| 244 | C4×M16 | C2×D5 | 1 | 1 | yes | characteristic |
| 245 | C2×C4×C8 | — | 5 | 1 | no | — |
| 246 | C2×C4×C8 | — | 5 | 2 | no | — |
| 247 | C23×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 248 | C22×D5 | — | 2 | 4 | no | — |
| 249 | C22×D5 | — | 4 | 4 | no | — |
| 250 | C22×D5 | — | 8 | 4 | no | — |
| 251 | C22×D5 | C22×D4 | 1 | 2 | yes | — |
| 252 | C5×Q8 | — | 2 | 8 | no | — |
| 253 | C5×Q8 | — | 4 | 4 | no | — |
| 254 | C5×Q8 | — | 4 | 4 | no | — |
| 255 | C2×C4×C5 | — | 2 | 4 | no | — |
| 256 | C2×C4×C5 | — | 2 | 4 | no | — |
| 257 | C2×C4×C5 | — | 2 | 4 | no | — |
| 258 | C2×C4×C5 | — | 4 | 4 | no | — |
| 259 | C2×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 260 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 261 | C2×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 262 | C2×C4×C5 | C2×#41 | 1 | 4 | yes | — |
| 263 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 264 | C22⋊D5 | — | 2 | 4 | no | — |
| 265 | C2×Dic5 | — | 2 | 4 | no | — |
| 266 | C2×Dic5 | C22×D4 | 1 | 4 | yes | — |
| 267 | C2×Dic5 | C22×D4 | 1 | 2 | yes | — |
| 268 | D20 | — | 2 | 2 | no | — |
| 269 | D20 | — | 2 | 8 | no | — |
| 270 | D20 | — | 4 | 4 | no | — |
| 271 | D20 | — | 4 | 8 | no | — |
| 272 | D20 | — | 8 | 4 | no | — |
| 273 | D20 | — | 8 | 8 | no | — |
| 274 | C4×D5 | — | 2 | 8 | no | — |
| 275 | C4×D5 | — | 2 | 4 | no | — |
| 276 | C4×D5 | — | 8 | 8 | no | — |
| 277 | Dic10 | — | 2 | 2 | no | — |
| 278 | Dic10 | — | 4 | 4 | no | — |
| 279 | C5×C8 | — | 2 | 4 | no | — |
| 280 | #168 | C2×#41 | 1 | 4 | yes | — |
| 281 | #168 | C2×#41 | 1 | 4 | yes | — |
| 282 | C2×#41 | — | 5 | 1 | no | — |
| 283 | C2×#41 | — | 10 | 4 | no | — |
| 284 | C22×Q8 | C22×D5 | 1 | 2 | yes | — |
| 285 | C22×D4 | — | 5 | 2 | no | — |
| 286 | C22×D4 | — | 10 | 2 | no | — |
| 287 | C2×SD16 | — | 5 | 8 | no | — |
| 288 | C2×SD16 | — | 5 | 8 | no | — |
| 289 | C2×SD16 | — | 10 | 16 | no | — |
| 290 | #131 | — | 10 | 8 | no | — |
| 291 | C2×M16 | — | 5 | 4 | no | — |
| 292 | C2×M16 | C22×D5 | 1 | 2 | yes | — |
| 293 | C22×C8 | — | 5 | 2 | no | — |
| 294 | C22×C8 | — | 5 | 4 | no | — |
| 295 | C4⋊Q8 | — | 2 | 2 | no | — |
| 296 | C4⋊Q8 | — | 5 | 2 | no | — |
| 297 | C4⋊Q8 | — | 10 | 2 | no | — |
| 298 | C4⋊Q8 | C22×D5 | 1 | 2 | yes | — |
| 299 | C4⋊Q8 | C22×D5 | 1 | 2 | yes | — |
| 300 | C4⋊Q8 | C22×D5 | 1 | 2 | yes | — |
| 301 | #127 | — | 5 | 2 | no | — |
| 302 | #127 | — | 5 | 2 | no | — |
| 303 | #127 | — | 10 | 2 | no | — |
| 304 | #127 | — | 10 | 2 | no | — |
| 305 | #126 | — | 10 | 8 | no | — |
| 306 | #125 | — | 5 | 2 | no | — |
| 307 | #125 | — | 10 | 4 | no | — |
| 308 | #125 | — | 10 | 8 | no | — |
| 309 | #125 | C22×D5 | 1 | 2 | yes | — |
| 310 | #124 | — | 10 | 2 | no | — |
| 311 | #124 | — | 10 | 4 | no | — |
| 312 | #124 | — | 10 | 2 | no | — |
| 313 | #123 | — | 10 | 8 | no | — |
| 314 | #123 | — | 10 | 4 | no | — |
| 315 | C22⋊Q8 | — | 2 | 2 | no | — |
| 316 | C22⋊Q8 | — | 5 | 8 | no | — |
| 317 | C22⋊Q8 | — | 10 | 4 | no | — |
| 318 | C22⋊Q8 | — | 10 | 2 | no | — |
| 319 | #121 | — | 5 | 8 | no | — |
| 320 | #121 | — | 10 | 8 | no | — |
| 321 | #121 | — | 10 | 4 | no | — |
| 322 | #120 | — | 10 | 4 | no | — |
| 323 | C4×Q8 | — | 2 | 2 | no | — |
| 324 | C4×Q8 | — | 5 | 2 | no | — |
| 325 | C4×Q8 | — | 5 | 8 | no | — |
| 326 | C4×Q8 | — | 10 | 4 | no | — |
| 327 | C4×Q8 | — | 10 | 4 | no | — |
| 328 | C4×Q8 | — | 10 | 2 | no | — |
| 329 | C4×D4 | — | 5 | 4 | no | — |
| 330 | C4×D4 | — | 5 | 8 | no | — |
| 331 | C4×D4 | — | 5 | 2 | no | — |
| 332 | C4×D4 | — | 10 | 4 | no | — |
| 333 | C4×D4 | — | 10 | 4 | no | — |
| 334 | #117 | — | 5 | 1 | no | — |
| 335 | #117 | — | 5 | 2 | no | — |
| 336 | #117 | — | 5 | 2 | no | — |
| 337 | #117 | — | 10 | 4 | no | — |
| 338 | #117 | — | 10 | 4 | no | — |
| 339 | #117 | C22×D5 | 1 | 2 | yes | — |
| 340 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 341 | C2×C22⋊C4 | — | 10 | 4 | no | — |
| 342 | C2×C42 | — | 5 | 2 | no | — |
| 343 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 344 | #107 | — | 5 | 8 | no | — |
| 345 | #106 | — | 5 | 8 | no | — |
| 346 | #103 | C22×D5 | 1 | 16 | yes | — |
| 347 | #102 | — | 5 | 16 | no | — |
| 348 | #97 | — | 5 | 4 | no | — |
| 349 | #97 | C22×D5 | 1 | 2 | yes | — |
| 350 | C4×C8 | — | 5 | 4 | no | — |
| 351 | C4×C8 | — | 5 | 1 | no | — |
| 352 | C4×C8 | — | 5 | 1 | no | — |
| 353 | C4×C8 | — | 5 | 2 | no | — |
| 354 | C4×C8 | C22×D5 | 1 | 2 | yes | — |
| 355 | C22×C5 | — | 2 | 2 | no | — |
| 356 | C22×C5 | #532 | 1 | 2 | yes | — |
| 357 | C22×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 358 | C2×D5 | — | 2 | 2 | no | — |
| 359 | C2×D5 | — | 2 | 4 | no | — |
| 360 | C2×D5 | — | 4 | 4 | no | — |
| 361 | C2×D5 | — | 4 | 8 | no | — |
| 362 | C2×D5 | — | 16 | 4 | no | — |
| 363 | C4×C5 | — | 2 | 2 | no | — |
| 364 | C4×C5 | — | 4 | 4 | no | — |
| 365 | C4×C5 | — | 4 | 4 | no | — |
| 366 | C4×C5 | #532 | 1 | 2 | yes | — |
| 367 | C4×C5 | #577 | 1 | 4 | yes | — |
| 368 | C4×C5 | C22×#41 | 1 | 2 | yes | — |
| 369 | Dic5 | — | 2 | 2 | no | — |
| 370 | Dic5 | — | 2 | 4 | no | — |
| 371 | Dic5 | — | 4 | 4 | no | — |
| 372 | C24 | — | 10 | 2 | no | — |
| 373 | #41 | — | 10 | 4 | no | — |
| 374 | #41 | — | 40 | 8 | no | — |
| 375 | C2×Q8 | — | 2 | 2 | no | — |
| 376 | C2×Q8 | — | 2 | 2 | no | — |
| 377 | C2×Q8 | — | 2 | 8 | no | — |
| 378 | C2×Q8 | — | 5 | 1 | no | — |
| 379 | C2×Q8 | — | 10 | 2 | no | — |
| 380 | C2×Q8 | C23×D5 | 1 | 4 | yes | — |
| 381 | C2×D4 | — | 5 | 2 | no | — |
| 382 | C2×D4 | — | 5 | 1 | no | — |
| 383 | C2×D4 | — | 5 | 4 | no | — |
| 384 | C2×D4 | — | 10 | 8 | no | — |
| 385 | C2×D4 | — | 10 | 2 | no | — |
| 386 | C2×D4 | — | 10 | 4 | no | — |
| 387 | C2×D4 | — | 10 | 4 | no | — |
| 388 | C2×D4 | — | 10 | 8 | no | — |
| 389 | C2×D4 | — | 40 | 4 | no | — |
| 390 | C22×C4 | — | 2 | 2 | no | — |
| 391 | C22×C4 | — | 5 | 4 | no | — |
| 392 | C22×C4 | — | 5 | 2 | no | — |
| 393 | C22×C4 | — | 10 | 8 | no | — |
| 394 | C22×C4 | D4×D5 | 1 | 2 | yes | — |
| 395 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 396 | SD16 | — | 10 | 16 | no | — |
| 397 | SD16 | — | 10 | 16 | no | — |
| 398 | M16 | — | 2 | 4 | no | — |
| 399 | M16 | — | 10 | 8 | no | — |
| 400 | C2×C8 | — | 5 | 8 | no | — |
| 401 | C2×C8 | — | 5 | 2 | no | — |
| 402 | C2×C8 | — | 5 | 2 | no | — |
| 403 | C2×C8 | — | 10 | 8 | no | — |
| 404 | C2×C8 | C23×D5 | 1 | 4 | yes | — |
| 405 | C4⋊C4 | — | 2 | 4 | no | — |
| 406 | C4⋊C4 | — | 2 | 4 | no | — |
| 407 | C4⋊C4 | — | 2 | 2 | no | — |
| 408 | C4⋊C4 | — | 2 | 4 | no | — |
| 409 | C4⋊C4 | — | 5 | 2 | no | — |
| 410 | C4⋊C4 | — | 5 | 4 | no | — |
| 411 | C4⋊C4 | — | 5 | 4 | no | — |
| 412 | C4⋊C4 | — | 10 | 8 | no | — |
| 413 | C4⋊C4 | — | 10 | 8 | no | — |
| 414 | C4⋊C4 | — | 10 | 2 | no | — |
| 415 | C4⋊C4 | — | 10 | 4 | no | — |
| 416 | C4⋊C4 | C23×D5 | 1 | 4 | yes | — |
| 417 | C22⋊C4 | — | 2 | 2 | no | — |
| 418 | C22⋊C4 | — | 5 | 2 | no | — |
| 419 | C22⋊C4 | — | 5 | 4 | no | — |
| 420 | C22⋊C4 | — | 10 | 8 | no | — |
| 421 | C22⋊C4 | — | 10 | 8 | no | — |
| 422 | C22⋊C4 | — | 10 | 8 | no | — |
| 423 | C22⋊C4 | — | 10 | 2 | no | — |
| 424 | C42 | — | 2 | 2 | no | — |
| 425 | C42 | — | 5 | 4 | no | — |
| 426 | C42 | — | 5 | 2 | no | — |
| 427 | C42 | — | 10 | 8 | no | — |
| 428 | C42 | — | 10 | 2 | no | — |
| 429 | C42 | D4×D5 | 1 | 2 | yes | — |
| 430 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 431 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 432 | C2×C5 | — | 2 | 2 | no | — |
| 433 | C2×C5 | C2×#532 | 1 | 1 | yes | characteristic |
| 434 | C2×C5 | C2×#577 | 1 | 2 | yes | — |
| 435 | D5 | — | 4 | 2 | no | — |
| 436 | D5 | — | 8 | 4 | no | — |
| 437 | C23 | — | 5 | 2 | no | — |
| 438 | C23 | — | 10 | 4 | no | — |
| 439 | C23 | — | 20 | 4 | no | — |
| 440 | C23 | — | 40 | 4 | no | — |
| 441 | C23 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 442 | Q8 | — | 2 | 8 | no | — |
| 443 | Q8 | — | 4 | 4 | no | — |
| 444 | Q8 | — | 4 | 4 | no | — |
| 445 | Q8 | — | 10 | 2 | no | — |
| 446 | Q8 | — | 20 | 4 | no | — |
| 447 | D4 | — | 10 | 4 | no | — |
| 448 | D4 | — | 10 | 2 | no | — |
| 449 | D4 | — | 10 | 8 | no | — |
| 450 | D4 | — | 20 | 8 | no | — |
| 451 | D4 | — | 20 | 4 | no | — |
| 452 | D4 | — | 40 | 4 | no | — |
| 453 | D4 | — | 40 | 8 | no | — |
| 454 | C2×C4 | — | 2 | 4 | no | — |
| 455 | C2×C4 | — | 2 | 4 | no | — |
| 456 | C2×C4 | — | 2 | 4 | no | — |
| 457 | C2×C4 | — | 4 | 4 | no | — |
| 458 | C2×C4 | — | 5 | 4 | no | — |
| 459 | C2×C4 | — | 5 | 2 | no | — |
| 460 | C2×C4 | — | 10 | 8 | no | — |
| 461 | C2×C4 | — | 10 | 4 | no | — |
| 462 | C2×C4 | — | 10 | 4 | no | — |
| 463 | C2×C4 | — | 40 | 8 | no | — |
| 464 | C2×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 465 | C2×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 466 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 467 | C2×C4 | D5×#41 | 1 | 4 | yes | — |
| 468 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 469 | C8 | — | 2 | 4 | no | — |
| 470 | C8 | — | 5 | 4 | no | — |
| 471 | C8 | — | 5 | 4 | no | — |
| 472 | C5 | #60712 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 473 | C22 | — | 2 | 2 | no | — |
| 474 | C22 | — | 10 | 2 | no | — |
| 475 | C22 | — | 10 | 4 | no | — |
| 476 | C22 | — | 20 | 4 | no | — |
| 477 | C22 | — | 20 | 8 | no | — |
| 478 | C22 | — | 80 | 4 | no | — |
| 479 | C22 | #66002 | 1 | 2 | yes | — |
| 480 | C22 | C22×D4×D5 | 1 | 1 | yes | characteristic |
| 481 | C4 | — | 2 | 2 | no | — |
| 482 | C4 | — | 4 | 4 | no | — |
| 483 | C4 | — | 4 | 4 | no | — |
| 484 | C4 | — | 10 | 2 | no | — |
| 485 | C4 | — | 10 | 4 | no | — |
| 486 | C4 | — | 20 | 4 | no | — |
| 487 | C4 | #66002 | 1 | 2 | yes | — |
| 488 | C4 | #66112 | 1 | 4 | yes | — |
| 489 | C4 | C2×D5×#41 | 1 | 2 | yes | — |
| 490 | C2 | — | 2 | 2 | no | — |
| 491 | C2 | — | 20 | 2 | no | — |
| 492 | C2 | — | 40 | 4 | no | — |
| 493 | C2 | C2×#66002 | 1 | 1 | yes | characteristic |
| 494 | C2 | C2×#66112 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10618105 | C2 | semidirect |
| 3. C5×#3139 | C2 | semidirect |
| 4. #10615070 | C2 | semidirect |
| 5. C2×#65374 | C2 | semidirect |
| 6. #10613460 | C2 | semidirect |
| 7. #10613326 | C2 | semidirect |
| 8. #10613323 | C2 | semidirect |
| 9. #10610694 | C2 | semidirect |
| 10. #10610678 | C2 | semidirect |
| 11. #10610257 | C2 | semidirect |
| 12. C4×#4053 | C2 | semidirect |
| 20. #66065 | C22 | semidirect |
| 21. #66062 | C22 | semidirect |
| 34. C5×#491 | C22 | semidirect |
| 35. C5×#487 | C22 | semidirect |
| 43. #65368 | C22 | semidirect |
| 44. #65367 | C22 | semidirect |
| 45. #65353 | C22 | semidirect |
| 48. #65106 | C22 | semidirect |
| 49. #65101 | C22 | semidirect |
| 50. #65096 | C22 | semidirect |
| 51. #65077 | C22 | semidirect |
| 53. #64997 | C22 | semidirect |
| 55. C4×#676 | C22 | semidirect |
| 56. C4×C8×D5 | C22 | semidirect |
| 138. #3139 | D5 | semidirect |
| 198. C2×#168 | #41 | semidirect |
| 230. #491 | C2×D5 | semidirect |
| 232. #487 | C2×D5 | semidirect |
| 472. C5 | #60712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10618162 | 2 |
| #10618105 | 2 |
| C5×#3139 | 2 |
| #10615070 | 2 |
| C2×#65374 | 2 |
| #10613460 | 2 |
| #10613326 | 2 |
| #10613323 | 2 |
| #10610694 | 2 |
| #10610678 | 2 |
| #10610257 | 2 |
| C4×#4053 | 2 |
| #60712 | 5 |