Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1984 conjugacy classes of subgroups.
The subgroup lattice has 502 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10617722 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×Q8×D20 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#2984 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10611706 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #10611704 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | Q8×#677 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10611655 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10611074 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #10611054 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #10611031 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #10611000 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C22×Q8×D5 | — | 2 | 1 | no | — |
| 13 | C2×C4×C5×Q8 | C22 | 1 | 1 | yes | characteristic |
| 14 | #66151 | — | 2 | 1 | no | — |
| 15 | #65919 | C22 | 1 | 3 | yes | complemented |
| 16 | #65916 | — | 2 | 3 | no | — |
| 17 | #65913 | C22 | 1 | 3 | yes | complemented |
| 18 | #65911 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | Q8×D20 | — | 2 | 1 | no | — |
| 20 | Q8×D20 | — | 2 | 3 | no | — |
| 21 | Q8×D20 | C22 | 1 | 2 | yes | — |
| 22 | Q8×D20 | C22 | 1 | 6 | yes | — |
| 23 | #65908 | — | 2 | 1 | no | — |
| 24 | Q8×Dic10 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#4043 | — | 2 | 3 | no | — |
| 26 | #65841 | — | 2 | 3 | no | — |
| 27 | #65813 | C22 | 1 | 3 | yes | — |
| 28 | #65811 | C22 | 1 | 3 | yes | — |
| 29 | C2×C4×D20 | C22 | 1 | 3 | yes | — |
| 30 | C2×#4015 | C22 | 1 | 3 | yes | — |
| 31 | C5×#446 | C22 | 1 | 6 | yes | complemented |
| 32 | C5×C8×Q8 | C22 | 1 | 2 | yes | complemented |
| 33 | C5×#432 | C22 | 1 | 3 | yes | — |
| 34 | C5×#431 | C22 | 1 | 3 | yes | — |
| 35 | #65140 | C22 | 1 | 6 | yes | complemented |
| 36 | #65136 | C22 | 1 | 6 | yes | — |
| 37 | #65135 | C22 | 1 | 6 | yes | complemented |
| 38 | #65133 | C22 | 1 | 6 | yes | — |
| 39 | #65132 | C22 | 1 | 6 | yes | — |
| 40 | #65131 | C22 | 1 | 6 | yes | — |
| 41 | #65131 | C22 | 1 | 12 | yes | complemented |
| 42 | #65024 | C22 | 1 | 3 | yes | — |
| 43 | #65024 | C22 | 1 | 6 | yes | — |
| 44 | #65021 | C22 | 1 | 3 | yes | — |
| 45 | #65020 | C22 | 1 | 1 | yes | characteristic |
| 46 | #65011 | C22 | 1 | 3 | yes | — |
| 47 | #65003 | C22 | 1 | 6 | yes | complemented |
| 48 | #65000 | C22 | 1 | 12 | yes | — |
| 49 | #64991 | C22 | 1 | 6 | yes | complemented |
| 50 | #64983 | C22 | 1 | 6 | yes | complemented |
| 51 | C4×D40 | C22 | 1 | 6 | yes | — |
| 52 | C4×#677 | C22 | 1 | 6 | yes | — |
| 53 | #64969 | C22 | 1 | 6 | yes | complemented |
| 54 | #61843 | — | 5 | 1 | no | maximal, Sylow |
| 55 | C22×C5×Q8 | D4 | 1 | 1 | yes | characteristic |
| 56 | C2×#713 | — | 2 | 1 | no | — |
| 57 | C2×Q8×D5 | — | 2 | 6 | no | — |
| 58 | C2×Q8×D5 | — | 2 | 2 | no | — |
| 59 | C2×Q8×D5 | — | 4 | 8 | no | — |
| 60 | C2×#709 | — | 2 | 3 | no | — |
| 61 | C22×D20 | C23 | 1 | 1 | yes | characteristic |
| 62 | C22×C4×D5 | — | 2 | 3 | no | — |
| 63 | C22×Dic10 | — | 2 | 3 | no | — |
| 64 | C4×C5×Q8 | D4 | 1 | 1 | yes | characteristic |
| 65 | C4×C5×Q8 | D4 | 1 | 3 | yes | — |
| 66 | C4×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 67 | C4×C5×Q8 | C23 | 1 | 3 | yes | — |
| 68 | C2×C5×C4⋊C4 | D4 | 1 | 3 | yes | — |
| 69 | C2×C42×C5 | C23 | 1 | 3 | yes | — |
| 70 | #4093 | — | 2 | 3 | no | — |
| 71 | #4092 | — | 2 | 3 | no | — |
| 72 | Q8×Dic5 | — | 2 | 1 | no | — |
| 73 | #4076 | — | 2 | 3 | no | — |
| 74 | #4076 | C23 | 1 | 3 | yes | — |
| 75 | #4075 | — | 2 | 3 | no | — |
| 76 | C4×C22⋊D5 | — | 2 | 3 | no | — |
| 77 | C2×#685 | — | 2 | 3 | no | — |
| 78 | C2×C4⋊Dic5 | — | 2 | 3 | no | — |
| 79 | C2×C4⋊Dic5 | C23 | 1 | 3 | yes | — |
| 80 | #4070 | C23 | 1 | 1 | yes | characteristic |
| 81 | C2×D40 | C23 | 1 | 6 | yes | — |
| 82 | C2×#677 | C23 | 1 | 2 | yes | — |
| 83 | #4043 | — | 2 | 6 | no | — |
| 84 | #4043 | — | 2 | 6 | no | — |
| 85 | #4043 | — | 2 | 12 | no | — |
| 86 | #4042 | — | 2 | 6 | no | — |
| 87 | #4041 | — | 2 | 3 | no | — |
| 88 | #4040 | — | 2 | 6 | no | — |
| 89 | #4039 | — | 2 | 3 | no | — |
| 90 | D5×C4⋊C4 | — | 2 | 3 | no | — |
| 91 | #4034 | — | 2 | 3 | no | — |
| 92 | #4022 | — | 2 | 3 | no | — |
| 93 | #4021 | — | 2 | 3 | no | — |
| 94 | #4021 | C23 | 1 | 3 | yes | — |
| 95 | #4020 | C23 | 1 | 3 | yes | — |
| 96 | C4×D20 | — | 2 | 3 | no | — |
| 97 | C4×D20 | — | 2 | 3 | no | — |
| 98 | C4×D20 | — | 2 | 3 | no | — |
| 99 | C4×D20 | C23 | 1 | 6 | yes | — |
| 100 | C4×D20 | C23 | 1 | 6 | yes | — |
| 101 | C4×D20 | C23 | 1 | 6 | yes | — |
| 102 | C4×D20 | C23 | 1 | 3 | yes | — |
| 103 | #4018 | — | 2 | 3 | no | — |
| 104 | #4016 | C23 | 1 | 3 | yes | — |
| 105 | #4015 | — | 2 | 3 | no | — |
| 106 | #4015 | — | 2 | 3 | no | — |
| 107 | #4015 | C23 | 1 | 6 | yes | — |
| 108 | #4015 | C23 | 1 | 6 | yes | — |
| 109 | #4015 | C23 | 1 | 3 | yes | — |
| 110 | C4×Dic10 | C23 | 1 | 3 | yes | — |
| 111 | C5×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 112 | C5×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 113 | C5×C22⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 114 | C5×C22⋊C8 | C23 | 1 | 3 | yes | — |
| 115 | C5×#97 | C23 | 1 | 6 | yes | — |
| 116 | C4×C5×C8 | C23 | 1 | 6 | yes | — |
| 117 | #3953 | C23 | 1 | 6 | yes | — |
| 118 | #3953 | C23 | 1 | 12 | yes | — |
| 119 | #3953 | C23 | 1 | 6 | yes | — |
| 120 | #3953 | C23 | 1 | 2 | yes | — |
| 121 | #3950 | C23 | 1 | 6 | yes | — |
| 122 | #3949 | C23 | 1 | 12 | yes | — |
| 123 | #3949 | C23 | 1 | 6 | yes | — |
| 124 | #3948 | C23 | 1 | 6 | yes | — |
| 125 | #3522 | — | 5 | 1 | no | — |
| 126 | C2×D4×Q8 | — | 5 | 1 | no | — |
| 127 | #3384 | — | 5 | 6 | no | — |
| 128 | Q8×SD16 | — | 5 | 2 | no | — |
| 129 | #3373 | — | 5 | 6 | no | — |
| 130 | #3358 | — | 5 | 2 | no | — |
| 131 | #3239 | — | 5 | 3 | no | — |
| 132 | #3227 | — | 5 | 3 | no | — |
| 133 | #3109 | — | 5 | 3 | no | — |
| 134 | #3105 | — | 5 | 3 | no | — |
| 135 | #2984 | D5 | 1 | 1 | yes | characteristic, complemented |
| 136 | C23×D5 | — | 2 | 1 | no | — |
| 137 | C2×C5×Q8 | — | 2 | 4 | no | — |
| 138 | C2×C5×Q8 | C2×D4 | 1 | 3 | yes | — |
| 139 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C22×C4×C5 | C2×D4 | 1 | 3 | yes | — |
| 141 | C22×C4×C5 | C2×D4 | 1 | 3 | yes | — |
| 142 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 143 | C2×C22⋊D5 | — | 2 | 3 | no | — |
| 144 | C22×Dic5 | — | 2 | 3 | no | — |
| 145 | #713 | — | 4 | 4 | no | — |
| 146 | Q8×D5 | — | 4 | 24 | no | — |
| 147 | Q8×D5 | — | 4 | 8 | no | — |
| 148 | #709 | — | 8 | 6 | no | — |
| 149 | C2×D20 | — | 2 | 1 | no | — |
| 150 | C2×D20 | — | 2 | 4 | no | — |
| 151 | C2×D20 | — | 2 | 3 | no | — |
| 152 | C2×D20 | — | 2 | 3 | no | — |
| 153 | C2×D20 | C24 | 1 | 3 | yes | — |
| 154 | C2×D20 | C24 | 1 | 2 | yes | — |
| 155 | C2×C4×D5 | — | 2 | 6 | no | — |
| 156 | C2×C4×D5 | — | 2 | 6 | no | — |
| 157 | C2×C4×D5 | — | 2 | 3 | no | — |
| 158 | C2×C4×D5 | — | 2 | 6 | no | — |
| 159 | C2×C4×D5 | — | 4 | 12 | no | — |
| 160 | C2×Dic10 | — | 2 | 6 | no | — |
| 161 | C2×Dic10 | — | 2 | 6 | no | — |
| 162 | C2×Dic10 | — | 2 | 3 | no | — |
| 163 | C2×Dic10 | — | 4 | 12 | no | — |
| 164 | C2×Dic10 | C24 | 1 | 1 | yes | characteristic |
| 165 | C2×C5×C8 | C24 | 1 | 6 | yes | — |
| 166 | C2×C5×C8 | C24 | 1 | 2 | yes | — |
| 167 | C5×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 168 | C5×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 169 | C5×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 170 | C42×C5 | C2×D4 | 1 | 3 | yes | — |
| 171 | C42×C5 | C2×D4 | 1 | 3 | yes | — |
| 172 | C42×C5 | C24 | 1 | 3 | yes | — |
| 173 | C42×C5 | C24 | 1 | 3 | yes | — |
| 174 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 175 | #685 | — | 2 | 3 | no | — |
| 176 | #685 | — | 2 | 3 | no | — |
| 177 | #685 | — | 2 | 6 | no | — |
| 178 | #685 | — | 2 | 6 | no | — |
| 179 | #685 | — | 2 | 6 | no | — |
| 180 | #685 | — | 2 | 3 | no | — |
| 181 | #685 | — | 2 | 3 | no | — |
| 182 | C4⋊Dic5 | — | 2 | 3 | no | — |
| 183 | C4⋊Dic5 | — | 2 | 6 | no | — |
| 184 | C4⋊Dic5 | — | 2 | 6 | no | — |
| 185 | C4⋊Dic5 | — | 2 | 3 | no | — |
| 186 | C4⋊Dic5 | C24 | 1 | 6 | yes | — |
| 187 | C4⋊Dic5 | C24 | 1 | 3 | yes | — |
| 188 | C4⋊Dic5 | C24 | 1 | 1 | yes | characteristic |
| 189 | #683 | — | 2 | 3 | no | — |
| 190 | #683 | — | 2 | 3 | no | — |
| 191 | #683 | — | 2 | 3 | no | — |
| 192 | #683 | — | 2 | 1 | no | — |
| 193 | C4×Dic5 | — | 2 | 3 | no | — |
| 194 | D40 | — | 2 | 12 | no | — |
| 195 | #677 | — | 2 | 4 | no | — |
| 196 | C23×Q8 | — | 10 | 1 | no | — |
| 197 | #559 | — | 5 | 3 | no | — |
| 198 | Q82 | — | 5 | 1 | no | — |
| 199 | #554 | — | 5 | 3 | no | — |
| 200 | #550 | — | 5 | 1 | no | — |
| 201 | D4×Q8 | — | 5 | 2 | no | — |
| 202 | D4×Q8 | — | 5 | 6 | no | — |
| 203 | D4×Q8 | — | 10 | 1 | no | — |
| 204 | D4×Q8 | — | 10 | 3 | no | — |
| 205 | #548 | — | 10 | 1 | no | — |
| 206 | #547 | — | 10 | 3 | no | — |
| 207 | #542 | — | 10 | 3 | no | — |
| 208 | #532 | — | 5 | 3 | no | — |
| 209 | C2×C4⋊Q8 | — | 5 | 3 | no | — |
| 210 | #529 | — | 5 | 3 | no | — |
| 211 | C2×C22⋊Q8 | — | 10 | 3 | no | — |
| 212 | #520 | — | 10 | 1 | no | — |
| 213 | C2×C4×Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 214 | C2×C4×D4 | — | 5 | 3 | no | — |
| 215 | #501 | — | 5 | 6 | no | — |
| 216 | #498 | — | 5 | 6 | no | — |
| 217 | #489 | — | 5 | 6 | no | — |
| 218 | #486 | — | 5 | 6 | no | — |
| 219 | #484 | — | 5 | 3 | no | — |
| 220 | #481 | — | 5 | 3 | no | — |
| 221 | #481 | — | 5 | 6 | no | — |
| 222 | #478 | — | 5 | 6 | no | — |
| 223 | #476 | — | 5 | 6 | no | — |
| 224 | #476 | — | 5 | 12 | no | — |
| 225 | #475 | — | 5 | 6 | no | — |
| 226 | #474 | — | 5 | 6 | no | — |
| 227 | #463 | — | 5 | 6 | no | — |
| 228 | #459 | — | 5 | 6 | no | — |
| 229 | #450 | — | 5 | 1 | no | — |
| 230 | #447 | — | 5 | 3 | no | — |
| 231 | #446 | C2×D5 | 1 | 6 | yes | complemented |
| 232 | C8×Q8 | C2×D5 | 1 | 2 | yes | complemented |
| 233 | #442 | — | 5 | 12 | no | — |
| 234 | C4×SD16 | — | 5 | 6 | no | — |
| 235 | C4×D8 | — | 5 | 6 | no | — |
| 236 | #432 | C2×D5 | 1 | 3 | yes | — |
| 237 | #431 | C2×D5 | 1 | 3 | yes | — |
| 238 | C23×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 239 | C22×D5 | — | 2 | 4 | no | — |
| 240 | C22×D5 | — | 2 | 2 | no | — |
| 241 | C22×D5 | — | 2 | 3 | no | — |
| 242 | C22×D5 | — | 4 | 2 | no | — |
| 243 | C22×D5 | — | 4 | 2 | no | — |
| 244 | C5×Q8 | — | 2 | 6 | no | — |
| 245 | C5×Q8 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 246 | C2×C4×C5 | — | 2 | 6 | no | — |
| 247 | C2×C4×C5 | — | 2 | 6 | no | — |
| 248 | C2×C4×C5 | — | 2 | 2 | no | — |
| 249 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 250 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 251 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 252 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 253 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 254 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 255 | C22⋊D5 | — | 4 | 6 | no | — |
| 256 | C2×Dic5 | — | 2 | 1 | no | — |
| 257 | C2×Dic5 | — | 2 | 3 | no | — |
| 258 | C2×Dic5 | — | 2 | 1 | no | — |
| 259 | C2×Dic5 | — | 2 | 6 | no | — |
| 260 | C2×Dic5 | — | 4 | 6 | no | — |
| 261 | D20 | — | 2 | 4 | no | — |
| 262 | D20 | — | 2 | 2 | no | — |
| 263 | D20 | — | 2 | 6 | no | — |
| 264 | D20 | — | 4 | 6 | no | — |
| 265 | D20 | — | 8 | 3 | no | — |
| 266 | D20 | 2−1+4 | 1 | 4 | yes | — |
| 267 | C4×D5 | — | 4 | 12 | no | — |
| 268 | C4×D5 | — | 4 | 12 | no | — |
| 269 | C4×D5 | — | 4 | 6 | no | — |
| 270 | C4×D5 | — | 8 | 6 | no | — |
| 271 | Dic10 | — | 2 | 2 | no | — |
| 272 | Dic10 | — | 4 | 12 | no | — |
| 273 | Dic10 | — | 4 | 12 | no | — |
| 274 | Dic10 | — | 8 | 3 | no | — |
| 275 | C5×C8 | — | 2 | 2 | no | — |
| 276 | C5×C8 | — | 2 | 6 | no | — |
| 277 | C2×#41 | — | 10 | 1 | no | — |
| 278 | C2×#41 | — | 10 | 3 | no | — |
| 279 | C22×Q8 | — | 10 | 6 | no | — |
| 280 | C22×Q8 | — | 10 | 2 | no | — |
| 281 | C22×Q8 | — | 10 | 3 | no | — |
| 282 | C22×Q8 | — | 20 | 8 | no | — |
| 283 | C22×Q8 | D20 | 1 | 1 | yes | characteristic |
| 284 | C22×D4 | — | 5 | 1 | no | — |
| 285 | C23×C4 | — | 10 | 3 | no | — |
| 286 | C2×SD16 | — | 5 | 2 | no | — |
| 287 | C2×D8 | — | 5 | 6 | no | — |
| 288 | C4⋊Q8 | — | 5 | 6 | no | — |
| 289 | C4⋊Q8 | — | 5 | 6 | no | — |
| 290 | C4⋊Q8 | — | 5 | 3 | no | — |
| 291 | C4⋊Q8 | — | 10 | 3 | no | — |
| 292 | C4⋊Q8 | — | 10 | 3 | no | — |
| 293 | C4⋊Q8 | — | 10 | 3 | no | — |
| 294 | #127 | — | 5 | 3 | no | — |
| 295 | #126 | — | 10 | 3 | no | — |
| 296 | #125 | — | 5 | 3 | no | — |
| 297 | #124 | — | 5 | 3 | no | — |
| 298 | #124 | — | 10 | 3 | no | — |
| 299 | #124 | — | 10 | 3 | no | — |
| 300 | #123 | — | 10 | 3 | no | — |
| 301 | #123 | — | 10 | 6 | no | — |
| 302 | C22⋊Q8 | — | 5 | 1 | no | — |
| 303 | C22⋊Q8 | — | 10 | 3 | no | — |
| 304 | C22⋊Q8 | — | 10 | 6 | no | — |
| 305 | C22⋊Q8 | — | 10 | 6 | no | — |
| 306 | C22⋊Q8 | — | 10 | 12 | no | — |
| 307 | C22⋊Q8 | — | 10 | 6 | no | — |
| 308 | #121 | — | 5 | 3 | no | — |
| 309 | #121 | — | 10 | 3 | no | — |
| 310 | #121 | — | 10 | 3 | no | — |
| 311 | C4×Q8 | — | 5 | 3 | no | — |
| 312 | C4×Q8 | — | 10 | 1 | no | — |
| 313 | C4×Q8 | D20 | 1 | 1 | yes | characteristic |
| 314 | C4×Q8 | D20 | 1 | 3 | yes | — |
| 315 | C4×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 316 | C4×Q8 | C22×D5 | 1 | 3 | yes | — |
| 317 | C4×D4 | — | 5 | 6 | no | — |
| 318 | C4×D4 | — | 5 | 6 | no | — |
| 319 | C4×D4 | — | 5 | 3 | no | — |
| 320 | C4×D4 | — | 5 | 6 | no | — |
| 321 | C4×D4 | — | 10 | 3 | no | — |
| 322 | C4×D4 | — | 10 | 3 | no | — |
| 323 | C4×D4 | — | 10 | 3 | no | — |
| 324 | C4×D4 | — | 10 | 3 | no | — |
| 325 | C4×D4 | — | 10 | 3 | no | — |
| 326 | #117 | — | 10 | 3 | no | — |
| 327 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 328 | C2×C4⋊C4 | — | 10 | 3 | no | — |
| 329 | C2×C4⋊C4 | — | 10 | 3 | no | — |
| 330 | C2×C4⋊C4 | D20 | 1 | 3 | yes | — |
| 331 | C2×C22⋊C4 | — | 10 | 3 | no | — |
| 332 | C2×C42 | C22×D5 | 1 | 3 | yes | — |
| 333 | #107 | — | 5 | 6 | no | — |
| 334 | #106 | — | 5 | 6 | no | — |
| 335 | #106 | — | 5 | 12 | no | — |
| 336 | C4⋊C8 | C22×D5 | 1 | 6 | yes | — |
| 337 | C4⋊C8 | C22×D5 | 1 | 6 | yes | — |
| 338 | #103 | — | 5 | 6 | no | — |
| 339 | #102 | — | 5 | 2 | no | — |
| 340 | #102 | — | 5 | 6 | no | — |
| 341 | #102 | — | 5 | 6 | no | — |
| 342 | #102 | — | 5 | 12 | no | — |
| 343 | C22⋊C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 344 | C22⋊C8 | C22×D5 | 1 | 3 | yes | — |
| 345 | #97 | C22×D5 | 1 | 6 | yes | — |
| 346 | C4×C8 | C22×D5 | 1 | 6 | yes | — |
| 347 | C22×C5 | — | 2 | 1 | no | — |
| 348 | C22×C5 | — | 2 | 1 | no | — |
| 349 | C22×C5 | #577 | 1 | 2 | yes | — |
| 350 | C22×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 351 | C2×D5 | — | 2 | 4 | no | — |
| 352 | C2×D5 | — | 4 | 8 | no | — |
| 353 | C2×D5 | — | 4 | 2 | no | — |
| 354 | C2×D5 | — | 4 | 2 | no | — |
| 355 | C2×D5 | — | 4 | 3 | no | — |
| 356 | C2×D5 | — | 4 | 3 | no | — |
| 357 | C2×D5 | — | 4 | 3 | no | — |
| 358 | C4×C5 | — | 2 | 1 | no | — |
| 359 | C4×C5 | — | 2 | 3 | no | — |
| 360 | C4×C5 | — | 2 | 3 | no | — |
| 361 | C4×C5 | — | 2 | 3 | no | — |
| 362 | C4×C5 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 363 | C4×C5 | C2×2−1+4 | 1 | 2 | yes | — |
| 364 | Dic5 | — | 4 | 1 | no | — |
| 365 | Dic5 | — | 4 | 6 | no | — |
| 366 | Dic5 | — | 4 | 1 | no | — |
| 367 | Dic5 | — | 4 | 3 | no | — |
| 368 | C24 | — | 10 | 1 | no | — |
| 369 | #41 | — | 20 | 4 | no | — |
| 370 | #41 | — | 40 | 6 | no | — |
| 371 | C2×Q8 | — | 2 | 4 | no | — |
| 372 | C2×Q8 | — | 5 | 1 | no | — |
| 373 | C2×Q8 | — | 10 | 6 | no | — |
| 374 | C2×Q8 | — | 10 | 6 | no | — |
| 375 | C2×Q8 | — | 10 | 3 | no | — |
| 376 | C2×Q8 | — | 20 | 12 | no | — |
| 377 | C2×Q8 | — | 20 | 24 | no | — |
| 378 | C2×Q8 | — | 20 | 8 | no | — |
| 379 | C2×Q8 | C2×D20 | 1 | 3 | yes | — |
| 380 | C2×Q8 | C2×D20 | 1 | 1 | yes | characteristic |
| 381 | C2×D4 | — | 5 | 2 | no | — |
| 382 | C2×D4 | — | 5 | 3 | no | — |
| 383 | C2×D4 | — | 10 | 4 | no | — |
| 384 | C2×D4 | — | 10 | 3 | no | — |
| 385 | C2×D4 | — | 10 | 1 | no | — |
| 386 | C2×D4 | — | 10 | 3 | no | — |
| 387 | C2×D4 | — | 10 | 3 | no | — |
| 388 | C22×C4 | — | 10 | 3 | no | — |
| 389 | C22×C4 | — | 10 | 3 | no | — |
| 390 | C22×C4 | — | 10 | 6 | no | — |
| 391 | C22×C4 | — | 10 | 6 | no | — |
| 392 | C22×C4 | — | 10 | 6 | no | — |
| 393 | C22×C4 | — | 20 | 12 | no | — |
| 394 | C22×C4 | C2×D20 | 1 | 3 | yes | — |
| 395 | C22×C4 | C2×D20 | 1 | 3 | yes | — |
| 396 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 397 | SD16 | — | 10 | 4 | no | — |
| 398 | D8 | — | 10 | 12 | no | — |
| 399 | C2×C8 | C23×D5 | 1 | 2 | yes | — |
| 400 | C2×C8 | C23×D5 | 1 | 6 | yes | — |
| 401 | C4⋊C4 | — | 5 | 6 | no | — |
| 402 | C4⋊C4 | — | 5 | 3 | no | — |
| 403 | C4⋊C4 | — | 5 | 1 | no | — |
| 404 | C4⋊C4 | — | 10 | 3 | no | — |
| 405 | C4⋊C4 | — | 10 | 3 | no | — |
| 406 | C4⋊C4 | — | 10 | 3 | no | — |
| 407 | C4⋊C4 | — | 10 | 6 | no | — |
| 408 | C4⋊C4 | — | 10 | 6 | no | — |
| 409 | C4⋊C4 | — | 10 | 1 | no | — |
| 410 | C4⋊C4 | — | 10 | 3 | no | — |
| 411 | C4⋊C4 | — | 10 | 3 | no | — |
| 412 | C4⋊C4 | C2×D20 | 1 | 3 | yes | — |
| 413 | C4⋊C4 | C2×D20 | 1 | 3 | yes | — |
| 414 | C4⋊C4 | C2×D20 | 1 | 6 | yes | — |
| 415 | C22⋊C4 | — | 10 | 1 | no | — |
| 416 | C22⋊C4 | — | 10 | 6 | no | — |
| 417 | C22⋊C4 | — | 10 | 6 | no | — |
| 418 | C22⋊C4 | — | 10 | 3 | no | — |
| 419 | C22⋊C4 | — | 10 | 3 | no | — |
| 420 | C22⋊C4 | — | 10 | 3 | no | — |
| 421 | C22⋊C4 | — | 10 | 6 | no | — |
| 422 | C22⋊C4 | — | 10 | 3 | no | — |
| 423 | C42 | — | 10 | 3 | no | — |
| 424 | C42 | C2×D20 | 1 | 3 | yes | — |
| 425 | C42 | C2×D20 | 1 | 3 | yes | — |
| 426 | C42 | C23×D5 | 1 | 3 | yes | — |
| 427 | C42 | C23×D5 | 1 | 3 | yes | — |
| 428 | C2×C5 | — | 2 | 2 | no | — |
| 429 | C2×C5 | #3486 | 1 | 1 | yes | characteristic |
| 430 | C2×C5 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 431 | C2×C5 | C2×#577 | 1 | 1 | yes | characteristic |
| 432 | D5 | — | 4 | 4 | no | — |
| 433 | D5 | — | 8 | 3 | no | — |
| 434 | C23 | — | 10 | 4 | no | — |
| 435 | C23 | — | 10 | 2 | no | — |
| 436 | C23 | — | 10 | 3 | no | — |
| 437 | C23 | — | 20 | 2 | no | — |
| 438 | C23 | — | 20 | 2 | no | — |
| 439 | C23 | C22×D20 | 1 | 1 | yes | characteristic |
| 440 | Q8 | — | 2 | 6 | no | — |
| 441 | Q8 | — | 10 | 2 | no | — |
| 442 | Q8 | — | 20 | 12 | no | — |
| 443 | Q8 | — | 20 | 12 | no | — |
| 444 | Q8 | — | 40 | 3 | no | — |
| 445 | Q8 | #4054 | 1 | 4 | yes | — |
| 446 | D4 | — | 5 | 4 | no | — |
| 447 | D4 | — | 10 | 4 | no | — |
| 448 | D4 | — | 10 | 2 | no | — |
| 449 | D4 | — | 10 | 6 | no | — |
| 450 | D4 | — | 20 | 6 | no | — |
| 451 | D4 | — | 20 | 6 | no | — |
| 452 | D4 | — | 40 | 3 | no | — |
| 453 | C2×C4 | — | 2 | 6 | no | — |
| 454 | C2×C4 | — | 2 | 6 | no | — |
| 455 | C2×C4 | — | 2 | 2 | no | — |
| 456 | C2×C4 | — | 10 | 1 | no | — |
| 457 | C2×C4 | — | 10 | 3 | no | — |
| 458 | C2×C4 | — | 10 | 1 | no | — |
| 459 | C2×C4 | — | 10 | 6 | no | — |
| 460 | C2×C4 | — | 20 | 12 | no | — |
| 461 | C2×C4 | — | 20 | 6 | no | — |
| 462 | C2×C4 | — | 20 | 12 | no | — |
| 463 | C2×C4 | — | 20 | 6 | no | — |
| 464 | C2×C4 | — | 40 | 6 | no | — |
| 465 | C2×C4 | C22×D20 | 1 | 1 | yes | characteristic |
| 466 | C2×C4 | C22×D20 | 1 | 3 | yes | — |
| 467 | C2×C4 | C22×D20 | 1 | 3 | yes | — |
| 468 | C2×C4 | C22×D20 | 1 | 3 | yes | — |
| 469 | C2×C4 | C22×D20 | 1 | 3 | yes | — |
| 470 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 471 | C8 | — | 2 | 6 | no | — |
| 472 | C8 | — | 2 | 2 | no | — |
| 473 | C5 | #61843 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 474 | C22 | — | 2 | 1 | no | — |
| 475 | C22 | — | 2 | 1 | no | — |
| 476 | C22 | — | 10 | 4 | no | — |
| 477 | C22 | — | 20 | 8 | no | — |
| 478 | C22 | — | 20 | 2 | no | — |
| 479 | C22 | — | 20 | 2 | no | — |
| 480 | C22 | — | 20 | 3 | no | — |
| 481 | C22 | — | 20 | 3 | no | — |
| 482 | C22 | — | 20 | 3 | no | — |
| 483 | C22 | #66085 | 1 | 2 | yes | — |
| 484 | C22 | C23×D20 | 1 | 1 | yes | characteristic |
| 485 | C4 | — | 2 | 3 | no | — |
| 486 | C4 | — | 2 | 1 | no | — |
| 487 | C4 | — | 2 | 3 | no | — |
| 488 | C4 | — | 2 | 3 | no | — |
| 489 | C4 | — | 20 | 6 | no | — |
| 490 | C4 | — | 20 | 1 | no | — |
| 491 | C4 | — | 20 | 1 | no | — |
| 492 | C4 | — | 20 | 3 | no | — |
| 493 | C4 | C2×#4054 | 1 | 6 | yes | — |
| 494 | C4 | D5×2−1+4 | 1 | 2 | yes | — |
| 495 | C2 | — | 2 | 2 | no | — |
| 496 | C2 | — | 20 | 4 | no | — |
| 497 | C2 | — | 40 | 3 | no | — |
| 498 | C2 | #10617782 | 1 | 1 | yes | characteristic |
| 499 | C2 | C22×#4054 | 1 | 1 | yes | characteristic |
| 500 | C2 | C2×#66085 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10617722 | C2 | semidirect |
| 2. C2×Q8×D20 | C2 | semidirect |
| 3. C5×#2984 | C2 | semidirect |
| 4. #10611706 | C2 | semidirect |
| 5. #10611704 | C2 | semidirect |
| 6. Q8×#677 | C2 | semidirect |
| 7. #10611655 | C2 | semidirect |
| 8. #10611074 | C2 | semidirect |
| 9. #10611054 | C2 | semidirect |
| 10. #10611031 | C2 | semidirect |
| 11. #10611000 | C2 | semidirect |
| 15. #65919 | C22 | semidirect |
| 17. #65913 | C22 | semidirect |
| 18. #65911 | C22 | semidirect |
| 24. Q8×Dic10 | C22 | semidirect |
| 31. C5×#446 | C22 | semidirect |
| 32. C5×C8×Q8 | C22 | semidirect |
| 35. #65140 | C22 | semidirect |
| 37. #65135 | C22 | semidirect |
| 41. #65131 | C22 | semidirect |
| 47. #65003 | C22 | semidirect |
| 49. #64991 | C22 | semidirect |
| 50. #64983 | C22 | semidirect |
| 53. #64969 | C22 | semidirect |
| 135. #2984 | D5 | semidirect |
| 231. #446 | C2×D5 | semidirect |
| 232. C8×Q8 | C2×D5 | semidirect |
| 473. C5 | #61843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617722 | 2 |
| C2×Q8×D20 | 2 |
| C5×#2984 | 2 |
| #10611706 | 2 |
| #10611704 | 2 |
| Q8×#677 | 2 |
| #10611655 | 2 |
| #10611074 | 2 |
| #10611054 | 2 |
| #10611031 | 2 |
| #10611000 | 2 |
| #61843 | 5 |