Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2018 conjugacy classes of subgroups.
The subgroup lattice has 648 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10618164 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10618144 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#3135 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10615068 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10615020 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10613472 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10613449 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10613420 | C2 | 1 | 8 | yes | maximal, complemented |
| 9 | #10610596 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10610594 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10610568 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10610567 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | C2×#65004 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #10610220 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C2×#4150 | C22 | 1 | 2 | yes | — |
| 16 | C5×#533 | C22 | 1 | 1 | yes | characteristic |
| 17 | C5×#532 | C22 | 1 | 1 | yes | characteristic |
| 18 | #66159 | C22 | 1 | 2 | yes | — |
| 19 | C2×#4097 | C22 | 1 | 2 | yes | — |
| 20 | C2×#4095 | C22 | 1 | 2 | yes | — |
| 21 | C22×Dic20 | C22 | 1 | 2 | yes | — |
| 22 | C22×#677 | C22 | 1 | 2 | yes | — |
| 23 | #66067 | C22 | 1 | 4 | yes | — |
| 24 | D5×C4⋊Q8 | C22 | 1 | 2 | yes | complemented |
| 25 | #66050 | C22 | 1 | 2 | yes | complemented |
| 26 | #66025 | C22 | 1 | 4 | yes | — |
| 27 | #66009 | C22 | 1 | 4 | yes | complemented |
| 28 | #65971 | — | 2 | 4 | no | — |
| 29 | #65945 | — | 2 | 4 | no | — |
| 30 | #65919 | — | 2 | 2 | no | — |
| 31 | #65918 | — | 2 | 2 | no | — |
| 32 | #65885 | — | 2 | 2 | no | — |
| 33 | D4×Dic10 | — | 2 | 2 | no | — |
| 34 | #65860 | C22 | 1 | 1 | yes | characteristic |
| 35 | #65859 | C22 | 1 | 1 | yes | characteristic |
| 36 | #65855 | C22 | 1 | 1 | yes | characteristic |
| 37 | #65850 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×#4021 | C22 | 1 | 1 | yes | characteristic |
| 39 | C4×#709 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#4015 | C22 | 1 | 1 | yes | characteristic |
| 41 | C5×#491 | C22 | 1 | 2 | yes | complemented |
| 42 | C5×#490 | C22 | 1 | 2 | yes | complemented |
| 43 | C5×#489 | C22 | 1 | 4 | yes | complemented |
| 44 | C5×#416 | C22 | 1 | 2 | yes | — |
| 45 | C5×#416 | C22 | 1 | 2 | yes | — |
| 46 | C2×C5×#97 | C22 | 1 | 1 | yes | characteristic |
| 47 | #65399 | C22 | 1 | 2 | yes | — |
| 48 | #65391 | C22 | 1 | 2 | yes | — |
| 49 | #65382 | C22 | 1 | 4 | yes | complemented |
| 50 | #65375 | C22 | 1 | 2 | yes | — |
| 51 | #65363 | C22 | 1 | 2 | yes | — |
| 52 | #65358 | C22 | 1 | 4 | yes | complemented |
| 53 | #65348 | C22 | 1 | 4 | yes | — |
| 54 | #65293 | C22 | 1 | 2 | yes | — |
| 55 | #65293 | C22 | 1 | 2 | yes | — |
| 56 | C4×#681 | C22 | 1 | 1 | yes | characteristic |
| 57 | #65107 | C22 | 1 | 8 | yes | — |
| 58 | #65097 | C22 | 1 | 8 | yes | complemented |
| 59 | #65095 | C22 | 1 | 8 | yes | — |
| 60 | #65082 | C22 | 1 | 8 | yes | complemented |
| 61 | #65076 | C22 | 1 | 8 | yes | — |
| 62 | #65072 | C22 | 1 | 8 | yes | complemented |
| 63 | #65070 | C22 | 1 | 8 | yes | — |
| 64 | #65056 | C22 | 1 | 8 | yes | complemented |
| 65 | #65004 | C22 | 1 | 4 | yes | — |
| 66 | #65004 | C22 | 1 | 4 | yes | — |
| 67 | #64998 | C22 | 1 | 4 | yes | complemented |
| 68 | #64994 | C22 | 1 | 4 | yes | complemented |
| 69 | #60828 | — | 5 | 1 | no | maximal, Sylow |
| 70 | C2×C5×#41 | C23 | 1 | 2 | yes | — |
| 71 | #4150 | — | 4 | 4 | no | — |
| 72 | #4150 | — | 4 | 4 | no | — |
| 73 | C2×Q8×D5 | C23 | 1 | 4 | yes | — |
| 74 | C2×#711 | — | 2 | 4 | no | — |
| 75 | C2×#711 | C23 | 1 | 4 | yes | — |
| 76 | C2×#709 | — | 2 | 2 | no | — |
| 77 | C2×#709 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×D20 | C23 | 1 | 1 | yes | characteristic |
| 79 | C22×Dic10 | — | 2 | 2 | no | — |
| 80 | C22×Dic10 | C23 | 1 | 2 | yes | — |
| 81 | C22×Dic10 | C23 | 1 | 1 | yes | characteristic |
| 82 | C22×C5×C8 | C23 | 1 | 2 | yes | — |
| 83 | C5×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 84 | C5×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 85 | C5×#127 | C23 | 1 | 1 | yes | characteristic |
| 86 | C5×#125 | C23 | 1 | 2 | yes | — |
| 87 | C5×#124 | C23 | 1 | 2 | yes | — |
| 88 | C5×C22⋊Q8 | — | 2 | 2 | no | — |
| 89 | C5×#121 | — | 2 | 2 | no | — |
| 90 | C4×C5×Q8 | — | 2 | 2 | no | — |
| 91 | C4×C5×D4 | — | 2 | 2 | no | — |
| 92 | C5×#117 | C23 | 1 | 1 | yes | characteristic |
| 93 | C5×#117 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 95 | #4097 | — | 4 | 4 | no | — |
| 96 | #4095 | — | 4 | 4 | no | — |
| 97 | #4093 | — | 2 | 4 | no | — |
| 98 | #4092 | — | 2 | 4 | no | — |
| 99 | #4090 | C23 | 1 | 4 | yes | — |
| 100 | C2×#689 | C23 | 1 | 4 | yes | — |
| 101 | C2×#688 | C23 | 1 | 4 | yes | — |
| 102 | #4084 | — | 2 | 4 | no | — |
| 103 | #4082 | C23 | 1 | 4 | yes | — |
| 104 | #4081 | — | 2 | 4 | no | — |
| 105 | D4×Dic5 | — | 2 | 4 | no | — |
| 106 | C2×#687 | C23 | 1 | 4 | yes | — |
| 107 | C2×#686 | C23 | 1 | 4 | yes | — |
| 108 | C4×C22⋊D5 | D4 | 1 | 4 | yes | — |
| 109 | C2×#685 | — | 2 | 2 | no | — |
| 110 | #4072 | C23 | 1 | 1 | yes | characteristic |
| 111 | C2×C4⋊Dic5 | — | 2 | 2 | no | — |
| 112 | #4070 | — | 2 | 4 | no | — |
| 113 | C2×#681 | C23 | 1 | 2 | yes | — |
| 114 | C2×Dic20 | — | 4 | 4 | no | — |
| 115 | C2×Dic20 | C23 | 1 | 8 | yes | — |
| 116 | C2×#677 | — | 4 | 4 | no | — |
| 117 | C2×#677 | C23 | 1 | 8 | yes | — |
| 118 | #4044 | — | 2 | 4 | no | — |
| 119 | #4044 | — | 2 | 4 | no | — |
| 120 | #4043 | C23 | 1 | 4 | yes | — |
| 121 | #4041 | C23 | 1 | 4 | yes | — |
| 122 | #4040 | — | 2 | 4 | no | — |
| 123 | #4040 | — | 2 | 4 | no | — |
| 124 | #4039 | — | 2 | 4 | no | — |
| 125 | #4039 | C23 | 1 | 4 | yes | — |
| 126 | #4038 | — | 2 | 4 | no | — |
| 127 | D5×C4⋊C4 | — | 2 | 4 | no | — |
| 128 | #4034 | — | 2 | 4 | no | — |
| 129 | #4033 | C23 | 1 | 4 | yes | — |
| 130 | #4032 | — | 2 | 2 | no | — |
| 131 | #4029 | — | 2 | 8 | no | — |
| 132 | #4028 | — | 2 | 2 | no | — |
| 133 | D5×C22⋊C4 | — | 2 | 2 | no | — |
| 134 | #4024 | — | 2 | 8 | no | — |
| 135 | #4023 | — | 2 | 2 | no | — |
| 136 | #4021 | — | 2 | 1 | no | — |
| 137 | #4021 | — | 2 | 1 | no | — |
| 138 | #4021 | — | 2 | 2 | no | — |
| 139 | #4021 | C23 | 1 | 2 | yes | — |
| 140 | #4021 | C23 | 1 | 2 | yes | — |
| 141 | #4020 | — | 2 | 1 | no | — |
| 142 | C4×D20 | — | 2 | 2 | no | — |
| 143 | C4×D20 | D4 | 1 | 2 | yes | — |
| 144 | #4018 | C23 | 1 | 2 | yes | — |
| 145 | C42×D5 | C23 | 1 | 2 | yes | — |
| 146 | #4015 | — | 2 | 1 | no | — |
| 147 | #4015 | — | 2 | 2 | no | — |
| 148 | #4015 | C23 | 1 | 2 | yes | — |
| 149 | #4015 | C23 | 1 | 2 | yes | — |
| 150 | C4×Dic10 | — | 2 | 2 | no | — |
| 151 | C4×Dic10 | D4 | 1 | 2 | yes | — |
| 152 | C5×#103 | C23 | 1 | 4 | yes | — |
| 153 | C5×#103 | C23 | 1 | 4 | yes | — |
| 154 | C5×#102 | C23 | 1 | 4 | yes | — |
| 155 | C5×#102 | C23 | 1 | 4 | yes | — |
| 156 | C5×#97 | C23 | 1 | 2 | yes | — |
| 157 | C5×#97 | C23 | 1 | 2 | yes | — |
| 158 | #3952 | C23 | 1 | 8 | yes | — |
| 159 | #3946 | C23 | 1 | 8 | yes | — |
| 160 | #3942 | C23 | 1 | 8 | yes | — |
| 161 | #3942 | C23 | 1 | 8 | yes | — |
| 162 | #3935 | C23 | 1 | 2 | yes | — |
| 163 | C4×#168 | C23 | 1 | 2 | yes | — |
| 164 | #3510 | — | 5 | 1 | no | — |
| 165 | #3499 | — | 5 | 1 | no | — |
| 166 | #3225 | — | 5 | 8 | no | — |
| 167 | #3219 | — | 5 | 4 | no | — |
| 168 | #3218 | — | 5 | 4 | no | — |
| 169 | #3153 | — | 5 | 1 | no | — |
| 170 | C2×#497 | — | 5 | 1 | no | — |
| 171 | #3139 | — | 5 | 1 | no | — |
| 172 | #3135 | D5 | 1 | 1 | yes | characteristic, complemented |
| 173 | #3044 | — | 5 | 2 | no | — |
| 174 | #3042 | — | 5 | 2 | no | — |
| 175 | #3011 | — | 5 | 2 | no | — |
| 176 | #3010 | — | 5 | 2 | no | — |
| 177 | #2923 | — | 5 | 1 | no | — |
| 178 | C23×D5 | — | 2 | 1 | no | — |
| 179 | C5×#41 | — | 2 | 4 | no | — |
| 180 | C5×#41 | — | 2 | 4 | no | — |
| 181 | C2×C5×Q8 | — | 2 | 2 | no | — |
| 182 | C2×C5×Q8 | C24 | 1 | 2 | yes | — |
| 183 | C2×C5×D4 | — | 2 | 2 | no | — |
| 184 | C2×C5×D4 | — | 2 | 2 | no | — |
| 185 | C2×C5×D4 | C24 | 1 | 2 | yes | — |
| 186 | C22×C4×C5 | — | 2 | 2 | no | — |
| 187 | C22×C4×C5 | C2×D4 | 1 | 2 | yes | — |
| 188 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 189 | C2×C22⋊D5 | — | 2 | 4 | no | — |
| 190 | C2×C22⋊D5 | C2×D4 | 1 | 2 | yes | — |
| 191 | C22×Dic5 | — | 2 | 2 | no | — |
| 192 | C22×Dic5 | — | 2 | 1 | no | — |
| 193 | C22×Dic5 | — | 2 | 4 | no | — |
| 194 | Q8×D5 | — | 4 | 4 | no | — |
| 195 | Q8×D5 | — | 4 | 4 | no | — |
| 196 | #711 | — | 4 | 4 | no | — |
| 197 | #711 | — | 4 | 4 | no | — |
| 198 | #711 | — | 4 | 16 | no | — |
| 199 | #709 | — | 2 | 4 | no | — |
| 200 | #709 | — | 4 | 8 | no | — |
| 201 | C2×D20 | — | 2 | 4 | no | — |
| 202 | C2×D20 | — | 2 | 1 | no | — |
| 203 | C2×D20 | — | 2 | 4 | no | — |
| 204 | C2×D20 | C2×D4 | 1 | 1 | yes | characteristic |
| 205 | C2×D20 | C24 | 1 | 2 | yes | — |
| 206 | C2×C4×D5 | — | 2 | 4 | no | — |
| 207 | C2×C4×D5 | — | 2 | 4 | no | — |
| 208 | C2×C4×D5 | C2×D4 | 1 | 4 | yes | — |
| 209 | C2×C4×D5 | C24 | 1 | 2 | yes | — |
| 210 | C2×Dic10 | — | 2 | 4 | no | — |
| 211 | C2×Dic10 | — | 2 | 4 | no | — |
| 212 | C2×Dic10 | — | 2 | 4 | no | — |
| 213 | C2×Dic10 | — | 2 | 2 | no | — |
| 214 | C2×Dic10 | — | 2 | 1 | no | — |
| 215 | C2×Dic10 | — | 2 | 4 | no | — |
| 216 | C2×Dic10 | — | 4 | 8 | no | — |
| 217 | C2×Dic10 | C2×D4 | 1 | 1 | yes | characteristic |
| 218 | C2×Dic10 | C24 | 1 | 4 | yes | — |
| 219 | C2×Dic10 | C24 | 1 | 2 | yes | — |
| 220 | C2×C5×C8 | — | 2 | 4 | no | — |
| 221 | C2×C5×C8 | C24 | 1 | 4 | yes | — |
| 222 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 223 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 224 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 225 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 226 | C5×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 227 | C5×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 228 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 229 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 230 | C5×C22⋊C4 | — | 2 | 4 | no | — |
| 231 | C42×C5 | — | 2 | 1 | no | — |
| 232 | C42×C5 | — | 2 | 1 | no | — |
| 233 | C42×C5 | C2×D4 | 1 | 2 | yes | — |
| 234 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 235 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 236 | C22⋊Dic5 | — | 2 | 8 | no | — |
| 237 | C22⋊Dic5 | C2×D4 | 1 | 2 | yes | — |
| 238 | #689 | — | 4 | 4 | no | — |
| 239 | #688 | — | 4 | 4 | no | — |
| 240 | #687 | — | 4 | 4 | no | — |
| 241 | #686 | — | 4 | 4 | no | — |
| 242 | #685 | — | 2 | 4 | no | — |
| 243 | #685 | — | 2 | 4 | no | — |
| 244 | #685 | — | 2 | 4 | no | — |
| 245 | #685 | — | 2 | 4 | no | — |
| 246 | #685 | — | 2 | 4 | no | — |
| 247 | #685 | C2×D4 | 1 | 4 | yes | — |
| 248 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 249 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 250 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 251 | C4⋊Dic5 | C2×D4 | 1 | 2 | yes | — |
| 252 | #683 | — | 2 | 4 | no | — |
| 253 | #683 | — | 2 | 8 | no | — |
| 254 | #683 | C2×D4 | 1 | 4 | yes | — |
| 255 | C4×Dic5 | — | 2 | 4 | no | — |
| 256 | C4×Dic5 | C2×D4 | 1 | 4 | yes | — |
| 257 | C4×Dic5 | C24 | 1 | 2 | yes | — |
| 258 | #681 | — | 2 | 4 | no | — |
| 259 | C2×#168 | C24 | 1 | 4 | yes | — |
| 260 | Dic20 | — | 4 | 8 | no | — |
| 261 | #677 | — | 4 | 8 | no | — |
| 262 | C2×2−1+4 | — | 5 | 2 | no | — |
| 263 | C2×#137 | — | 5 | 2 | no | — |
| 264 | C2×AGL(1,ℤ/8) | — | 5 | 2 | no | — |
| 265 | C22×Q16 | — | 5 | 2 | no | — |
| 266 | C22×SD16 | — | 5 | 2 | no | — |
| 267 | #559 | — | 10 | 2 | no | — |
| 268 | #556 | — | 10 | 2 | no | — |
| 269 | #551 | — | 10 | 4 | no | — |
| 270 | D4×Q8 | — | 10 | 2 | no | — |
| 271 | #547 | — | 10 | 2 | no | — |
| 272 | #547 | — | 10 | 4 | no | — |
| 273 | #542 | — | 5 | 4 | no | — |
| 274 | #536 | — | 5 | 2 | no | — |
| 275 | #536 | — | 5 | 4 | no | — |
| 276 | #536 | — | 5 | 1 | no | — |
| 277 | #535 | — | 5 | 1 | no | — |
| 278 | #533 | C2×D5 | 1 | 1 | yes | characteristic |
| 279 | #532 | — | 5 | 2 | no | — |
| 280 | #532 | C2×D5 | 1 | 1 | yes | characteristic |
| 281 | C2×C4⋊Q8 | — | 5 | 2 | no | — |
| 282 | C2×C4⋊Q8 | — | 5 | 1 | no | — |
| 283 | #529 | — | 5 | 4 | no | — |
| 284 | C2×#124 | — | 5 | 1 | no | — |
| 285 | #519 | — | 5 | 1 | no | — |
| 286 | #518 | — | 5 | 1 | no | — |
| 287 | C4×#41 | — | 5 | 1 | no | — |
| 288 | #497 | — | 5 | 2 | no | — |
| 289 | #497 | — | 5 | 4 | no | — |
| 290 | #497 | — | 5 | 4 | no | — |
| 291 | #496 | — | 5 | 2 | no | — |
| 292 | #495 | — | 5 | 4 | no | — |
| 293 | #491 | — | 5 | 4 | no | — |
| 294 | #491 | C2×D5 | 1 | 2 | yes | complemented |
| 295 | #490 | C2×D5 | 1 | 2 | yes | complemented |
| 296 | #489 | C2×D5 | 1 | 4 | yes | complemented |
| 297 | #487 | — | 5 | 4 | no | — |
| 298 | #464 | — | 5 | 8 | no | — |
| 299 | #463 | — | 5 | 8 | no | — |
| 300 | #462 | — | 5 | 8 | no | — |
| 301 | #461 | — | 5 | 8 | no | — |
| 302 | #452 | — | 5 | 8 | no | — |
| 303 | #451 | — | 5 | 8 | no | — |
| 304 | #449 | — | 5 | 8 | no | — |
| 305 | #448 | — | 5 | 8 | no | — |
| 306 | #433 | — | 5 | 4 | no | — |
| 307 | #432 | — | 5 | 4 | no | — |
| 308 | #424 | — | 5 | 2 | no | — |
| 309 | #419 | — | 5 | 2 | no | — |
| 310 | #419 | — | 5 | 2 | no | — |
| 311 | #416 | C2×D5 | 1 | 2 | yes | — |
| 312 | #416 | C2×D5 | 1 | 2 | yes | — |
| 313 | #408 | — | 5 | 2 | no | — |
| 314 | C4×M16 | — | 5 | 1 | no | — |
| 315 | C2×#97 | C2×D5 | 1 | 1 | yes | characteristic |
| 316 | C23×C5 | — | 2 | 2 | no | — |
| 317 | C23×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 318 | C22×D5 | — | 2 | 2 | no | — |
| 319 | C22×D5 | — | 4 | 2 | no | — |
| 320 | C22×D5 | — | 8 | 2 | no | — |
| 321 | C22×D5 | C22×D4 | 1 | 2 | yes | — |
| 322 | C5×Q8 | — | 2 | 2 | no | — |
| 323 | C5×Q8 | — | 2 | 2 | no | — |
| 324 | C5×Q8 | — | 8 | 2 | no | — |
| 325 | C5×D4 | — | 2 | 2 | no | — |
| 326 | C5×D4 | — | 2 | 2 | no | — |
| 327 | C5×D4 | — | 4 | 4 | no | — |
| 328 | C5×D4 | — | 4 | 4 | no | — |
| 329 | C2×C4×C5 | — | 2 | 2 | no | — |
| 330 | C2×C4×C5 | — | 2 | 2 | no | — |
| 331 | C2×C4×C5 | — | 2 | 2 | no | — |
| 332 | C2×C4×C5 | — | 4 | 2 | no | — |
| 333 | C2×C4×C5 | — | 4 | 4 | no | — |
| 334 | C2×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 335 | C2×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 336 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 337 | C2×C4×C5 | H(5,𝔽2) | 1 | 4 | yes | — |
| 338 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 339 | C22⋊D5 | — | 2 | 4 | no | — |
| 340 | C22⋊D5 | — | 4 | 8 | no | — |
| 341 | C2×Dic5 | — | 2 | 2 | no | — |
| 342 | C2×Dic5 | — | 2 | 4 | no | — |
| 343 | C2×Dic5 | — | 4 | 8 | no | — |
| 344 | C2×Dic5 | — | 4 | 4 | no | — |
| 345 | C2×Dic5 | — | 4 | 2 | no | — |
| 346 | C2×Dic5 | C22×D4 | 1 | 4 | yes | — |
| 347 | C2×Dic5 | C22×D4 | 1 | 2 | yes | — |
| 348 | D20 | — | 2 | 2 | no | — |
| 349 | D20 | — | 2 | 4 | no | — |
| 350 | D20 | — | 4 | 2 | no | — |
| 351 | D20 | — | 8 | 4 | no | — |
| 352 | C4×D5 | — | 2 | 4 | no | — |
| 353 | C4×D5 | — | 4 | 4 | no | — |
| 354 | C4×D5 | — | 4 | 8 | no | — |
| 355 | C4×D5 | — | 8 | 4 | no | — |
| 356 | Dic10 | — | 2 | 2 | no | — |
| 357 | Dic10 | — | 2 | 4 | no | — |
| 358 | Dic10 | — | 2 | 4 | no | — |
| 359 | Dic10 | — | 2 | 4 | no | — |
| 360 | Dic10 | — | 4 | 8 | no | — |
| 361 | Dic10 | — | 4 | 2 | no | — |
| 362 | Dic10 | — | 4 | 4 | no | — |
| 363 | C5×C8 | — | 2 | 4 | no | — |
| 364 | #168 | — | 2 | 4 | no | — |
| 365 | 2−1+4 | — | 20 | 4 | no | — |
| 366 | 2−1+4 | — | 20 | 4 | no | — |
| 367 | C2×#41 | — | 5 | 1 | no | — |
| 368 | C2×#41 | — | 5 | 4 | no | — |
| 369 | C2×#41 | — | 10 | 2 | no | — |
| 370 | C2×#41 | — | 10 | 4 | no | — |
| 371 | C2×#41 | C22×D5 | 1 | 2 | yes | — |
| 372 | C22×Q8 | — | 5 | 4 | no | — |
| 373 | C22×Q8 | — | 5 | 1 | no | — |
| 374 | C22×Q8 | — | 5 | 2 | no | — |
| 375 | C22×Q8 | — | 10 | 2 | no | — |
| 376 | C22×D4 | — | 5 | 1 | no | — |
| 377 | #137 | — | 20 | 4 | no | — |
| 378 | AGL(1,ℤ/8) | — | 20 | 4 | no | — |
| 379 | C2×Q16 | — | 5 | 4 | no | — |
| 380 | C2×Q16 | — | 5 | 8 | no | — |
| 381 | C2×Q16 | — | 20 | 4 | no | — |
| 382 | C2×SD16 | — | 5 | 4 | no | — |
| 383 | C2×SD16 | — | 5 | 4 | no | — |
| 384 | C2×SD16 | — | 5 | 8 | no | — |
| 385 | C2×SD16 | — | 20 | 4 | no | — |
| 386 | C2×D8 | — | 5 | 4 | no | — |
| 387 | C2×M16 | — | 5 | 2 | no | — |
| 388 | C22×C8 | C22×D5 | 1 | 2 | yes | — |
| 389 | C4⋊Q8 | — | 5 | 4 | no | — |
| 390 | C4⋊Q8 | — | 5 | 2 | no | — |
| 391 | C4⋊Q8 | — | 5 | 2 | no | — |
| 392 | C4⋊Q8 | — | 10 | 1 | no | — |
| 393 | C4⋊Q8 | — | 10 | 4 | no | — |
| 394 | C4⋊Q8 | — | 10 | 2 | no | — |
| 395 | C4⋊Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 396 | C4⋊Q8 | C22×D5 | 1 | 2 | yes | — |
| 397 | #127 | — | 10 | 1 | no | — |
| 398 | #127 | C22×D5 | 1 | 1 | yes | characteristic |
| 399 | #126 | — | 10 | 4 | no | — |
| 400 | #126 | — | 10 | 4 | no | — |
| 401 | #125 | C22×D5 | 1 | 2 | yes | — |
| 402 | #124 | — | 5 | 4 | no | — |
| 403 | #124 | — | 5 | 2 | no | — |
| 404 | #124 | — | 5 | 2 | no | — |
| 405 | #124 | — | 10 | 1 | no | — |
| 406 | #124 | — | 10 | 1 | no | — |
| 407 | #124 | — | 10 | 4 | no | — |
| 408 | #124 | — | 10 | 2 | no | — |
| 409 | #124 | C22×D5 | 1 | 2 | yes | — |
| 410 | #123 | — | 10 | 8 | no | — |
| 411 | #123 | — | 10 | 2 | no | — |
| 412 | #123 | — | 10 | 4 | no | — |
| 413 | #123 | — | 10 | 4 | no | — |
| 414 | #123 | — | 10 | 4 | no | — |
| 415 | C22⋊Q8 | — | 2 | 2 | no | — |
| 416 | C22⋊Q8 | — | 5 | 4 | no | — |
| 417 | C22⋊Q8 | — | 10 | 8 | no | — |
| 418 | C22⋊Q8 | — | 10 | 4 | no | — |
| 419 | C22⋊Q8 | — | 10 | 4 | no | — |
| 420 | #121 | — | 2 | 2 | no | — |
| 421 | #121 | — | 5 | 4 | no | — |
| 422 | #121 | — | 10 | 4 | no | — |
| 423 | #120 | — | 10 | 2 | no | — |
| 424 | C4×Q8 | — | 2 | 2 | no | — |
| 425 | C4×Q8 | — | 5 | 2 | no | — |
| 426 | C4×Q8 | — | 5 | 4 | no | — |
| 427 | C4×Q8 | — | 10 | 2 | no | — |
| 428 | C4×D4 | — | 2 | 2 | no | — |
| 429 | C4×D4 | — | 5 | 4 | no | — |
| 430 | C4×D4 | — | 5 | 4 | no | — |
| 431 | C4×D4 | — | 5 | 2 | no | — |
| 432 | C4×D4 | — | 10 | 2 | no | — |
| 433 | C4×D4 | — | 10 | 4 | no | — |
| 434 | C4×D4 | — | 10 | 4 | no | — |
| 435 | #117 | — | 5 | 1 | no | — |
| 436 | #117 | — | 5 | 2 | no | — |
| 437 | #117 | — | 10 | 4 | no | — |
| 438 | #117 | — | 10 | 2 | no | — |
| 439 | #117 | C22×D5 | 1 | 1 | yes | characteristic |
| 440 | #117 | C22×D5 | 1 | 1 | yes | characteristic |
| 441 | C2×C4⋊C4 | — | 10 | 4 | no | — |
| 442 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 443 | C2×C22⋊C4 | — | 10 | 2 | no | — |
| 444 | C2×C22⋊C4 | — | 10 | 2 | no | — |
| 445 | C2×C42 | — | 5 | 2 | no | — |
| 446 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 447 | C4⋊C8 | — | 5 | 8 | no | — |
| 448 | #103 | — | 5 | 8 | no | — |
| 449 | #103 | — | 5 | 8 | no | — |
| 450 | #103 | C22×D5 | 1 | 4 | yes | — |
| 451 | #103 | C22×D5 | 1 | 4 | yes | — |
| 452 | #102 | C22×D5 | 1 | 4 | yes | — |
| 453 | #102 | C22×D5 | 1 | 4 | yes | — |
| 454 | C22⋊C8 | — | 5 | 8 | no | — |
| 455 | #97 | — | 5 | 2 | no | — |
| 456 | #97 | C22×D5 | 1 | 2 | yes | — |
| 457 | #97 | C22×D5 | 1 | 2 | yes | — |
| 458 | C4×C8 | — | 5 | 2 | no | — |
| 459 | C22×C5 | — | 2 | 2 | no | — |
| 460 | C22×C5 | — | 4 | 4 | no | — |
| 461 | C22×C5 | — | 4 | 2 | no | — |
| 462 | C22×C5 | #535 | 1 | 2 | yes | — |
| 463 | C22×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 464 | C2×D5 | — | 2 | 4 | no | — |
| 465 | C2×D5 | — | 2 | 2 | no | — |
| 466 | C2×D5 | — | 4 | 4 | no | — |
| 467 | C2×D5 | — | 4 | 2 | no | — |
| 468 | C2×D5 | — | 16 | 2 | no | — |
| 469 | C4×C5 | — | 2 | 2 | no | — |
| 470 | C4×C5 | — | 2 | 2 | no | — |
| 471 | C4×C5 | — | 4 | 2 | no | — |
| 472 | C4×C5 | — | 4 | 2 | no | — |
| 473 | C4×C5 | — | 4 | 2 | no | — |
| 474 | C4×C5 | #535 | 1 | 2 | yes | — |
| 475 | C4×C5 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 476 | Dic5 | — | 2 | 4 | no | — |
| 477 | Dic5 | — | 2 | 2 | no | — |
| 478 | Dic5 | — | 4 | 4 | no | — |
| 479 | Dic5 | — | 4 | 2 | no | — |
| 480 | C24 | — | 10 | 1 | no | — |
| 481 | #41 | — | 2 | 4 | no | — |
| 482 | #41 | — | 2 | 4 | no | — |
| 483 | #41 | — | 10 | 4 | no | — |
| 484 | #41 | — | 20 | 8 | no | — |
| 485 | #41 | — | 20 | 4 | no | — |
| 486 | #41 | — | 20 | 4 | no | — |
| 487 | #41 | — | 20 | 16 | no | — |
| 488 | C2×Q8 | — | 2 | 2 | no | — |
| 489 | C2×Q8 | — | 5 | 1 | no | — |
| 490 | C2×Q8 | — | 5 | 4 | no | — |
| 491 | C2×Q8 | — | 5 | 2 | no | — |
| 492 | C2×Q8 | — | 10 | 4 | no | — |
| 493 | C2×Q8 | — | 10 | 1 | no | — |
| 494 | C2×Q8 | — | 10 | 2 | no | — |
| 495 | C2×Q8 | — | 10 | 4 | no | — |
| 496 | C2×Q8 | — | 10 | 4 | no | — |
| 497 | C2×Q8 | — | 10 | 4 | no | — |
| 498 | C2×Q8 | — | 20 | 8 | no | — |
| 499 | C2×Q8 | — | 20 | 4 | no | — |
| 500 | C2×Q8 | — | 20 | 4 | no | — |
| 501 | C2×Q8 | C23×D5 | 1 | 2 | yes | — |
| 502 | C2×D4 | — | 2 | 2 | no | — |
| 503 | C2×D4 | — | 2 | 2 | no | — |
| 504 | C2×D4 | — | 5 | 2 | no | — |
| 505 | C2×D4 | — | 5 | 1 | no | — |
| 506 | C2×D4 | — | 5 | 2 | no | — |
| 507 | C2×D4 | — | 10 | 4 | no | — |
| 508 | C2×D4 | — | 10 | 4 | no | — |
| 509 | C2×D4 | — | 10 | 1 | no | — |
| 510 | C2×D4 | — | 10 | 4 | no | — |
| 511 | C2×D4 | C23×D5 | 1 | 2 | yes | — |
| 512 | C22×C4 | — | 2 | 2 | no | — |
| 513 | C22×C4 | — | 5 | 2 | no | — |
| 514 | C22×C4 | — | 5 | 4 | no | — |
| 515 | C22×C4 | — | 10 | 4 | no | — |
| 516 | C22×C4 | — | 10 | 4 | no | — |
| 517 | C22×C4 | — | 10 | 4 | no | — |
| 518 | C22×C4 | — | 10 | 1 | no | — |
| 519 | C22×C4 | — | 10 | 2 | no | — |
| 520 | C22×C4 | D4×D5 | 1 | 2 | yes | — |
| 521 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 522 | Q16 | — | 20 | 8 | no | — |
| 523 | Q16 | — | 20 | 4 | no | — |
| 524 | SD16 | — | 20 | 8 | no | — |
| 525 | SD16 | — | 20 | 4 | no | — |
| 526 | SD16 | — | 20 | 4 | no | — |
| 527 | D8 | — | 20 | 4 | no | — |
| 528 | M16 | — | 10 | 4 | no | — |
| 529 | C2×C8 | — | 2 | 4 | no | — |
| 530 | C2×C8 | — | 5 | 4 | no | — |
| 531 | C2×C8 | C23×D5 | 1 | 4 | yes | — |
| 532 | C4⋊C4 | — | 2 | 2 | no | — |
| 533 | C4⋊C4 | — | 2 | 2 | no | — |
| 534 | C4⋊C4 | — | 2 | 2 | no | — |
| 535 | C4⋊C4 | — | 2 | 2 | no | — |
| 536 | C4⋊C4 | — | 5 | 2 | no | — |
| 537 | C4⋊C4 | — | 5 | 4 | no | — |
| 538 | C4⋊C4 | — | 10 | 8 | no | — |
| 539 | C4⋊C4 | — | 10 | 4 | no | — |
| 540 | C4⋊C4 | — | 10 | 4 | no | — |
| 541 | C4⋊C4 | — | 10 | 4 | no | — |
| 542 | C4⋊C4 | — | 10 | 4 | no | — |
| 543 | C4⋊C4 | C23×D5 | 1 | 2 | yes | — |
| 544 | C4⋊C4 | C23×D5 | 1 | 2 | yes | — |
| 545 | C22⋊C4 | — | 2 | 1 | no | — |
| 546 | C22⋊C4 | — | 2 | 1 | no | — |
| 547 | C22⋊C4 | — | 2 | 4 | no | — |
| 548 | C22⋊C4 | — | 5 | 2 | no | — |
| 549 | C22⋊C4 | — | 5 | 4 | no | — |
| 550 | C22⋊C4 | — | 10 | 4 | no | — |
| 551 | C22⋊C4 | — | 10 | 4 | no | — |
| 552 | C22⋊C4 | — | 10 | 4 | no | — |
| 553 | C22⋊C4 | — | 10 | 8 | no | — |
| 554 | C22⋊C4 | — | 10 | 4 | no | — |
| 555 | C22⋊C4 | — | 10 | 4 | no | — |
| 556 | C42 | — | 2 | 1 | no | — |
| 557 | C42 | — | 2 | 1 | no | — |
| 558 | C42 | — | 5 | 4 | no | — |
| 559 | C42 | — | 5 | 2 | no | — |
| 560 | C42 | — | 10 | 4 | no | — |
| 561 | C42 | D4×D5 | 1 | 2 | yes | — |
| 562 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 563 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 564 | C2×C5 | — | 2 | 2 | no | — |
| 565 | C2×C5 | — | 8 | 2 | no | — |
| 566 | C2×C5 | C2×#535 | 1 | 1 | yes | characteristic |
| 567 | C2×C5 | #3586 | 1 | 2 | yes | — |
| 568 | D5 | — | 4 | 2 | no | — |
| 569 | D5 | — | 8 | 2 | no | — |
| 570 | C23 | — | 2 | 2 | no | — |
| 571 | C23 | — | 5 | 2 | no | — |
| 572 | C23 | — | 10 | 2 | no | — |
| 573 | C23 | — | 20 | 2 | no | — |
| 574 | C23 | — | 40 | 2 | no | — |
| 575 | C23 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 576 | Q8 | — | 2 | 2 | no | — |
| 577 | Q8 | — | 2 | 2 | no | — |
| 578 | Q8 | — | 8 | 2 | no | — |
| 579 | Q8 | — | 10 | 2 | no | — |
| 580 | Q8 | — | 10 | 4 | no | — |
| 581 | Q8 | — | 10 | 4 | no | — |
| 582 | Q8 | — | 10 | 4 | no | — |
| 583 | Q8 | — | 20 | 8 | no | — |
| 584 | Q8 | — | 20 | 4 | no | — |
| 585 | Q8 | — | 20 | 2 | no | — |
| 586 | D4 | — | 2 | 2 | no | — |
| 587 | D4 | — | 2 | 2 | no | — |
| 588 | D4 | — | 4 | 4 | no | — |
| 589 | D4 | — | 4 | 4 | no | — |
| 590 | D4 | — | 10 | 4 | no | — |
| 591 | D4 | — | 10 | 2 | no | — |
| 592 | D4 | — | 10 | 4 | no | — |
| 593 | D4 | — | 20 | 8 | no | — |
| 594 | D4 | — | 20 | 2 | no | — |
| 595 | D4 | — | 40 | 4 | no | — |
| 596 | C2×C4 | — | 2 | 2 | no | — |
| 597 | C2×C4 | — | 2 | 2 | no | — |
| 598 | C2×C4 | — | 2 | 2 | no | — |
| 599 | C2×C4 | — | 4 | 2 | no | — |
| 600 | C2×C4 | — | 4 | 4 | no | — |
| 601 | C2×C4 | — | 5 | 4 | no | — |
| 602 | C2×C4 | — | 5 | 2 | no | — |
| 603 | C2×C4 | — | 10 | 4 | no | — |
| 604 | C2×C4 | — | 10 | 2 | no | — |
| 605 | C2×C4 | — | 10 | 4 | no | — |
| 606 | C2×C4 | — | 20 | 4 | no | — |
| 607 | C2×C4 | — | 20 | 8 | no | — |
| 608 | C2×C4 | — | 20 | 8 | no | — |
| 609 | C2×C4 | — | 20 | 4 | no | — |
| 610 | C2×C4 | — | 20 | 2 | no | — |
| 611 | C2×C4 | — | 40 | 4 | no | — |
| 612 | C2×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 613 | C2×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 614 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 615 | C2×C4 | #4149 | 1 | 4 | yes | — |
| 616 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 617 | C8 | — | 2 | 4 | no | — |
| 618 | C8 | — | 10 | 4 | no | — |
| 619 | C5 | #60828 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 620 | C22 | — | 2 | 2 | no | — |
| 621 | C22 | — | 4 | 2 | no | — |
| 622 | C22 | — | 4 | 4 | no | — |
| 623 | C22 | — | 10 | 2 | no | — |
| 624 | C22 | — | 10 | 4 | no | — |
| 625 | C22 | — | 20 | 2 | no | — |
| 626 | C22 | — | 20 | 4 | no | — |
| 627 | C22 | — | 80 | 2 | no | — |
| 628 | C22 | #66008 | 1 | 2 | yes | — |
| 629 | C22 | C22×D4×D5 | 1 | 1 | yes | characteristic |
| 630 | C4 | — | 2 | 2 | no | — |
| 631 | C4 | — | 2 | 2 | no | — |
| 632 | C4 | — | 4 | 2 | no | — |
| 633 | C4 | — | 4 | 2 | no | — |
| 634 | C4 | — | 4 | 2 | no | — |
| 635 | C4 | — | 10 | 2 | no | — |
| 636 | C4 | — | 10 | 4 | no | — |
| 637 | C4 | — | 20 | 4 | no | — |
| 638 | C4 | — | 20 | 2 | no | — |
| 639 | C4 | #66008 | 1 | 2 | yes | — |
| 640 | C4 | C2×#4149 | 1 | 2 | yes | — |
| 641 | C2 | — | 2 | 2 | no | — |
| 642 | C2 | — | 8 | 2 | no | — |
| 643 | C2 | — | 20 | 2 | no | — |
| 644 | C2 | — | 40 | 2 | no | — |
| 645 | C2 | C2×#66008 | 1 | 1 | yes | characteristic |
| 646 | C2 | #10619102 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10618164 | C2 | semidirect |
| 2. #10618144 | C2 | semidirect |
| 3. C5×#3135 | C2 | semidirect |
| 4. #10615068 | C2 | semidirect |
| 5. #10615020 | C2 | semidirect |
| 6. #10613472 | C2 | semidirect |
| 7. #10613449 | C2 | semidirect |
| 8. #10613420 | C2 | semidirect |
| 9. #10610596 | C2 | semidirect |
| 10. #10610594 | C2 | semidirect |
| 11. #10610568 | C2 | semidirect |
| 12. #10610567 | C2 | semidirect |
| 13. C2×#65004 | C2 | semidirect |
| 14. #10610220 | C2 | semidirect |
| 24. D5×C4⋊Q8 | C22 | semidirect |
| 25. #66050 | C22 | semidirect |
| 27. #66009 | C22 | semidirect |
| 41. C5×#491 | C22 | semidirect |
| 42. C5×#490 | C22 | semidirect |
| 43. C5×#489 | C22 | semidirect |
| 49. #65382 | C22 | semidirect |
| 52. #65358 | C22 | semidirect |
| 58. #65097 | C22 | semidirect |
| 60. #65082 | C22 | semidirect |
| 62. #65072 | C22 | semidirect |
| 64. #65056 | C22 | semidirect |
| 67. #64998 | C22 | semidirect |
| 68. #64994 | C22 | semidirect |
| 172. #3135 | D5 | semidirect |
| 294. #491 | C2×D5 | semidirect |
| 295. #490 | C2×D5 | semidirect |
| 296. #489 | C2×D5 | semidirect |
| 619. C5 | #60828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10618164 | 2 |
| #10618144 | 2 |
| C5×#3135 | 2 |
| #10615068 | 2 |
| #10615020 | 2 |
| #10613472 | 2 |
| #10613449 | 2 |
| #10613420 | 2 |
| #10610596 | 2 |
| #10610594 | 2 |
| #10610568 | 2 |
| #10610567 | 2 |
| C2×#65004 | 2 |
| #10610220 | 2 |
| #60828 | 5 |