Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2116 conjugacy classes of subgroups.
The subgroup lattice has 670 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10617802 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10617786 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#2913 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10615537 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10615524 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10614301 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10614292 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10610953 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #10610951 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #10610949 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #10610947 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #10610916 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #10610906 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | C2×#65177 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | #10610872 | C2 | 1 | 3 | yes | maximal, complemented |
| 16 | C2×#4150 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×D5×#41 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C5×#131 | C22 | 1 | 1 | yes | characteristic |
| 19 | C5×#520 | C22 | 1 | 1 | yes | characteristic |
| 20 | C5×#520 | C22 | 1 | 1 | yes | characteristic |
| 21 | #66161 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#4094 | C22 | 1 | 1 | yes | characteristic |
| 23 | #65910 | — | 2 | 1 | no | — |
| 24 | Q8×D20 | — | 2 | 1 | no | — |
| 25 | C4×#713 | — | 2 | 1 | no | — |
| 26 | #65906 | — | 2 | 1 | no | — |
| 27 | #65889 | — | 2 | 3 | no | — |
| 28 | #65888 | — | 2 | 3 | no | — |
| 29 | #65879 | — | 2 | 3 | no | — |
| 30 | C4×#711 | — | 2 | 3 | no | — |
| 31 | #65860 | C22 | 1 | 3 | yes | — |
| 32 | #65858 | C22 | 1 | 3 | yes | — |
| 33 | #65857 | C22 | 1 | 3 | yes | — |
| 34 | D5×#117 | C22 | 1 | 3 | yes | — |
| 35 | #65844 | C22 | 1 | 3 | yes | — |
| 36 | C2×#4043 | C22 | 1 | 3 | yes | — |
| 37 | #65838 | C22 | 1 | 3 | yes | — |
| 38 | C2×#4038 | C22 | 1 | 3 | yes | — |
| 39 | C5×#428 | C22 | 1 | 3 | yes | complemented |
| 40 | C5×#428 | C22 | 1 | 3 | yes | complemented |
| 41 | C5×#427 | C22 | 1 | 3 | yes | complemented |
| 42 | C2×C5×#107 | C22 | 1 | 3 | yes | complemented |
| 43 | #65422 | C22 | 1 | 3 | yes | complemented |
| 44 | #65418 | C22 | 1 | 3 | yes | — |
| 45 | #65415 | C22 | 1 | 3 | yes | — |
| 46 | #65409 | C22 | 1 | 3 | yes | complemented |
| 47 | #65402 | C22 | 1 | 3 | yes | complemented |
| 48 | #65399 | C22 | 1 | 3 | yes | — |
| 49 | C2×#3952 | C22 | 1 | 3 | yes | — |
| 50 | C2×#3948 | C22 | 1 | 3 | yes | complemented |
| 51 | #65293 | C22 | 1 | 3 | yes | complemented |
| 52 | #65291 | C22 | 1 | 3 | yes | complemented |
| 53 | #65287 | C22 | 1 | 3 | yes | complemented |
| 54 | #65284 | C22 | 1 | 3 | yes | complemented |
| 55 | C2×#3942 | C22 | 1 | 3 | yes | complemented |
| 56 | #65255 | C22 | 1 | 3 | yes | complemented |
| 57 | #65253 | C22 | 1 | 3 | yes | complemented |
| 58 | C2×#3940 | C22 | 1 | 3 | yes | complemented |
| 59 | #65177 | C22 | 1 | 6 | yes | — |
| 60 | #65177 | C22 | 1 | 3 | yes | — |
| 61 | #65177 | C22 | 1 | 6 | yes | complemented |
| 62 | #65177 | C22 | 1 | 6 | yes | complemented |
| 63 | #65174 | C22 | 1 | 1 | yes | characteristic |
| 64 | #65174 | C22 | 1 | 6 | yes | complemented |
| 65 | #65173 | C22 | 1 | 6 | yes | complemented |
| 66 | #65173 | C22 | 1 | 3 | yes | complemented |
| 67 | #65171 | C22 | 1 | 3 | yes | complemented |
| 68 | #65156 | C22 | 1 | 3 | yes | — |
| 69 | #65156 | C22 | 1 | 6 | yes | complemented |
| 70 | #65155 | C22 | 1 | 3 | yes | — |
| 71 | #65152 | C22 | 1 | 3 | yes | complemented |
| 72 | #65151 | C22 | 1 | 6 | yes | complemented |
| 73 | #65151 | C22 | 1 | 3 | yes | complemented |
| 74 | #60524 | — | 5 | 1 | no | maximal, Sylow |
| 75 | C2×C5×#41 | C23 | 1 | 1 | yes | characteristic |
| 76 | #4150 | — | 2 | 4 | no | — |
| 77 | #4150 | — | 2 | 4 | no | — |
| 78 | D5×#41 | — | 2 | 4 | no | — |
| 79 | D5×#41 | — | 2 | 4 | no | — |
| 80 | C2×#713 | D4 | 1 | 1 | yes | characteristic |
| 81 | C2×Q8×D5 | — | 2 | 1 | no | — |
| 82 | C2×Q8×D5 | D4 | 1 | 1 | yes | characteristic |
| 83 | C2×#711 | — | 2 | 3 | no | — |
| 84 | C2×#711 | D4 | 1 | 3 | yes | — |
| 85 | C2×D4×D5 | D4 | 1 | 3 | yes | — |
| 86 | C2×#709 | C23 | 1 | 3 | yes | — |
| 87 | C2×#709 | C23 | 1 | 3 | yes | — |
| 88 | C22×C4×D5 | C23 | 1 | 3 | yes | — |
| 89 | C22×Dic10 | C23 | 1 | 3 | yes | — |
| 90 | C5×#131 | — | 2 | 4 | no | — |
| 91 | C2×C5×M16 | C23 | 1 | 3 | yes | — |
| 92 | C22×C5×C8 | C23 | 1 | 3 | yes | — |
| 93 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 94 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 95 | C4×C5×D4 | — | 2 | 3 | no | — |
| 96 | C4×C5×D4 | — | 2 | 3 | no | — |
| 97 | C5×#117 | C23 | 1 | 3 | yes | — |
| 98 | C5×#117 | C23 | 1 | 3 | yes | — |
| 99 | C2×C5×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 100 | C2×C5×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 101 | #4094 | — | 2 | 4 | no | — |
| 102 | Q8×Dic5 | — | 2 | 1 | no | — |
| 103 | D4×Dic5 | — | 2 | 3 | no | — |
| 104 | #4076 | — | 2 | 6 | no | — |
| 105 | C4×C22⋊D5 | — | 2 | 6 | no | — |
| 106 | C2×#685 | — | 2 | 3 | no | — |
| 107 | C2×#685 | — | 2 | 3 | no | — |
| 108 | #4072 | C23 | 1 | 3 | yes | — |
| 109 | C2×C4⋊Dic5 | — | 2 | 3 | no | — |
| 110 | C2×C4⋊Dic5 | C23 | 1 | 3 | yes | — |
| 111 | C2×C4×Dic5 | — | 2 | 3 | no | — |
| 112 | C2×#681 | C23 | 1 | 3 | yes | — |
| 113 | C22×#168 | C23 | 1 | 3 | yes | — |
| 114 | #4043 | — | 2 | 3 | no | — |
| 115 | #4043 | — | 2 | 3 | no | — |
| 116 | #4043 | — | 2 | 3 | no | — |
| 117 | #4043 | C23 | 1 | 3 | yes | — |
| 118 | #4043 | C23 | 1 | 6 | yes | — |
| 119 | #4043 | C23 | 1 | 3 | yes | — |
| 120 | #4041 | — | 2 | 3 | no | — |
| 121 | #4041 | C23 | 1 | 3 | yes | — |
| 122 | #4041 | C23 | 1 | 1 | yes | characteristic |
| 123 | #4039 | — | 2 | 3 | no | — |
| 124 | #4038 | — | 2 | 3 | no | — |
| 125 | #4038 | — | 2 | 3 | no | — |
| 126 | #4038 | C23 | 1 | 3 | yes | — |
| 127 | #4038 | C23 | 1 | 6 | yes | — |
| 128 | #4038 | C23 | 1 | 1 | yes | characteristic |
| 129 | D5×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 130 | D5×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 131 | #4033 | — | 2 | 3 | no | — |
| 132 | #4032 | — | 2 | 6 | no | — |
| 133 | #4032 | — | 2 | 3 | no | — |
| 134 | #4028 | — | 2 | 3 | no | — |
| 135 | #4027 | — | 2 | 6 | no | — |
| 136 | D5×C22⋊C4 | — | 2 | 3 | no | — |
| 137 | #4023 | — | 2 | 3 | no | — |
| 138 | #4021 | — | 2 | 3 | no | — |
| 139 | C4×D20 | — | 2 | 3 | no | — |
| 140 | C4×D20 | — | 2 | 3 | no | — |
| 141 | C4×D20 | — | 2 | 3 | no | — |
| 142 | #4018 | — | 2 | 3 | no | — |
| 143 | C42×D5 | — | 2 | 3 | no | — |
| 144 | #4015 | — | 2 | 3 | no | — |
| 145 | C4×Dic10 | — | 2 | 3 | no | — |
| 146 | C5×#107 | C23 | 1 | 3 | yes | — |
| 147 | C5×#107 | C23 | 1 | 6 | yes | — |
| 148 | C5×#107 | C23 | 1 | 1 | yes | characteristic |
| 149 | C5×#106 | C23 | 1 | 3 | yes | — |
| 150 | C5×#106 | C23 | 1 | 3 | yes | — |
| 151 | #3953 | C23 | 1 | 1 | yes | characteristic |
| 152 | #3953 | C23 | 1 | 3 | yes | — |
| 153 | #3952 | C23 | 1 | 1 | yes | characteristic |
| 154 | #3952 | C23 | 1 | 3 | yes | — |
| 155 | #3952 | C23 | 1 | 3 | yes | — |
| 156 | #3952 | C23 | 1 | 3 | yes | — |
| 157 | #3952 | C23 | 1 | 6 | yes | — |
| 158 | #3948 | C23 | 1 | 3 | yes | — |
| 159 | #3948 | C23 | 1 | 6 | yes | — |
| 160 | #3948 | C23 | 1 | 3 | yes | — |
| 161 | #3942 | C23 | 1 | 3 | yes | — |
| 162 | #3942 | C23 | 1 | 3 | yes | — |
| 163 | #3942 | C23 | 1 | 6 | yes | — |
| 164 | #3941 | C23 | 1 | 1 | yes | characteristic |
| 165 | #3941 | C23 | 1 | 3 | yes | — |
| 166 | #3940 | C23 | 1 | 6 | yes | — |
| 167 | #3940 | C23 | 1 | 1 | yes | characteristic |
| 168 | #3940 | C23 | 1 | 3 | yes | — |
| 169 | #3939 | C23 | 1 | 3 | yes | — |
| 170 | #3939 | C23 | 1 | 3 | yes | — |
| 171 | #3489 | — | 5 | 1 | no | — |
| 172 | #3428 | — | 5 | 1 | no | — |
| 173 | #3099 | — | 5 | 3 | no | — |
| 174 | #3098 | — | 5 | 3 | no | — |
| 175 | #3097 | — | 5 | 3 | no | — |
| 176 | #3097 | — | 5 | 3 | no | — |
| 177 | #3095 | — | 5 | 3 | no | — |
| 178 | #3093 | — | 5 | 3 | no | — |
| 179 | #3091 | — | 5 | 3 | no | — |
| 180 | C2×#485 | — | 5 | 3 | no | — |
| 181 | #2913 | D5 | 1 | 1 | yes | characteristic, complemented |
| 182 | #2912 | — | 5 | 1 | no | — |
| 183 | #2898 | — | 5 | 1 | no | — |
| 184 | #2898 | — | 5 | 1 | no | — |
| 185 | #2880 | — | 5 | 1 | no | — |
| 186 | C23×D5 | C2×D4 | 1 | 3 | yes | — |
| 187 | C5×#41 | #41 | 1 | 4 | yes | — |
| 188 | C5×#41 | #41 | 1 | 4 | yes | — |
| 189 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C2×C5×D4 | C2×D4 | 1 | 3 | yes | — |
| 191 | C22×C4×C5 | — | 2 | 3 | no | — |
| 192 | C22×C4×C5 | — | 2 | 3 | no | — |
| 193 | C22×C4×C5 | C24 | 1 | 3 | yes | — |
| 194 | C2×C22⋊D5 | — | 2 | 3 | no | — |
| 195 | C2×C22⋊D5 | C2×D4 | 1 | 6 | yes | — |
| 196 | C22×Dic5 | — | 2 | 3 | no | — |
| 197 | C22×Dic5 | — | 2 | 3 | no | — |
| 198 | C22×Dic5 | C2×D4 | 1 | 3 | yes | — |
| 199 | #713 | — | 2 | 4 | no | — |
| 200 | Q8×D5 | — | 2 | 4 | no | — |
| 201 | Q8×D5 | — | 4 | 4 | no | — |
| 202 | #711 | — | 2 | 12 | no | — |
| 203 | #711 | — | 4 | 12 | no | — |
| 204 | D4×D5 | — | 2 | 12 | no | — |
| 205 | #709 | — | 2 | 6 | no | — |
| 206 | #709 | — | 2 | 6 | no | — |
| 207 | #709 | — | 2 | 6 | no | — |
| 208 | #709 | — | 2 | 6 | no | — |
| 209 | C2×D20 | — | 2 | 1 | no | — |
| 210 | C2×D20 | — | 2 | 3 | no | — |
| 211 | C2×D20 | C2×D4 | 1 | 3 | yes | — |
| 212 | C2×D20 | C24 | 1 | 1 | yes | characteristic |
| 213 | C2×C4×D5 | — | 2 | 6 | no | — |
| 214 | C2×C4×D5 | — | 2 | 6 | no | — |
| 215 | C2×C4×D5 | — | 2 | 3 | no | — |
| 216 | C2×C4×D5 | — | 2 | 3 | no | — |
| 217 | C2×C4×D5 | — | 2 | 3 | no | — |
| 218 | C2×C4×D5 | C2×D4 | 1 | 3 | yes | — |
| 219 | C2×C4×D5 | C2×D4 | 1 | 3 | yes | — |
| 220 | C2×C4×D5 | C24 | 1 | 1 | yes | characteristic |
| 221 | C2×C4×D5 | C24 | 1 | 3 | yes | — |
| 222 | C2×Dic10 | — | 2 | 6 | no | — |
| 223 | C2×Dic10 | — | 2 | 6 | no | — |
| 224 | C2×Dic10 | — | 2 | 3 | no | — |
| 225 | C2×Dic10 | C2×D4 | 1 | 3 | yes | — |
| 226 | C2×Dic10 | C24 | 1 | 3 | yes | — |
| 227 | C5×M16 | — | 2 | 6 | no | — |
| 228 | C2×C5×C8 | — | 2 | 6 | no | — |
| 229 | C2×C5×C8 | C24 | 1 | 1 | yes | characteristic |
| 230 | C2×C5×C8 | C24 | 1 | 3 | yes | — |
| 231 | C5×C4⋊C4 | — | 2 | 3 | no | — |
| 232 | C5×C4⋊C4 | — | 2 | 3 | no | — |
| 233 | C5×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 234 | C5×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 235 | C5×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 236 | C5×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 237 | C5×C22⋊C4 | — | 2 | 3 | no | — |
| 238 | C5×C22⋊C4 | — | 2 | 3 | no | — |
| 239 | C42×C5 | — | 2 | 3 | no | — |
| 240 | C42×C5 | — | 2 | 3 | no | — |
| 241 | C22⋊Dic5 | — | 2 | 3 | no | — |
| 242 | #685 | — | 2 | 1 | no | — |
| 243 | #685 | — | 2 | 3 | no | — |
| 244 | #685 | — | 2 | 3 | no | — |
| 245 | #685 | — | 2 | 6 | no | — |
| 246 | #685 | — | 2 | 3 | no | — |
| 247 | #685 | — | 2 | 6 | no | — |
| 248 | #685 | — | 2 | 1 | no | — |
| 249 | #685 | — | 2 | 3 | no | — |
| 250 | C4⋊Dic5 | — | 2 | 3 | no | — |
| 251 | C4⋊Dic5 | — | 2 | 3 | no | — |
| 252 | C4⋊Dic5 | — | 2 | 6 | no | — |
| 253 | C4⋊Dic5 | — | 2 | 3 | no | — |
| 254 | C4⋊Dic5 | C24 | 1 | 1 | yes | characteristic |
| 255 | C4⋊Dic5 | C24 | 1 | 3 | yes | — |
| 256 | #683 | — | 2 | 3 | no | — |
| 257 | #683 | — | 2 | 3 | no | — |
| 258 | C4×Dic5 | — | 2 | 3 | no | — |
| 259 | C4×Dic5 | — | 2 | 6 | no | — |
| 260 | C4×Dic5 | — | 2 | 1 | no | — |
| 261 | C4×Dic5 | — | 2 | 3 | no | — |
| 262 | #681 | — | 2 | 6 | no | — |
| 263 | C2×#168 | — | 2 | 6 | no | — |
| 264 | C2×#168 | C24 | 1 | 3 | yes | — |
| 265 | C2×#168 | C24 | 1 | 1 | yes | characteristic |
| 266 | C2×2−1+4 | — | 5 | 1 | no | — |
| 267 | C22×#41 | — | 5 | 1 | no | — |
| 268 | C2×#131 | — | 5 | 1 | no | — |
| 269 | C2×#131 | C2×D5 | 1 | 1 | yes | characteristic |
| 270 | D4×Q8 | — | 10 | 1 | no | — |
| 271 | #548 | — | 10 | 1 | no | — |
| 272 | #547 | — | 10 | 3 | no | — |
| 273 | #546 | — | 10 | 3 | no | — |
| 274 | #537 | — | 5 | 3 | no | — |
| 275 | #536 | — | 5 | 3 | no | — |
| 276 | #525 | — | 5 | 3 | no | — |
| 277 | C2×C22⋊Q8 | — | 5 | 3 | no | — |
| 278 | #520 | — | 5 | 1 | no | — |
| 279 | #520 | — | 5 | 3 | no | — |
| 280 | #520 | — | 5 | 3 | no | — |
| 281 | #520 | C2×D5 | 1 | 1 | yes | characteristic |
| 282 | #520 | C2×D5 | 1 | 1 | yes | characteristic |
| 283 | #519 | — | 10 | 1 | no | — |
| 284 | #518 | — | 10 | 3 | no | — |
| 285 | C4×#41 | — | 10 | 3 | no | — |
| 286 | C4×#41 | — | 10 | 1 | no | — |
| 287 | C2×#117 | — | 5 | 3 | no | — |
| 288 | C2×#117 | — | 5 | 3 | no | — |
| 289 | #485 | — | 5 | 3 | no | — |
| 290 | #485 | — | 5 | 6 | no | — |
| 291 | #485 | — | 5 | 6 | no | — |
| 292 | #485 | — | 5 | 6 | no | — |
| 293 | #485 | — | 5 | 3 | no | — |
| 294 | #485 | — | 5 | 6 | no | — |
| 295 | #484 | — | 5 | 3 | no | — |
| 296 | #484 | — | 5 | 6 | no | — |
| 297 | #483 | — | 5 | 3 | no | — |
| 298 | #483 | — | 5 | 6 | no | — |
| 299 | #482 | — | 5 | 1 | no | — |
| 300 | #482 | — | 5 | 6 | no | — |
| 301 | #482 | — | 5 | 3 | no | — |
| 302 | #481 | — | 5 | 3 | no | — |
| 303 | #480 | — | 5 | 3 | no | — |
| 304 | #428 | — | 5 | 3 | no | — |
| 305 | #428 | — | 5 | 3 | no | — |
| 306 | #428 | C2×D5 | 1 | 3 | yes | complemented |
| 307 | #428 | C2×D5 | 1 | 3 | yes | complemented |
| 308 | #427 | — | 5 | 3 | no | — |
| 309 | #427 | C2×D5 | 1 | 3 | yes | complemented |
| 310 | C2×#107 | C2×D5 | 1 | 3 | yes | complemented |
| 311 | C2×#106 | — | 5 | 3 | no | — |
| 312 | #419 | — | 5 | 3 | no | — |
| 313 | #419 | — | 5 | 3 | no | — |
| 314 | #417 | — | 5 | 3 | no | — |
| 315 | #417 | — | 5 | 3 | no | — |
| 316 | #416 | — | 5 | 3 | no | — |
| 317 | #416 | — | 5 | 3 | no | — |
| 318 | C2×#103 | — | 5 | 3 | no | — |
| 319 | C2×#103 | — | 5 | 3 | no | — |
| 320 | #408 | — | 5 | 3 | no | — |
| 321 | #408 | — | 5 | 3 | no | — |
| 322 | #407 | — | 5 | 3 | no | — |
| 323 | C2×C22⋊C8 | — | 5 | 3 | no | — |
| 324 | C23×C5 | C22×D4 | 1 | 3 | yes | — |
| 325 | C22×D5 | — | 2 | 6 | no | — |
| 326 | C22×D5 | — | 2 | 1 | no | — |
| 327 | C22×D5 | — | 4 | 3 | no | — |
| 328 | C22×D5 | — | 4 | 3 | no | — |
| 329 | C22×D5 | C22×D4 | 1 | 1 | yes | characteristic |
| 330 | C22×D5 | C22×D4 | 1 | 3 | yes | — |
| 331 | C5×Q8 | #123 | 1 | 4 | yes | — |
| 332 | C5×D4 | #123 | 1 | 12 | yes | — |
| 333 | C2×C4×C5 | — | 2 | 3 | no | — |
| 334 | C2×C4×C5 | — | 2 | 1 | no | — |
| 335 | C2×C4×C5 | — | 2 | 1 | no | — |
| 336 | C2×C4×C5 | — | 2 | 3 | no | — |
| 337 | C2×C4×C5 | — | 8 | 3 | no | — |
| 338 | C2×C4×C5 | — | 8 | 3 | no | — |
| 339 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 340 | C2×C4×C5 | C2×#41 | 1 | 6 | yes | — |
| 341 | C2×C4×C5 | C2×#41 | 1 | 6 | yes | — |
| 342 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 343 | C22⋊D5 | — | 2 | 12 | no | — |
| 344 | C22⋊D5 | — | 4 | 6 | no | — |
| 345 | C2×Dic5 | — | 2 | 6 | no | — |
| 346 | C2×Dic5 | — | 2 | 1 | no | — |
| 347 | C2×Dic5 | — | 2 | 3 | no | — |
| 348 | C2×Dic5 | — | 2 | 3 | no | — |
| 349 | C2×Dic5 | — | 4 | 6 | no | — |
| 350 | C2×Dic5 | — | 8 | 3 | no | — |
| 351 | C2×Dic5 | C22×D4 | 1 | 1 | yes | characteristic |
| 352 | C2×Dic5 | C22×D4 | 1 | 3 | yes | — |
| 353 | D20 | — | 2 | 6 | no | — |
| 354 | D20 | — | 2 | 1 | no | — |
| 355 | D20 | — | 2 | 1 | no | — |
| 356 | D20 | — | 4 | 2 | no | — |
| 357 | D20 | — | 8 | 3 | no | — |
| 358 | C4×D5 | — | 2 | 6 | no | — |
| 359 | C4×D5 | — | 2 | 6 | no | — |
| 360 | C4×D5 | — | 2 | 1 | no | — |
| 361 | C4×D5 | — | 2 | 1 | no | — |
| 362 | C4×D5 | — | 2 | 3 | no | — |
| 363 | C4×D5 | — | 2 | 3 | no | — |
| 364 | C4×D5 | — | 4 | 6 | no | — |
| 365 | C4×D5 | — | 8 | 3 | no | — |
| 366 | C4×D5 | — | 8 | 3 | no | — |
| 367 | Dic10 | — | 2 | 6 | no | — |
| 368 | Dic10 | — | 2 | 3 | no | — |
| 369 | Dic10 | — | 2 | 3 | no | — |
| 370 | Dic10 | — | 4 | 6 | no | — |
| 371 | C5×C8 | — | 2 | 1 | no | — |
| 372 | C5×C8 | — | 2 | 3 | no | — |
| 373 | #168 | — | 2 | 1 | no | — |
| 374 | #168 | — | 2 | 3 | no | — |
| 375 | 2−1+4 | — | 10 | 4 | no | — |
| 376 | 2−1+4 | — | 10 | 4 | no | — |
| 377 | C2×#41 | — | 5 | 1 | no | — |
| 378 | C2×#41 | — | 5 | 3 | no | — |
| 379 | C2×#41 | — | 5 | 3 | no | — |
| 380 | C2×#41 | — | 5 | 3 | no | — |
| 381 | C2×#41 | — | 10 | 4 | no | — |
| 382 | C2×#41 | — | 10 | 4 | no | — |
| 383 | C2×#41 | — | 10 | 3 | no | — |
| 384 | C2×#41 | C22×D5 | 1 | 1 | yes | characteristic |
| 385 | C22×Q8 | — | 5 | 1 | no | — |
| 386 | C22×Q8 | — | 5 | 3 | no | — |
| 387 | C22×Q8 | — | 10 | 1 | no | — |
| 388 | C22×D4 | — | 5 | 3 | no | — |
| 389 | C23×C4 | — | 5 | 3 | no | — |
| 390 | #131 | — | 2 | 4 | no | — |
| 391 | #131 | — | 10 | 4 | no | — |
| 392 | C2×M16 | — | 5 | 3 | no | — |
| 393 | C2×M16 | C22×D5 | 1 | 3 | yes | — |
| 394 | C22×C8 | — | 5 | 3 | no | — |
| 395 | C22×C8 | C22×D5 | 1 | 3 | yes | — |
| 396 | C4⋊Q8 | — | 10 | 3 | no | — |
| 397 | #124 | — | 10 | 3 | no | — |
| 398 | #123 | — | 10 | 3 | no | — |
| 399 | #123 | — | 10 | 6 | no | — |
| 400 | C22⋊Q8 | — | 5 | 3 | no | — |
| 401 | C22⋊Q8 | — | 5 | 6 | no | — |
| 402 | C22⋊Q8 | — | 5 | 3 | no | — |
| 403 | C22⋊Q8 | — | 10 | 3 | no | — |
| 404 | C22⋊Q8 | — | 10 | 3 | no | — |
| 405 | C22⋊Q8 | — | 10 | 3 | no | — |
| 406 | #121 | — | 5 | 1 | no | — |
| 407 | #121 | — | 5 | 3 | no | — |
| 408 | #121 | — | 10 | 3 | no | — |
| 409 | #121 | — | 10 | 6 | no | — |
| 410 | #120 | — | 10 | 3 | no | — |
| 411 | C4×Q8 | — | 2 | 1 | no | — |
| 412 | C4×Q8 | — | 2 | 1 | no | — |
| 413 | C4×Q8 | — | 10 | 3 | no | — |
| 414 | C4×Q8 | — | 10 | 3 | no | — |
| 415 | C4×Q8 | — | 10 | 1 | no | — |
| 416 | C4×D4 | — | 2 | 3 | no | — |
| 417 | C4×D4 | — | 2 | 3 | no | — |
| 418 | C4×D4 | — | 10 | 3 | no | — |
| 419 | C4×D4 | — | 10 | 3 | no | — |
| 420 | C4×D4 | — | 10 | 3 | no | — |
| 421 | C4×D4 | — | 10 | 6 | no | — |
| 422 | C4×D4 | — | 10 | 3 | no | — |
| 423 | C4×D4 | — | 10 | 6 | no | — |
| 424 | C4×D4 | — | 10 | 3 | no | — |
| 425 | #117 | — | 5 | 3 | no | — |
| 426 | #117 | — | 5 | 3 | no | — |
| 427 | #117 | — | 5 | 1 | no | — |
| 428 | #117 | — | 5 | 6 | no | — |
| 429 | #117 | — | 10 | 3 | no | — |
| 430 | #117 | — | 10 | 3 | no | — |
| 431 | #117 | — | 10 | 3 | no | — |
| 432 | #117 | — | 10 | 3 | no | — |
| 433 | #117 | C22×D5 | 1 | 3 | yes | — |
| 434 | #117 | C22×D5 | 1 | 3 | yes | — |
| 435 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 436 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 437 | C2×C4⋊C4 | — | 5 | 3 | no | — |
| 438 | C2×C4⋊C4 | — | 10 | 3 | no | — |
| 439 | C2×C4⋊C4 | C22×D5 | 1 | 3 | yes | — |
| 440 | C2×C4⋊C4 | C22×D5 | 1 | 3 | yes | — |
| 441 | C2×C22⋊C4 | — | 10 | 3 | no | — |
| 442 | C2×C22⋊C4 | — | 10 | 3 | no | — |
| 443 | C2×C22⋊C4 | — | 10 | 3 | no | — |
| 444 | C2×C42 | — | 10 | 3 | no | — |
| 445 | C2×C42 | — | 10 | 3 | no | — |
| 446 | #107 | — | 5 | 3 | no | — |
| 447 | #107 | — | 5 | 3 | no | — |
| 448 | #107 | C22×D5 | 1 | 3 | yes | — |
| 449 | #107 | C22×D5 | 1 | 6 | yes | — |
| 450 | #107 | C22×D5 | 1 | 1 | yes | characteristic |
| 451 | #106 | — | 5 | 3 | no | — |
| 452 | #106 | — | 5 | 6 | no | — |
| 453 | #106 | — | 5 | 1 | no | — |
| 454 | #106 | C22×D5 | 1 | 3 | yes | — |
| 455 | #106 | C22×D5 | 1 | 3 | yes | — |
| 456 | #103 | — | 5 | 3 | no | — |
| 457 | #103 | — | 5 | 6 | no | — |
| 458 | #103 | — | 5 | 3 | no | — |
| 459 | #103 | — | 5 | 3 | no | — |
| 460 | #103 | — | 5 | 6 | no | — |
| 461 | #103 | — | 5 | 3 | no | — |
| 462 | #102 | — | 5 | 1 | no | — |
| 463 | #102 | — | 5 | 3 | no | — |
| 464 | #102 | — | 5 | 1 | no | — |
| 465 | #102 | — | 5 | 3 | no | — |
| 466 | C22⋊C8 | — | 5 | 1 | no | — |
| 467 | C22⋊C8 | — | 5 | 3 | no | — |
| 468 | C22⋊C8 | — | 5 | 3 | no | — |
| 469 | C22⋊C8 | — | 5 | 3 | no | — |
| 470 | C22⋊C8 | — | 5 | 6 | no | — |
| 471 | C22×C5 | — | 2 | 3 | no | — |
| 472 | C22×C5 | — | 2 | 3 | no | — |
| 473 | C22×C5 | C2×#123 | 1 | 6 | yes | — |
| 474 | C22×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 475 | C2×D5 | — | 2 | 3 | no | — |
| 476 | C2×D5 | — | 2 | 1 | no | — |
| 477 | C2×D5 | — | 2 | 3 | no | — |
| 478 | C2×D5 | — | 2 | 1 | no | — |
| 479 | C2×D5 | — | 2 | 1 | no | — |
| 480 | C2×D5 | — | 2 | 3 | no | — |
| 481 | C2×D5 | — | 4 | 1 | no | — |
| 482 | C2×D5 | — | 4 | 1 | no | — |
| 483 | C2×D5 | — | 4 | 1 | no | — |
| 484 | C2×D5 | — | 8 | 6 | no | — |
| 485 | C4×C5 | — | 4 | 3 | no | — |
| 486 | C4×C5 | — | 4 | 3 | no | — |
| 487 | C4×C5 | — | 4 | 1 | no | — |
| 488 | C4×C5 | — | 4 | 1 | no | — |
| 489 | C4×C5 | C2×#123 | 1 | 6 | yes | — |
| 490 | C4×C5 | C22×#41 | 1 | 1 | yes | characteristic |
| 491 | C4×C5 | C22×#41 | 1 | 1 | yes | characteristic |
| 492 | Dic5 | — | 2 | 3 | no | — |
| 493 | Dic5 | — | 2 | 1 | no | — |
| 494 | Dic5 | — | 4 | 1 | no | — |
| 495 | Dic5 | — | 4 | 3 | no | — |
| 496 | Dic5 | — | 4 | 3 | no | — |
| 497 | C24 | — | 5 | 3 | no | — |
| 498 | #41 | — | 10 | 4 | no | — |
| 499 | #41 | — | 10 | 12 | no | — |
| 500 | #41 | — | 10 | 6 | no | — |
| 501 | #41 | — | 10 | 6 | no | — |
| 502 | #41 | — | 10 | 6 | no | — |
| 503 | #41 | — | 10 | 6 | no | — |
| 504 | #41 | — | 20 | 12 | no | — |
| 505 | #41 | #709 | 1 | 4 | yes | — |
| 506 | #41 | #713 | 1 | 4 | yes | — |
| 507 | C2×Q8 | — | 5 | 3 | no | — |
| 508 | C2×Q8 | — | 5 | 3 | no | — |
| 509 | C2×Q8 | — | 10 | 4 | no | — |
| 510 | C2×Q8 | — | 10 | 3 | no | — |
| 511 | C2×Q8 | — | 10 | 6 | no | — |
| 512 | C2×Q8 | — | 10 | 6 | no | — |
| 513 | C2×Q8 | — | 20 | 4 | no | — |
| 514 | C2×Q8 | D4×D5 | 1 | 1 | yes | characteristic |
| 515 | C2×D4 | — | 5 | 6 | no | — |
| 516 | C2×D4 | — | 5 | 3 | no | — |
| 517 | C2×D4 | — | 5 | 1 | no | — |
| 518 | C2×D4 | — | 10 | 1 | no | — |
| 519 | C2×D4 | — | 10 | 3 | no | — |
| 520 | C2×D4 | — | 10 | 12 | no | — |
| 521 | C2×D4 | — | 10 | 3 | no | — |
| 522 | C2×D4 | D4×D5 | 1 | 3 | yes | — |
| 523 | C22×C4 | — | 2 | 3 | no | — |
| 524 | C22×C4 | — | 2 | 3 | no | — |
| 525 | C22×C4 | — | 5 | 3 | no | — |
| 526 | C22×C4 | — | 5 | 3 | no | — |
| 527 | C22×C4 | — | 5 | 3 | no | — |
| 528 | C22×C4 | — | 5 | 3 | no | — |
| 529 | C22×C4 | — | 5 | 1 | no | — |
| 530 | C22×C4 | — | 10 | 3 | no | — |
| 531 | C22×C4 | — | 10 | 3 | no | — |
| 532 | C22×C4 | — | 10 | 6 | no | — |
| 533 | C22×C4 | — | 10 | 6 | no | — |
| 534 | C22×C4 | — | 10 | 3 | no | — |
| 535 | C22×C4 | — | 10 | 3 | no | — |
| 536 | C22×C4 | — | 10 | 3 | no | — |
| 537 | C22×C4 | C23×D5 | 1 | 3 | yes | — |
| 538 | M16 | — | 2 | 6 | no | — |
| 539 | M16 | — | 10 | 6 | no | — |
| 540 | C2×C8 | — | 2 | 6 | no | — |
| 541 | C2×C8 | — | 5 | 1 | no | — |
| 542 | C2×C8 | — | 5 | 3 | no | — |
| 543 | C2×C8 | — | 10 | 6 | no | — |
| 544 | C2×C8 | C23×D5 | 1 | 3 | yes | — |
| 545 | C2×C8 | C23×D5 | 1 | 1 | yes | characteristic |
| 546 | C4⋊C4 | — | 2 | 3 | no | — |
| 547 | C4⋊C4 | — | 2 | 3 | no | — |
| 548 | C4⋊C4 | — | 5 | 3 | no | — |
| 549 | C4⋊C4 | — | 5 | 1 | no | — |
| 550 | C4⋊C4 | — | 10 | 3 | no | — |
| 551 | C4⋊C4 | — | 10 | 3 | no | — |
| 552 | C4⋊C4 | — | 10 | 3 | no | — |
| 553 | C4⋊C4 | — | 10 | 6 | no | — |
| 554 | C4⋊C4 | — | 10 | 3 | no | — |
| 555 | C4⋊C4 | — | 10 | 3 | no | — |
| 556 | C4⋊C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 557 | C4⋊C4 | C23×D5 | 1 | 3 | yes | — |
| 558 | C4⋊C4 | C23×D5 | 1 | 3 | yes | — |
| 559 | C4⋊C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 560 | C22⋊C4 | — | 2 | 3 | no | — |
| 561 | C22⋊C4 | — | 2 | 3 | no | — |
| 562 | C22⋊C4 | — | 10 | 1 | no | — |
| 563 | C22⋊C4 | — | 10 | 3 | no | — |
| 564 | C22⋊C4 | — | 10 | 1 | no | — |
| 565 | C22⋊C4 | — | 10 | 3 | no | — |
| 566 | C22⋊C4 | — | 10 | 3 | no | — |
| 567 | C22⋊C4 | — | 10 | 6 | no | — |
| 568 | C22⋊C4 | — | 10 | 6 | no | — |
| 569 | C22⋊C4 | — | 10 | 3 | no | — |
| 570 | C22⋊C4 | — | 10 | 3 | no | — |
| 571 | C42 | — | 2 | 3 | no | — |
| 572 | C42 | — | 2 | 3 | no | — |
| 573 | C42 | — | 10 | 1 | no | — |
| 574 | C42 | — | 10 | 3 | no | — |
| 575 | C42 | — | 10 | 6 | no | — |
| 576 | C42 | — | 10 | 3 | no | — |
| 577 | C2×C5 | — | 2 | 6 | no | — |
| 578 | C2×C5 | C22×#123 | 1 | 1 | yes | characteristic |
| 579 | C2×C5 | #3584 | 1 | 1 | yes | characteristic |
| 580 | C2×C5 | #3586 | 1 | 1 | yes | characteristic |
| 581 | D5 | — | 4 | 3 | no | — |
| 582 | D5 | — | 4 | 1 | no | — |
| 583 | D5 | — | 8 | 1 | no | — |
| 584 | C23 | — | 5 | 1 | no | — |
| 585 | C23 | — | 5 | 3 | no | — |
| 586 | C23 | — | 10 | 6 | no | — |
| 587 | C23 | — | 10 | 1 | no | — |
| 588 | C23 | — | 20 | 3 | no | — |
| 589 | C23 | — | 20 | 3 | no | — |
| 590 | C23 | C2×D4×D5 | 1 | 3 | yes | — |
| 591 | Q8 | — | 10 | 6 | no | — |
| 592 | Q8 | — | 10 | 3 | no | — |
| 593 | Q8 | — | 10 | 3 | no | — |
| 594 | Q8 | — | 20 | 6 | no | — |
| 595 | Q8 | #4040 | 1 | 4 | yes | — |
| 596 | D4 | — | 10 | 12 | no | — |
| 597 | D4 | — | 10 | 6 | no | — |
| 598 | D4 | — | 10 | 1 | no | — |
| 599 | D4 | — | 10 | 1 | no | — |
| 600 | D4 | — | 20 | 2 | no | — |
| 601 | D4 | — | 20 | 6 | no | — |
| 602 | D4 | — | 40 | 3 | no | — |
| 603 | D4 | #4040 | 1 | 12 | yes | — |
| 604 | C2×C4 | — | 2 | 1 | no | — |
| 605 | C2×C4 | — | 2 | 1 | no | — |
| 606 | C2×C4 | — | 2 | 3 | no | — |
| 607 | C2×C4 | — | 2 | 3 | no | — |
| 608 | C2×C4 | — | 5 | 1 | no | — |
| 609 | C2×C4 | — | 5 | 3 | no | — |
| 610 | C2×C4 | — | 8 | 3 | no | — |
| 611 | C2×C4 | — | 8 | 3 | no | — |
| 612 | C2×C4 | — | 10 | 6 | no | — |
| 613 | C2×C4 | — | 10 | 6 | no | — |
| 614 | C2×C4 | — | 10 | 6 | no | — |
| 615 | C2×C4 | — | 10 | 1 | no | — |
| 616 | C2×C4 | — | 10 | 3 | no | — |
| 617 | C2×C4 | — | 10 | 1 | no | — |
| 618 | C2×C4 | — | 10 | 3 | no | — |
| 619 | C2×C4 | — | 10 | 1 | no | — |
| 620 | C2×C4 | — | 10 | 3 | no | — |
| 621 | C2×C4 | — | 10 | 3 | no | — |
| 622 | C2×C4 | — | 20 | 6 | no | — |
| 623 | C2×C4 | — | 20 | 6 | no | — |
| 624 | C2×C4 | — | 40 | 3 | no | — |
| 625 | C2×C4 | — | 40 | 3 | no | — |
| 626 | C2×C4 | — | 40 | 3 | no | — |
| 627 | C2×C4 | C2×#709 | 1 | 6 | yes | — |
| 628 | C2×C4 | C2×D4×D5 | 1 | 3 | yes | — |
| 629 | C2×C4 | C2×#713 | 1 | 6 | yes | — |
| 630 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 631 | C8 | — | 2 | 1 | no | — |
| 632 | C8 | — | 2 | 3 | no | — |
| 633 | C8 | — | 10 | 1 | no | — |
| 634 | C8 | — | 10 | 3 | no | — |
| 635 | C5 | #60524 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 636 | C22 | — | 2 | 3 | no | — |
| 637 | C22 | — | 2 | 3 | no | — |
| 638 | C22 | — | 10 | 1 | no | — |
| 639 | C22 | — | 10 | 3 | no | — |
| 640 | C22 | — | 10 | 3 | no | — |
| 641 | C22 | — | 10 | 1 | no | — |
| 642 | C22 | — | 10 | 3 | no | — |
| 643 | C22 | — | 10 | 1 | no | — |
| 644 | C22 | — | 20 | 1 | no | — |
| 645 | C22 | — | 20 | 1 | no | — |
| 646 | C22 | — | 20 | 1 | no | — |
| 647 | C22 | — | 40 | 6 | no | — |
| 648 | C22 | C2×#4040 | 1 | 6 | yes | — |
| 649 | C22 | C22×D4×D5 | 1 | 1 | yes | characteristic |
| 650 | C4 | — | 4 | 3 | no | — |
| 651 | C4 | — | 4 | 3 | no | — |
| 652 | C4 | — | 4 | 1 | no | — |
| 653 | C4 | — | 4 | 1 | no | — |
| 654 | C4 | — | 10 | 1 | no | — |
| 655 | C4 | — | 10 | 3 | no | — |
| 656 | C4 | — | 20 | 3 | no | — |
| 657 | C4 | — | 20 | 1 | no | — |
| 658 | C4 | — | 20 | 3 | no | — |
| 659 | C4 | C2×#4040 | 1 | 6 | yes | — |
| 660 | C4 | C22×#709 | 1 | 1 | yes | characteristic |
| 661 | C4 | C22×#713 | 1 | 1 | yes | characteristic |
| 662 | C2 | — | 2 | 6 | no | — |
| 663 | C2 | — | 20 | 1 | no | — |
| 664 | C2 | — | 20 | 3 | no | — |
| 665 | C2 | — | 40 | 1 | no | — |
| 666 | C2 | C22×#4040 | 1 | 1 | yes | characteristic |
| 667 | C2 | #10619104 | 1 | 1 | yes | characteristic |
| 668 | C2 | #10619112 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10617786 | C2 | semidirect |
| 3. C5×#2913 | C2 | semidirect |
| 4. #10615537 | C2 | semidirect |
| 5. #10615524 | C2 | semidirect |
| 6. #10614301 | C2 | semidirect |
| 7. #10614292 | C2 | semidirect |
| 8. #10610953 | C2 | semidirect |
| 9. #10610951 | C2 | semidirect |
| 10. #10610949 | C2 | semidirect |
| 11. #10610947 | C2 | semidirect |
| 12. #10610916 | C2 | semidirect |
| 13. #10610906 | C2 | semidirect |
| 14. C2×#65177 | C2 | semidirect |
| 15. #10610872 | C2 | semidirect |
| 39. C5×#428 | C22 | semidirect |
| 40. C5×#428 | C22 | semidirect |
| 41. C5×#427 | C22 | semidirect |
| 42. C2×C5×#107 | C22 | semidirect |
| 43. #65422 | C22 | semidirect |
| 46. #65409 | C22 | semidirect |
| 47. #65402 | C22 | semidirect |
| 50. C2×#3948 | C22 | semidirect |
| 51. #65293 | C22 | semidirect |
| 52. #65291 | C22 | semidirect |
| 53. #65287 | C22 | semidirect |
| 54. #65284 | C22 | semidirect |
| 55. C2×#3942 | C22 | semidirect |
| 56. #65255 | C22 | semidirect |
| 57. #65253 | C22 | semidirect |
| 58. C2×#3940 | C22 | semidirect |
| 61. #65177 | C22 | semidirect |
| 62. #65177 | C22 | semidirect |
| 64. #65174 | C22 | semidirect |
| 65. #65173 | C22 | semidirect |
| 66. #65173 | C22 | semidirect |
| 67. #65171 | C22 | semidirect |
| 69. #65156 | C22 | semidirect |
| 71. #65152 | C22 | semidirect |
| 72. #65151 | C22 | semidirect |
| 73. #65151 | C22 | semidirect |
| 181. #2913 | D5 | semidirect |
| 306. #428 | C2×D5 | semidirect |
| 307. #428 | C2×D5 | semidirect |
| 309. #427 | C2×D5 | semidirect |
| 310. C2×#107 | C2×D5 | semidirect |
| 635. C5 | #60524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617802 | 2 |
| #10617786 | 2 |
| C5×#2913 | 2 |
| #10615537 | 2 |
| #10615524 | 2 |
| #10614301 | 2 |
| #10614292 | 2 |
| #10610953 | 2 |
| #10610951 | 2 |
| #10610949 | 2 |
| #10610947 | 2 |
| #10610916 | 2 |
| #10610906 | 2 |
| C2×#65177 | 2 |
| #10610872 | 2 |
| #60524 | 5 |