Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1732 conjugacy classes of subgroups.
The subgroup lattice has 660 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10617999 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10617731 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C5×#3080 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#65358 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10614237 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #10612951 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10612950 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10612886 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10612885 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #10610977 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10610933 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10610788 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #10610776 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #10610643 | C2 | 1 | 2 | yes | maximal |
| 15 | #10610608 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | C2×C5×#125 | C22 | 1 | 1 | yes | characteristic |
| 17 | C4×C5×#41 | C22 | 1 | 1 | yes | characteristic |
| 18 | #66159 | C22 | 1 | 2 | yes | — |
| 19 | C2×#4096 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#4055 | C22 | 1 | 2 | yes | — |
| 21 | #66024 | C22 | 1 | 4 | yes | — |
| 22 | #66023 | — | 2 | 2 | no | — |
| 23 | #66022 | — | 2 | 1 | no | — |
| 24 | D5×#125 | — | 2 | 1 | no | — |
| 25 | #66019 | C22 | 1 | 4 | yes | — |
| 26 | #65901 | C22 | 1 | 4 | yes | — |
| 27 | #65876 | C22 | 1 | 4 | yes | — |
| 28 | #65875 | — | 2 | 4 | no | — |
| 29 | #65852 | — | 2 | 1 | no | — |
| 30 | #65852 | — | 2 | 1 | no | — |
| 31 | #65850 | C22 | 1 | 2 | yes | — |
| 32 | #65845 | — | 2 | 4 | no | — |
| 33 | #65838 | C22 | 1 | 2 | yes | — |
| 34 | #65834 | C22 | 1 | 2 | yes | — |
| 35 | C4×#709 | C22 | 1 | 1 | yes | characteristic |
| 36 | #65804 | — | 2 | 2 | no | — |
| 37 | #65804 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×#4015 | C22 | 1 | 1 | yes | characteristic |
| 39 | C5×#479 | C22 | 1 | 4 | yes | — |
| 40 | C5×#478 | C22 | 1 | 4 | yes | — |
| 41 | C5×#428 | C22 | 1 | 2 | yes | — |
| 42 | C5×#423 | C22 | 1 | 1 | yes | characteristic |
| 43 | C5×#417 | C22 | 1 | 2 | yes | — |
| 44 | #65522 | C22 | 1 | 1 | yes | characteristic |
| 45 | #65411 | C22 | 1 | 2 | yes | — |
| 46 | #65409 | C22 | 1 | 2 | yes | — |
| 47 | #65408 | C22 | 1 | 2 | yes | — |
| 48 | #65358 | C22 | 1 | 4 | yes | — |
| 49 | #65358 | C22 | 1 | 4 | yes | — |
| 50 | #65319 | C22 | 1 | 2 | yes | — |
| 51 | #65315 | C22 | 1 | 2 | yes | — |
| 52 | #65307 | C22 | 1 | 2 | yes | — |
| 53 | #65303 | C22 | 1 | 2 | yes | — |
| 54 | #65291 | C22 | 1 | 1 | yes | characteristic |
| 55 | #65287 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×#3942 | C22 | 1 | 2 | yes | — |
| 57 | C2×#3942 | C22 | 1 | 2 | yes | — |
| 58 | C2×#3935 | C22 | 1 | 1 | yes | characteristic |
| 59 | #65178 | C22 | 1 | 4 | yes | — |
| 60 | #65166 | C22 | 1 | 4 | yes | — |
| 61 | #65164 | C22 | 1 | 4 | yes | — |
| 62 | #65162 | C22 | 1 | 4 | yes | — |
| 63 | #65146 | C22 | 1 | 4 | yes | — |
| 64 | #65143 | C22 | 1 | 4 | yes | — |
| 65 | #65142 | C22 | 1 | 4 | yes | — |
| 66 | #65141 | C22 | 1 | 4 | yes | — |
| 67 | #65138 | C22 | 1 | 4 | yes | — |
| 68 | #65130 | C22 | 1 | 4 | yes | — |
| 69 | #65117 | C22 | 1 | 4 | yes | — |
| 70 | #65117 | C22 | 1 | 4 | yes | — |
| 71 | #65107 | C22 | 1 | 4 | yes | — |
| 72 | #65086 | C22 | 1 | 4 | yes | — |
| 73 | #65082 | C22 | 1 | 4 | yes | — |
| 74 | #65081 | C22 | 1 | 4 | yes | — |
| 75 | #65076 | C22 | 1 | 4 | yes | — |
| 76 | #65057 | C22 | 1 | 4 | yes | — |
| 77 | #65056 | C22 | 1 | 4 | yes | — |
| 78 | #65054 | C22 | 1 | 4 | yes | — |
| 79 | #61338 | — | 5 | 1 | no | maximal, Sylow |
| 80 | C2×C5×#41 | C23 | 1 | 1 | yes | characteristic |
| 81 | C2×#709 | C23 | 1 | 1 | yes | characteristic |
| 82 | C22×Dic10 | C23 | 1 | 2 | yes | — |
| 83 | C2×C5×M16 | C23 | 1 | 2 | yes | — |
| 84 | C5×#125 | — | 2 | 1 | no | — |
| 85 | C5×#125 | — | 2 | 1 | no | — |
| 86 | C5×#125 | C23 | 1 | 4 | yes | — |
| 87 | C4×C5×Q8 | C23 | 1 | 2 | yes | — |
| 88 | C4×C5×D4 | — | 2 | 2 | no | — |
| 89 | C4×C5×D4 | C23 | 1 | 2 | yes | — |
| 90 | C5×#117 | — | 2 | 1 | no | — |
| 91 | C5×#117 | C23 | 1 | 1 | yes | characteristic |
| 92 | C2×C5×C4⋊C4 | — | 2 | 2 | no | — |
| 93 | C2×C5×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 94 | C2×C42×C5 | — | 2 | 1 | no | — |
| 95 | C2×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 96 | #4096 | — | 2 | 4 | no | — |
| 97 | #4090 | C23 | 1 | 4 | yes | — |
| 98 | C2×#689 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×#688 | C23 | 1 | 1 | yes | characteristic |
| 100 | #4082 | C23 | 1 | 4 | yes | — |
| 101 | #4081 | — | 2 | 4 | no | — |
| 102 | C2×#687 | C23 | 1 | 1 | yes | characteristic |
| 103 | C2×#686 | C23 | 1 | 1 | yes | characteristic |
| 104 | C4×C22⋊D5 | — | 2 | 2 | no | — |
| 105 | C4×C22⋊D5 | — | 2 | 4 | no | — |
| 106 | #4072 | — | 2 | 4 | no | — |
| 107 | #4072 | C23 | 1 | 1 | yes | characteristic |
| 108 | #4072 | C23 | 1 | 2 | yes | — |
| 109 | C2×C4⋊Dic5 | — | 2 | 2 | no | — |
| 110 | #4070 | — | 2 | 4 | no | — |
| 111 | #4070 | — | 2 | 4 | no | — |
| 112 | #4070 | — | 2 | 2 | no | — |
| 113 | #4070 | — | 2 | 2 | no | — |
| 114 | #4070 | D4 | 1 | 4 | yes | — |
| 115 | C22×#168 | C23 | 1 | 1 | yes | characteristic |
| 116 | C22×#168 | C23 | 1 | 1 | yes | characteristic |
| 117 | #4055 | — | 2 | 8 | no | — |
| 118 | C2×Dic20 | C23 | 1 | 4 | yes | — |
| 119 | C2×#677 | C23 | 1 | 4 | yes | — |
| 120 | #4043 | — | 2 | 4 | no | — |
| 121 | #4042 | — | 2 | 4 | no | — |
| 122 | #4042 | — | 2 | 4 | no | — |
| 123 | #4039 | C23 | 1 | 4 | yes | — |
| 124 | #4038 | — | 2 | 2 | no | — |
| 125 | D5×C4⋊C4 | — | 2 | 2 | no | — |
| 126 | D5×C4⋊C4 | — | 2 | 4 | no | — |
| 127 | #4036 | — | 2 | 2 | no | — |
| 128 | #4036 | C23 | 1 | 4 | yes | — |
| 129 | #4035 | — | 2 | 4 | no | — |
| 130 | #4035 | — | 2 | 4 | no | — |
| 131 | #4035 | — | 2 | 4 | no | — |
| 132 | #4035 | — | 2 | 4 | no | — |
| 133 | #4034 | — | 2 | 4 | no | — |
| 134 | #4034 | — | 2 | 2 | no | — |
| 135 | #4034 | C23 | 1 | 4 | yes | — |
| 136 | #4033 | — | 2 | 4 | no | — |
| 137 | #4033 | C23 | 1 | 4 | yes | — |
| 138 | #4033 | C23 | 1 | 4 | yes | — |
| 139 | #4033 | C23 | 1 | 4 | yes | — |
| 140 | #4025 | — | 2 | 4 | no | — |
| 141 | #4025 | — | 2 | 4 | no | — |
| 142 | #4023 | — | 2 | 4 | no | — |
| 143 | C4×D20 | C23 | 1 | 2 | yes | — |
| 144 | #4018 | — | 2 | 1 | no | — |
| 145 | C42×D5 | — | 2 | 1 | no | — |
| 146 | #4016 | — | 2 | 4 | no | — |
| 147 | #4016 | D4 | 1 | 1 | yes | characteristic |
| 148 | #4016 | D4 | 1 | 1 | yes | characteristic |
| 149 | #4015 | — | 2 | 1 | no | — |
| 150 | #4015 | — | 2 | 1 | no | — |
| 151 | #4015 | D4 | 1 | 2 | yes | — |
| 152 | #4015 | C23 | 1 | 4 | yes | — |
| 153 | C4×Dic10 | — | 2 | 4 | no | — |
| 154 | C4×Dic10 | — | 2 | 2 | no | — |
| 155 | C4×Dic10 | — | 2 | 2 | no | — |
| 156 | C4×Dic10 | C23 | 1 | 2 | yes | — |
| 157 | C4×Dic10 | C23 | 1 | 4 | yes | — |
| 158 | C5×#107 | C23 | 1 | 4 | yes | — |
| 159 | C5×#106 | C23 | 1 | 4 | yes | — |
| 160 | C5×C4⋊C8 | C23 | 1 | 4 | yes | — |
| 161 | C5×#103 | C23 | 1 | 4 | yes | — |
| 162 | C5×#102 | C23 | 1 | 4 | yes | — |
| 163 | #3967 | C23 | 1 | 2 | yes | — |
| 164 | #3964 | C23 | 1 | 2 | yes | — |
| 165 | #3948 | C23 | 1 | 4 | yes | — |
| 166 | #3948 | C23 | 1 | 4 | yes | — |
| 167 | #3947 | C23 | 1 | 4 | yes | — |
| 168 | #3946 | C23 | 1 | 4 | yes | — |
| 169 | #3946 | C23 | 1 | 4 | yes | — |
| 170 | C8×Dic5 | C23 | 1 | 4 | yes | — |
| 171 | #3942 | C23 | 1 | 2 | yes | — |
| 172 | #3942 | C23 | 1 | 4 | yes | — |
| 173 | #3942 | C23 | 1 | 4 | yes | — |
| 174 | #3942 | C23 | 1 | 4 | yes | — |
| 175 | #3942 | C23 | 1 | 4 | yes | — |
| 176 | #3941 | C23 | 1 | 2 | yes | — |
| 177 | #3940 | C23 | 1 | 2 | yes | — |
| 178 | #3939 | C23 | 1 | 2 | yes | — |
| 179 | #3935 | C23 | 1 | 2 | yes | — |
| 180 | #3935 | C23 | 1 | 2 | yes | — |
| 181 | #3509 | — | 5 | 1 | no | — |
| 182 | #3504 | — | 5 | 1 | no | — |
| 183 | #3377 | — | 5 | 4 | no | — |
| 184 | #3376 | — | 5 | 4 | no | — |
| 185 | #3374 | — | 5 | 4 | no | — |
| 186 | #3372 | — | 5 | 4 | no | — |
| 187 | #3137 | — | 5 | 2 | no | — |
| 188 | C2×#491 | — | 5 | 1 | no | — |
| 189 | #3082 | — | 5 | 2 | no | — |
| 190 | #3080 | D5 | 1 | 1 | yes | characteristic, complemented |
| 191 | #3046 | — | 5 | 2 | no | — |
| 192 | #3039 | — | 5 | 1 | no | — |
| 193 | #2961 | — | 5 | 1 | no | — |
| 194 | #2947 | — | 5 | 2 | no | — |
| 195 | #2943 | — | 5 | 1 | no | — |
| 196 | C5×#41 | — | 2 | 2 | no | — |
| 197 | C5×#41 | — | 2 | 2 | no | — |
| 198 | C2×C5×Q8 | C24 | 1 | 1 | yes | characteristic |
| 199 | C2×C5×D4 | — | 2 | 1 | no | — |
| 200 | C2×C5×D4 | C24 | 1 | 1 | yes | characteristic |
| 201 | C22×C4×C5 | — | 2 | 2 | no | — |
| 202 | C22×C4×C5 | — | 2 | 1 | no | — |
| 203 | C22×C4×C5 | — | 2 | 2 | no | — |
| 204 | C22×C4×C5 | C2×D4 | 1 | 2 | yes | — |
| 205 | C22×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 206 | C2×C22⋊D5 | — | 2 | 1 | no | — |
| 207 | C22×Dic5 | — | 2 | 2 | no | — |
| 208 | #709 | — | 2 | 2 | no | — |
| 209 | #709 | #41 | 1 | 4 | yes | — |
| 210 | C2×D20 | C24 | 1 | 1 | yes | characteristic |
| 211 | C2×C4×D5 | — | 2 | 1 | no | — |
| 212 | C2×C4×D5 | — | 2 | 2 | no | — |
| 213 | C2×C4×D5 | — | 2 | 4 | no | — |
| 214 | C2×Dic10 | — | 2 | 4 | no | — |
| 215 | C2×Dic10 | — | 2 | 4 | no | — |
| 216 | C2×Dic10 | — | 2 | 2 | no | — |
| 217 | C2×Dic10 | — | 2 | 4 | no | — |
| 218 | C2×Dic10 | C2×D4 | 1 | 4 | yes | — |
| 219 | C2×Dic10 | C24 | 1 | 4 | yes | — |
| 220 | C2×Dic10 | C24 | 1 | 1 | yes | characteristic |
| 221 | C5×M16 | — | 2 | 4 | no | — |
| 222 | C2×C5×C8 | C24 | 1 | 4 | yes | — |
| 223 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 224 | C5×C4⋊C4 | — | 2 | 4 | no | — |
| 225 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 226 | C5×C4⋊C4 | — | 2 | 2 | no | — |
| 227 | C5×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 228 | C5×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 229 | C5×C22⋊C4 | — | 2 | 1 | no | — |
| 230 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 231 | C42×C5 | — | 2 | 1 | no | — |
| 232 | C42×C5 | — | 2 | 2 | no | — |
| 233 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 234 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 235 | C42×C5 | C24 | 1 | 2 | yes | — |
| 236 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 237 | C22⋊Dic5 | — | 2 | 4 | no | — |
| 238 | C22⋊Dic5 | — | 2 | 4 | no | — |
| 239 | C22⋊Dic5 | C2×D4 | 1 | 4 | yes | — |
| 240 | #689 | — | 2 | 2 | no | — |
| 241 | #688 | — | 2 | 2 | no | — |
| 242 | #687 | — | 2 | 2 | no | — |
| 243 | #686 | — | 2 | 2 | no | — |
| 244 | #685 | — | 2 | 2 | no | — |
| 245 | #685 | — | 2 | 4 | no | — |
| 246 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 247 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 248 | C4⋊Dic5 | — | 2 | 4 | no | — |
| 249 | C4⋊Dic5 | C2×D4 | 1 | 2 | yes | — |
| 250 | C4⋊Dic5 | C2×D4 | 1 | 2 | yes | — |
| 251 | C4⋊Dic5 | C2×D4 | 1 | 4 | yes | — |
| 252 | C4⋊Dic5 | C24 | 1 | 2 | yes | — |
| 253 | #683 | — | 2 | 2 | no | — |
| 254 | #683 | — | 2 | 4 | no | — |
| 255 | #683 | — | 2 | 4 | no | — |
| 256 | #683 | — | 2 | 4 | no | — |
| 257 | #683 | — | 2 | 4 | no | — |
| 258 | #683 | — | 2 | 4 | no | — |
| 259 | #683 | — | 2 | 4 | no | — |
| 260 | #683 | — | 2 | 4 | no | — |
| 261 | #683 | C2×D4 | 1 | 4 | yes | — |
| 262 | #683 | C2×D4 | 1 | 4 | yes | — |
| 263 | C4×Dic5 | — | 2 | 2 | no | — |
| 264 | C4×Dic5 | — | 2 | 1 | no | — |
| 265 | C4×Dic5 | — | 2 | 4 | no | — |
| 266 | C4×Dic5 | — | 2 | 4 | no | — |
| 267 | C4×Dic5 | — | 2 | 4 | no | — |
| 268 | C4×Dic5 | C24 | 1 | 4 | yes | — |
| 269 | C2×#168 | — | 2 | 2 | no | — |
| 270 | C2×#168 | — | 2 | 2 | no | — |
| 271 | C2×#168 | C24 | 1 | 1 | yes | characteristic |
| 272 | C2×#168 | C24 | 1 | 1 | yes | characteristic |
| 273 | C2×#168 | C24 | 1 | 2 | yes | — |
| 274 | Dic20 | — | 2 | 8 | no | — |
| 275 | #677 | — | 2 | 8 | no | — |
| 276 | C2×#137 | — | 5 | 2 | no | — |
| 277 | C2×#135 | — | 5 | 1 | no | — |
| 278 | #557 | — | 5 | 4 | no | — |
| 279 | #557 | — | 5 | 4 | no | — |
| 280 | #556 | — | 5 | 4 | no | — |
| 281 | #554 | — | 5 | 4 | no | — |
| 282 | #554 | — | 10 | 4 | no | — |
| 283 | #552 | — | 10 | 4 | no | — |
| 284 | #544 | — | 5 | 2 | no | — |
| 285 | #544 | — | 10 | 2 | no | — |
| 286 | #541 | — | 10 | 1 | no | — |
| 287 | #541 | — | 10 | 1 | no | — |
| 288 | #536 | — | 5 | 2 | no | — |
| 289 | #533 | — | 5 | 1 | no | — |
| 290 | #533 | — | 10 | 2 | no | — |
| 291 | #533 | — | 10 | 1 | no | — |
| 292 | C2×C4⋊Q8 | — | 5 | 1 | no | — |
| 293 | C2×#125 | — | 10 | 1 | no | — |
| 294 | C2×#125 | C2×D5 | 1 | 1 | yes | characteristic |
| 295 | #520 | — | 5 | 2 | no | — |
| 296 | #519 | — | 5 | 2 | no | — |
| 297 | C4×#41 | — | 5 | 1 | no | — |
| 298 | C4×#41 | C2×D5 | 1 | 1 | yes | characteristic |
| 299 | #491 | — | 5 | 4 | no | — |
| 300 | #491 | — | 5 | 4 | no | — |
| 301 | #491 | — | 5 | 4 | no | — |
| 302 | #489 | — | 5 | 4 | no | — |
| 303 | #488 | — | 5 | 4 | no | — |
| 304 | #487 | — | 5 | 4 | no | — |
| 305 | #479 | — | 5 | 4 | no | — |
| 306 | #479 | — | 5 | 4 | no | — |
| 307 | #479 | C2×D5 | 1 | 4 | yes | — |
| 308 | #478 | C2×D5 | 1 | 4 | yes | — |
| 309 | #477 | — | 5 | 4 | no | — |
| 310 | #475 | — | 5 | 4 | no | — |
| 311 | #464 | — | 5 | 4 | no | — |
| 312 | #463 | — | 5 | 4 | no | — |
| 313 | #462 | — | 5 | 4 | no | — |
| 314 | #462 | — | 5 | 4 | no | — |
| 315 | #461 | — | 5 | 4 | no | — |
| 316 | #461 | — | 5 | 4 | no | — |
| 317 | #446 | — | 5 | 4 | no | — |
| 318 | #446 | — | 5 | 4 | no | — |
| 319 | #442 | — | 5 | 2 | no | — |
| 320 | #441 | — | 5 | 2 | no | — |
| 321 | #441 | — | 5 | 4 | no | — |
| 322 | #440 | — | 5 | 2 | no | — |
| 323 | #440 | — | 5 | 2 | no | — |
| 324 | #440 | — | 5 | 4 | no | — |
| 325 | C4×Q16 | — | 5 | 4 | no | — |
| 326 | C4×SD16 | — | 5 | 4 | no | — |
| 327 | #428 | C2×D5 | 1 | 2 | yes | — |
| 328 | #427 | — | 5 | 1 | no | — |
| 329 | #424 | — | 5 | 2 | no | — |
| 330 | #423 | C2×D5 | 1 | 1 | yes | characteristic |
| 331 | #419 | — | 5 | 2 | no | — |
| 332 | #417 | C2×D5 | 1 | 2 | yes | — |
| 333 | #416 | — | 5 | 1 | no | — |
| 334 | #416 | — | 5 | 1 | no | — |
| 335 | C2×#103 | — | 5 | 2 | no | — |
| 336 | C2×#103 | — | 5 | 2 | no | — |
| 337 | #405 | — | 5 | 2 | no | — |
| 338 | C2×#97 | — | 5 | 1 | no | — |
| 339 | C23×C5 | — | 2 | 1 | no | — |
| 340 | C23×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 341 | C22×D5 | — | 2 | 1 | no | — |
| 342 | C5×Q8 | — | 2 | 1 | no | — |
| 343 | C5×Q8 | — | 2 | 1 | no | — |
| 344 | C5×D4 | — | 2 | 1 | no | — |
| 345 | C5×D4 | — | 2 | 1 | no | — |
| 346 | C5×D4 | — | 4 | 2 | no | — |
| 347 | C2×C4×C5 | — | 2 | 2 | no | — |
| 348 | C2×C4×C5 | — | 2 | 4 | no | — |
| 349 | C2×C4×C5 | — | 2 | 1 | no | — |
| 350 | C2×C4×C5 | — | 4 | 2 | no | — |
| 351 | C2×C4×C5 | — | 4 | 4 | no | — |
| 352 | C2×C4×C5 | — | 4 | 2 | no | — |
| 353 | C2×C4×C5 | — | 8 | 2 | no | — |
| 354 | C2×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 355 | C2×C4×C5 | C22×D4 | 1 | 2 | yes | — |
| 356 | C2×C4×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 357 | C2×C4×C5 | C2×#41 | 1 | 2 | yes | — |
| 358 | C2×C4×C5 | 2−1+4 | 1 | 2 | yes | — |
| 359 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 360 | C22⋊D5 | — | 2 | 4 | no | — |
| 361 | C2×Dic5 | — | 2 | 1 | no | — |
| 362 | C2×Dic5 | — | 2 | 2 | no | — |
| 363 | C2×Dic5 | — | 2 | 4 | no | — |
| 364 | C2×Dic5 | — | 4 | 4 | no | — |
| 365 | C2×Dic5 | C22×D4 | 1 | 4 | yes | — |
| 366 | C2×Dic5 | C22×D4 | 1 | 4 | yes | — |
| 367 | D20 | — | 2 | 1 | no | — |
| 368 | D20 | C2×#41 | 1 | 2 | yes | — |
| 369 | C4×D5 | — | 2 | 4 | no | — |
| 370 | C4×D5 | — | 8 | 4 | no | — |
| 371 | C4×D5 | — | 8 | 2 | no | — |
| 372 | Dic10 | — | 2 | 1 | no | — |
| 373 | Dic10 | — | 2 | 4 | no | — |
| 374 | Dic10 | — | 2 | 4 | no | — |
| 375 | Dic10 | — | 4 | 4 | no | — |
| 376 | Dic10 | — | 4 | 4 | no | — |
| 377 | Dic10 | — | 8 | 4 | no | — |
| 378 | Dic10 | C2×#41 | 1 | 2 | yes | — |
| 379 | C5×C8 | — | 2 | 4 | no | — |
| 380 | #168 | — | 2 | 1 | no | — |
| 381 | #168 | — | 2 | 1 | no | — |
| 382 | #168 | — | 2 | 2 | no | — |
| 383 | C2×#41 | — | 5 | 1 | no | — |
| 384 | C2×#41 | C22×D5 | 1 | 1 | yes | characteristic |
| 385 | C22×Q8 | — | 5 | 2 | no | — |
| 386 | #137 | — | 10 | 8 | no | — |
| 387 | #135 | — | 10 | 4 | no | — |
| 388 | C2×Q16 | — | 5 | 1 | no | — |
| 389 | C2×Q16 | — | 5 | 4 | no | — |
| 390 | C2×SD16 | — | 5 | 1 | no | — |
| 391 | C2×SD16 | — | 5 | 1 | no | — |
| 392 | C2×SD16 | — | 5 | 4 | no | — |
| 393 | C2×D8 | — | 5 | 1 | no | — |
| 394 | C2×M16 | C22×D5 | 1 | 2 | yes | — |
| 395 | C22×C8 | — | 5 | 1 | no | — |
| 396 | C22×C8 | — | 5 | 1 | no | — |
| 397 | C4⋊Q8 | — | 5 | 4 | no | — |
| 398 | C4⋊Q8 | — | 5 | 4 | no | — |
| 399 | C4⋊Q8 | — | 5 | 2 | no | — |
| 400 | C4⋊Q8 | — | 5 | 4 | no | — |
| 401 | C4⋊Q8 | — | 10 | 2 | no | — |
| 402 | C4⋊Q8 | — | 10 | 4 | no | — |
| 403 | C4⋊Q8 | — | 10 | 1 | no | — |
| 404 | C4⋊Q8 | — | 10 | 1 | no | — |
| 405 | #126 | — | 10 | 4 | no | — |
| 406 | #126 | — | 10 | 4 | no | — |
| 407 | #125 | — | 2 | 1 | no | — |
| 408 | #125 | — | 2 | 1 | no | — |
| 409 | #125 | — | 5 | 4 | no | — |
| 410 | #125 | — | 5 | 1 | no | — |
| 411 | #125 | — | 5 | 1 | no | — |
| 412 | #125 | — | 10 | 4 | no | — |
| 413 | #125 | — | 10 | 2 | no | — |
| 414 | #125 | — | 10 | 4 | no | — |
| 415 | #125 | — | 10 | 4 | no | — |
| 416 | #125 | — | 10 | 4 | no | — |
| 417 | #125 | — | 10 | 4 | no | — |
| 418 | #125 | C22×D5 | 1 | 4 | yes | — |
| 419 | #124 | — | 5 | 4 | no | — |
| 420 | #123 | — | 10 | 4 | no | — |
| 421 | C22⋊Q8 | — | 5 | 4 | no | — |
| 422 | C22⋊Q8 | — | 10 | 4 | no | — |
| 423 | C22⋊Q8 | — | 10 | 4 | no | — |
| 424 | C22⋊Q8 | — | 10 | 4 | no | — |
| 425 | C22⋊Q8 | — | 10 | 4 | no | — |
| 426 | C22⋊Q8 | — | 10 | 2 | no | — |
| 427 | C22⋊Q8 | — | 10 | 2 | no | — |
| 428 | C22⋊Q8 | — | 10 | 4 | no | — |
| 429 | C4×Q8 | — | 5 | 4 | no | — |
| 430 | C4×Q8 | — | 5 | 4 | no | — |
| 431 | C4×Q8 | — | 5 | 4 | no | — |
| 432 | C4×Q8 | — | 5 | 4 | no | — |
| 433 | C4×Q8 | — | 5 | 2 | no | — |
| 434 | C4×Q8 | — | 10 | 2 | no | — |
| 435 | C4×Q8 | — | 10 | 2 | no | — |
| 436 | C4×Q8 | — | 10 | 4 | no | — |
| 437 | C4×Q8 | — | 10 | 4 | no | — |
| 438 | C4×Q8 | C22×D5 | 1 | 2 | yes | — |
| 439 | C4×D4 | — | 2 | 2 | no | — |
| 440 | C4×D4 | — | 5 | 4 | no | — |
| 441 | C4×D4 | — | 5 | 2 | no | — |
| 442 | C4×D4 | — | 10 | 4 | no | — |
| 443 | C4×D4 | — | 10 | 2 | no | — |
| 444 | C4×D4 | C22×D5 | 1 | 2 | yes | — |
| 445 | #117 | — | 2 | 1 | no | — |
| 446 | #117 | — | 5 | 2 | no | — |
| 447 | #117 | — | 5 | 1 | no | — |
| 448 | #117 | — | 10 | 4 | no | — |
| 449 | #117 | — | 10 | 2 | no | — |
| 450 | #117 | — | 10 | 4 | no | — |
| 451 | #117 | — | 10 | 1 | no | — |
| 452 | #117 | C22×D5 | 1 | 1 | yes | characteristic |
| 453 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 454 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 455 | C2×C4⋊C4 | — | 10 | 4 | no | — |
| 456 | C2×C4⋊C4 | — | 10 | 2 | no | — |
| 457 | C2×C4⋊C4 | C22×D5 | 1 | 2 | yes | — |
| 458 | C2×C42 | — | 2 | 1 | no | — |
| 459 | C2×C42 | — | 10 | 1 | no | — |
| 460 | C2×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 461 | #107 | — | 5 | 2 | no | — |
| 462 | #107 | C22×D5 | 1 | 4 | yes | — |
| 463 | #106 | — | 5 | 2 | no | — |
| 464 | #106 | C22×D5 | 1 | 4 | yes | — |
| 465 | C4⋊C8 | — | 5 | 4 | no | — |
| 466 | C4⋊C8 | — | 5 | 4 | no | — |
| 467 | C4⋊C8 | C22×D5 | 1 | 4 | yes | — |
| 468 | #103 | — | 5 | 2 | no | — |
| 469 | #103 | — | 5 | 4 | no | — |
| 470 | #103 | — | 5 | 4 | no | — |
| 471 | #103 | — | 5 | 4 | no | — |
| 472 | #103 | — | 5 | 4 | no | — |
| 473 | #103 | — | 5 | 4 | no | — |
| 474 | #103 | — | 5 | 4 | no | — |
| 475 | #103 | — | 5 | 2 | no | — |
| 476 | #103 | C22×D5 | 1 | 4 | yes | — |
| 477 | #102 | — | 5 | 2 | no | — |
| 478 | #102 | — | 5 | 2 | no | — |
| 479 | #102 | C22×D5 | 1 | 4 | yes | — |
| 480 | #97 | — | 5 | 4 | no | — |
| 481 | #97 | — | 5 | 2 | no | — |
| 482 | #97 | — | 5 | 2 | no | — |
| 483 | C4×C8 | — | 5 | 4 | no | — |
| 484 | C22×C5 | — | 2 | 2 | no | — |
| 485 | C22×C5 | — | 4 | 2 | no | — |
| 486 | C22×C5 | — | 4 | 1 | no | — |
| 487 | C22×C5 | #548 | 1 | 2 | yes | — |
| 488 | C22×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 489 | C2×D5 | — | 2 | 2 | no | — |
| 490 | C2×D5 | — | 4 | 2 | no | — |
| 491 | C4×C5 | — | 2 | 2 | no | — |
| 492 | C4×C5 | — | 2 | 2 | no | — |
| 493 | C4×C5 | — | 4 | 4 | no | — |
| 494 | C4×C5 | — | 4 | 2 | no | — |
| 495 | C4×C5 | — | 4 | 1 | no | — |
| 496 | C4×C5 | #548 | 1 | 2 | yes | — |
| 497 | C4×C5 | C22×#41 | 1 | 1 | yes | characteristic |
| 498 | C4×C5 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 499 | Dic5 | — | 2 | 4 | no | — |
| 500 | Dic5 | — | 2 | 4 | no | — |
| 501 | Dic5 | — | 2 | 2 | no | — |
| 502 | Dic5 | — | 4 | 2 | no | — |
| 503 | Dic5 | — | 4 | 4 | no | — |
| 504 | #41 | — | 2 | 2 | no | — |
| 505 | #41 | — | 2 | 2 | no | — |
| 506 | #41 | — | 5 | 4 | no | — |
| 507 | #41 | — | 10 | 2 | no | — |
| 508 | C2×Q8 | — | 5 | 4 | no | — |
| 509 | C2×Q8 | — | 5 | 1 | no | — |
| 510 | C2×Q8 | — | 5 | 4 | no | — |
| 511 | C2×Q8 | — | 10 | 4 | no | — |
| 512 | C2×Q8 | — | 10 | 2 | no | — |
| 513 | C2×Q8 | — | 10 | 4 | no | — |
| 514 | C2×Q8 | — | 10 | 4 | no | — |
| 515 | C2×Q8 | C23×D5 | 1 | 1 | yes | characteristic |
| 516 | C2×D4 | — | 2 | 1 | no | — |
| 517 | C2×D4 | — | 5 | 1 | no | — |
| 518 | C2×D4 | — | 10 | 1 | no | — |
| 519 | C2×D4 | C23×D5 | 1 | 1 | yes | characteristic |
| 520 | C22×C4 | — | 2 | 2 | no | — |
| 521 | C22×C4 | — | 2 | 1 | no | — |
| 522 | C22×C4 | — | 2 | 2 | no | — |
| 523 | C22×C4 | — | 10 | 4 | no | — |
| 524 | C22×C4 | — | 10 | 1 | no | — |
| 525 | C22×C4 | — | 10 | 2 | no | — |
| 526 | C22×C4 | — | 10 | 2 | no | — |
| 527 | C22×C4 | D4×D5 | 1 | 2 | yes | — |
| 528 | C22×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 529 | Q16 | — | 10 | 8 | no | — |
| 530 | Q16 | — | 10 | 2 | no | — |
| 531 | SD16 | — | 10 | 8 | no | — |
| 532 | SD16 | — | 10 | 2 | no | — |
| 533 | SD16 | — | 10 | 2 | no | — |
| 534 | D8 | — | 10 | 2 | no | — |
| 535 | M16 | — | 2 | 4 | no | — |
| 536 | C2×C8 | — | 5 | 2 | no | — |
| 537 | C2×C8 | — | 5 | 1 | no | — |
| 538 | C2×C8 | — | 5 | 1 | no | — |
| 539 | C2×C8 | — | 10 | 2 | no | — |
| 540 | C2×C8 | — | 10 | 2 | no | — |
| 541 | C2×C8 | C23×D5 | 1 | 4 | yes | — |
| 542 | C4⋊C4 | — | 2 | 4 | no | — |
| 543 | C4⋊C4 | — | 2 | 4 | no | — |
| 544 | C4⋊C4 | — | 2 | 2 | no | — |
| 545 | C4⋊C4 | — | 2 | 2 | no | — |
| 546 | C4⋊C4 | — | 5 | 2 | no | — |
| 547 | C4⋊C4 | — | 5 | 4 | no | — |
| 548 | C4⋊C4 | — | 5 | 2 | no | — |
| 549 | C4⋊C4 | — | 5 | 4 | no | — |
| 550 | C4⋊C4 | — | 5 | 4 | no | — |
| 551 | C4⋊C4 | — | 5 | 2 | no | — |
| 552 | C4⋊C4 | — | 10 | 4 | no | — |
| 553 | C4⋊C4 | — | 10 | 4 | no | — |
| 554 | C4⋊C4 | — | 10 | 4 | no | — |
| 555 | C4⋊C4 | — | 10 | 4 | no | — |
| 556 | C4⋊C4 | — | 10 | 4 | no | — |
| 557 | C4⋊C4 | — | 10 | 4 | no | — |
| 558 | C4⋊C4 | — | 10 | 4 | no | — |
| 559 | C4⋊C4 | — | 10 | 4 | no | — |
| 560 | C4⋊C4 | — | 10 | 4 | no | — |
| 561 | C4⋊C4 | — | 10 | 4 | no | — |
| 562 | C4⋊C4 | — | 10 | 2 | no | — |
| 563 | C4⋊C4 | C23×D5 | 1 | 2 | yes | — |
| 564 | C4⋊C4 | C23×D5 | 1 | 4 | yes | — |
| 565 | C22⋊C4 | — | 2 | 1 | no | — |
| 566 | C22⋊C4 | — | 2 | 2 | no | — |
| 567 | C22⋊C4 | — | 5 | 4 | no | — |
| 568 | C22⋊C4 | — | 10 | 4 | no | — |
| 569 | C22⋊C4 | — | 10 | 4 | no | — |
| 570 | C22⋊C4 | — | 10 | 4 | no | — |
| 571 | C22⋊C4 | — | 10 | 1 | no | — |
| 572 | C22⋊C4 | — | 10 | 2 | no | — |
| 573 | C42 | — | 2 | 1 | no | — |
| 574 | C42 | — | 2 | 2 | no | — |
| 575 | C42 | — | 5 | 4 | no | — |
| 576 | C42 | — | 10 | 4 | no | — |
| 577 | C42 | — | 10 | 4 | no | — |
| 578 | C42 | — | 10 | 4 | no | — |
| 579 | C42 | — | 10 | 1 | no | — |
| 580 | C42 | — | 10 | 2 | no | — |
| 581 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 582 | C42 | D4×D5 | 1 | 1 | yes | characteristic |
| 583 | C42 | C23×D5 | 1 | 2 | yes | — |
| 584 | C2×C5 | — | 2 | 2 | no | — |
| 585 | C2×C5 | — | 8 | 1 | no | — |
| 586 | C2×C5 | C2×#548 | 1 | 1 | yes | characteristic |
| 587 | C2×C5 | #3586 | 1 | 2 | yes | — |
| 588 | D5 | — | 4 | 2 | no | — |
| 589 | C23 | — | 2 | 1 | no | — |
| 590 | C23 | — | 10 | 1 | no | — |
| 591 | C23 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 592 | Q8 | — | 2 | 1 | no | — |
| 593 | Q8 | — | 2 | 1 | no | — |
| 594 | Q8 | — | 5 | 2 | no | — |
| 595 | Q8 | — | 10 | 1 | no | — |
| 596 | Q8 | — | 10 | 4 | no | — |
| 597 | Q8 | — | 10 | 4 | no | — |
| 598 | Q8 | — | 20 | 4 | no | — |
| 599 | Q8 | — | 20 | 4 | no | — |
| 600 | Q8 | — | 40 | 4 | no | — |
| 601 | D4 | — | 2 | 1 | no | — |
| 602 | D4 | — | 2 | 1 | no | — |
| 603 | D4 | — | 4 | 2 | no | — |
| 604 | D4 | — | 5 | 2 | no | — |
| 605 | D4 | — | 10 | 4 | no | — |
| 606 | D4 | — | 10 | 1 | no | — |
| 607 | C2×C4 | — | 2 | 2 | no | — |
| 608 | C2×C4 | — | 2 | 1 | no | — |
| 609 | C2×C4 | — | 2 | 4 | no | — |
| 610 | C2×C4 | — | 4 | 2 | no | — |
| 611 | C2×C4 | — | 4 | 4 | no | — |
| 612 | C2×C4 | — | 4 | 2 | no | — |
| 613 | C2×C4 | — | 5 | 4 | no | — |
| 614 | C2×C4 | — | 5 | 4 | no | — |
| 615 | C2×C4 | — | 8 | 2 | no | — |
| 616 | C2×C4 | — | 10 | 1 | no | — |
| 617 | C2×C4 | — | 10 | 4 | no | — |
| 618 | C2×C4 | — | 10 | 2 | no | — |
| 619 | C2×C4 | — | 10 | 4 | no | — |
| 620 | C2×C4 | — | 20 | 4 | no | — |
| 621 | C2×C4 | — | 40 | 2 | no | — |
| 622 | C2×C4 | — | 40 | 4 | no | — |
| 623 | C2×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 624 | C2×C4 | C2×D4×D5 | 1 | 2 | yes | — |
| 625 | C2×C4 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 626 | C2×C4 | #4147 | 1 | 2 | yes | — |
| 627 | C2×C4 | D5×#41 | 1 | 2 | yes | — |
| 628 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 629 | C8 | — | 2 | 4 | no | — |
| 630 | C8 | — | 10 | 2 | no | — |
| 631 | C8 | — | 10 | 1 | no | — |
| 632 | C8 | — | 10 | 1 | no | — |
| 633 | C5 | #61338 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 634 | C22 | — | 2 | 2 | no | — |
| 635 | C22 | — | 4 | 1 | no | — |
| 636 | C22 | — | 4 | 2 | no | — |
| 637 | C22 | — | 10 | 2 | no | — |
| 638 | C22 | — | 20 | 2 | no | — |
| 639 | C22 | #65967 | 1 | 2 | yes | — |
| 640 | C22 | C22×D4×D5 | 1 | 1 | yes | characteristic |
| 641 | C4 | — | 2 | 2 | no | — |
| 642 | C4 | — | 2 | 2 | no | — |
| 643 | C4 | — | 4 | 1 | no | — |
| 644 | C4 | — | 4 | 2 | no | — |
| 645 | C4 | — | 4 | 4 | no | — |
| 646 | C4 | — | 10 | 2 | no | — |
| 647 | C4 | — | 10 | 4 | no | — |
| 648 | C4 | — | 10 | 4 | no | — |
| 649 | C4 | — | 20 | 4 | no | — |
| 650 | C4 | — | 20 | 2 | no | — |
| 651 | C4 | #65967 | 1 | 2 | yes | — |
| 652 | C4 | C2×#4147 | 1 | 1 | yes | characteristic |
| 653 | C4 | C2×D5×#41 | 1 | 1 | yes | characteristic |
| 654 | C2 | — | 2 | 2 | no | — |
| 655 | C2 | — | 8 | 1 | no | — |
| 656 | C2 | — | 20 | 2 | no | — |
| 657 | C2 | C2×#65967 | 1 | 1 | yes | characteristic |
| 658 | C2 | #10619102 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10617999 | C2 | semidirect |
| 2. #10617731 | C2 | semidirect |
| 3. C5×#3080 | C2 | semidirect |
| 4. C2×#65358 | C2 | semidirect |
| 6. #10612951 | C2 | semidirect |
| 7. #10612950 | C2 | semidirect |
| 8. #10612886 | C2 | semidirect |
| 9. #10612885 | C2 | semidirect |
| 10. #10610977 | C2 | semidirect |
| 11. #10610933 | C2 | semidirect |
| 12. #10610788 | C2 | semidirect |
| 13. #10610776 | C2 | semidirect |
| 15. #10610608 | C2 | semidirect |
| 190. #3080 | D5 | semidirect |
| 633. C5 | #61338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617999 | 2 |
| #10617731 | 2 |
| C5×#3080 | 2 |
| C2×#65358 | 2 |
| #10614237 | 2 |
| #10612951 | 2 |
| #10612950 | 2 |
| #10612886 | 2 |
| #10612885 | 2 |
| #10610977 | 2 |
| #10610933 | 2 |
| #10610788 | 2 |
| #10610776 | 2 |
| #10610643 | 2 |
| #10610608 | 2 |
| #61338 | 5 |