Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
4666 conjugacy classes of subgroups.
The subgroup lattice has 686 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10619440 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10619200 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10619069 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10617728 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#2901 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10615546 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10614267 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10610727 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #10610726 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | C2×#65115 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | #10610717 | C2 | 1 | 6 | yes | maximal, complemented |
| 12 | C5×#585 | C22 | 1 | 1 | yes | characteristic |
| 13 | D5×2−1+4 | — | 2 | 4 | no | — |
| 14 | D5×2−1+4 | — | 2 | 2 | no | — |
| 15 | #66285 | — | 2 | 4 | no | — |
| 16 | #66285 | — | 2 | 6 | no | — |
| 17 | #66283 | — | 2 | 4 | no | — |
| 18 | #66283 | C22 | 1 | 6 | yes | — |
| 19 | #66283 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#4150 | — | 2 | 4 | no | — |
| 21 | C2×#4150 | C22 | 1 | 6 | yes | — |
| 22 | C2×#4150 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#4150 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C5×#568 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C4×C5×#41 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #66172 | — | 2 | 4 | no | — |
| 27 | #66170 | — | 2 | 4 | no | — |
| 28 | C2×#4097 | C22 | 1 | 6 | yes | complemented |
| 29 | #66156 | C22 | 1 | 6 | yes | complemented |
| 30 | #66153 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #66087 | — | 2 | 4 | no | — |
| 32 | #66085 | — | 2 | 4 | no | — |
| 33 | #66082 | C22 | 1 | 6 | yes | complemented |
| 34 | C2×#4055 | C22 | 1 | 6 | yes | complemented |
| 35 | Q8×D20 | — | 2 | 2 | no | — |
| 36 | #65889 | — | 2 | 6 | no | — |
| 37 | #65860 | C22 | 1 | 3 | yes | complemented |
| 38 | #65860 | C22 | 1 | 3 | yes | complemented |
| 39 | #65811 | C22 | 1 | 3 | yes | complemented |
| 40 | C2×#4015 | C22 | 1 | 3 | yes | complemented |
| 41 | C5×#421 | C22 | 1 | 6 | yes | complemented |
| 42 | C2×C5×#104 | C22 | 1 | 6 | yes | complemented |
| 43 | C2×#3956 | C22 | 1 | 6 | yes | complemented |
| 44 | #65421 | C22 | 1 | 6 | yes | complemented |
| 45 | #65294 | C22 | 1 | 6 | yes | complemented |
| 46 | C2×#3937 | C22 | 1 | 6 | yes | complemented |
| 47 | #65116 | C22 | 1 | 12 | yes | complemented |
| 48 | #65115 | C22 | 1 | 12 | yes | complemented |
| 49 | #65115 | C22 | 1 | 24 | yes | complemented |
| 50 | #65114 | C22 | 1 | 12 | yes | complemented |
| 51 | #65111 | C22 | 1 | 4 | yes | complemented |
| 52 | #60391 | — | 5 | 1 | no | maximal, Sylow |
| 53 | C5×2−1+4 | — | 2 | 1 | no | — |
| 54 | C5×2−1+4 | D4 | 1 | 4 | yes | complemented |
| 55 | C5×H(5,𝔽2) | — | 2 | 3 | no | — |
| 56 | C5×H(5,𝔽2) | D4 | 1 | 4 | yes | complemented |
| 57 | C2×C5×#41 | — | 2 | 4 | no | — |
| 58 | C2×C5×#41 | C23 | 1 | 6 | yes | — |
| 59 | C2×C5×#41 | C23 | 1 | 1 | yes | characteristic |
| 60 | #4150 | — | 2 | 8 | no | — |
| 61 | #4150 | — | 2 | 24 | no | — |
| 62 | #4150 | — | 2 | 4 | no | — |
| 63 | #4150 | — | 2 | 12 | no | — |
| 64 | #4150 | — | 2 | 4 | no | — |
| 65 | #4150 | — | 2 | 4 | no | — |
| 66 | #4150 | — | 2 | 4 | no | — |
| 67 | #4150 | — | 2 | 12 | no | — |
| 68 | #4150 | — | 2 | 6 | no | — |
| 69 | #4150 | — | 2 | 12 | no | — |
| 70 | #4150 | D4 | 1 | 4 | yes | complemented |
| 71 | #4150 | C23 | 1 | 12 | yes | — |
| 72 | #4149 | — | 2 | 6 | no | — |
| 73 | #4149 | D4 | 1 | 4 | yes | complemented |
| 74 | #4149 | C23 | 1 | 4 | yes | — |
| 75 | D5×#41 | — | 2 | 8 | no | — |
| 76 | D5×#41 | — | 2 | 24 | no | — |
| 77 | D5×#41 | — | 2 | 12 | no | — |
| 78 | D5×#41 | — | 2 | 4 | no | — |
| 79 | D5×#41 | — | 2 | 12 | no | — |
| 80 | #4147 | — | 2 | 8 | no | — |
| 81 | #4147 | — | 2 | 6 | no | — |
| 82 | #4147 | — | 2 | 1 | no | — |
| 83 | C2×Q8×D5 | — | 2 | 8 | no | — |
| 84 | C2×Q8×D5 | — | 2 | 6 | no | — |
| 85 | C2×Q8×D5 | — | 2 | 1 | no | — |
| 86 | C2×Q8×D5 | D4 | 1 | 2 | yes | — |
| 87 | #4144 | — | 2 | 24 | no | — |
| 88 | #4144 | — | 2 | 6 | no | — |
| 89 | #4144 | — | 2 | 3 | no | — |
| 90 | #4144 | — | 2 | 12 | no | — |
| 91 | C2×#711 | — | 2 | 24 | no | — |
| 92 | C2×#711 | — | 2 | 6 | no | — |
| 93 | C2×#711 | — | 2 | 12 | no | — |
| 94 | C2×#711 | — | 2 | 3 | no | — |
| 95 | C2×#711 | D4 | 1 | 6 | yes | — |
| 96 | C2×#709 | — | 2 | 12 | no | — |
| 97 | C2×#709 | — | 2 | 6 | no | — |
| 98 | C2×#709 | C23 | 1 | 6 | yes | — |
| 99 | C2×#709 | C23 | 1 | 3 | yes | — |
| 100 | C2×#709 | C23 | 1 | 3 | yes | — |
| 101 | C22×Dic10 | — | 2 | 6 | no | — |
| 102 | C22×Dic10 | C23 | 1 | 3 | yes | — |
| 103 | C22×Dic10 | C23 | 1 | 3 | yes | — |
| 104 | C5×#131 | — | 2 | 4 | no | — |
| 105 | C2×C5×M16 | C23 | 1 | 6 | yes | — |
| 106 | C4×C5×Q8 | — | 2 | 1 | no | — |
| 107 | C4×C5×D4 | — | 2 | 3 | no | — |
| 108 | C5×#117 | C23 | 1 | 3 | yes | — |
| 109 | C2×C42×C5 | C23 | 1 | 3 | yes | — |
| 110 | #4097 | — | 2 | 12 | no | — |
| 111 | #4097 | C23 | 1 | 12 | yes | — |
| 112 | #4096 | — | 2 | 12 | no | — |
| 113 | #4095 | C23 | 1 | 4 | yes | — |
| 114 | #4094 | — | 2 | 4 | no | — |
| 115 | C2×#689 | — | 2 | 6 | no | — |
| 116 | #4088 | — | 2 | 6 | no | — |
| 117 | C2×#687 | — | 2 | 6 | no | — |
| 118 | #4078 | — | 2 | 6 | no | — |
| 119 | #4076 | — | 2 | 6 | no | — |
| 120 | C2×C4⋊Dic5 | — | 2 | 6 | no | — |
| 121 | C2×#681 | C23 | 1 | 6 | yes | — |
| 122 | #4055 | — | 2 | 12 | no | — |
| 123 | #4055 | — | 2 | 6 | no | — |
| 124 | #4055 | C23 | 1 | 12 | yes | — |
| 125 | #4054 | — | 2 | 6 | no | — |
| 126 | #4054 | C23 | 1 | 4 | yes | — |
| 127 | C2×Dic20 | — | 2 | 6 | no | — |
| 128 | #4050 | — | 2 | 12 | no | — |
| 129 | C2×#677 | — | 2 | 6 | no | — |
| 130 | #4043 | — | 2 | 6 | no | — |
| 131 | #4043 | — | 2 | 6 | no | — |
| 132 | #4032 | — | 2 | 6 | no | — |
| 133 | #4032 | — | 2 | 6 | no | — |
| 134 | #4021 | C23 | 1 | 3 | yes | — |
| 135 | #4021 | C23 | 1 | 3 | yes | — |
| 136 | #4020 | C23 | 1 | 1 | yes | characteristic |
| 137 | C4×D20 | — | 2 | 6 | no | — |
| 138 | #4015 | — | 2 | 6 | no | — |
| 139 | #4015 | C23 | 1 | 3 | yes | — |
| 140 | #4015 | C23 | 1 | 6 | yes | — |
| 141 | C5×#104 | C23 | 1 | 4 | yes | — |
| 142 | C5×#104 | C23 | 1 | 12 | yes | — |
| 143 | #3956 | C23 | 1 | 12 | yes | — |
| 144 | #3955 | C23 | 1 | 4 | yes | — |
| 145 | #3937 | C23 | 1 | 12 | yes | — |
| 146 | #3937 | C23 | 1 | 4 | yes | — |
| 147 | 2−1+6 | — | 5 | 1 | no | — |
| 148 | #3586 | — | 5 | 1 | no | — |
| 149 | #3586 | — | 5 | 1 | no | — |
| 150 | #3499 | — | 5 | 1 | no | — |
| 151 | #3022 | — | 5 | 6 | no | — |
| 152 | #3020 | — | 5 | 6 | no | — |
| 153 | #3018 | — | 5 | 6 | no | — |
| 154 | C2×#456 | — | 5 | 6 | no | — |
| 155 | #2901 | — | 5 | 1 | no | — |
| 156 | #2901 | D5 | 1 | 1 | yes | characteristic, complemented |
| 157 | #2889 | — | 5 | 1 | no | — |
| 158 | C5×#41 | — | 2 | 4 | no | — |
| 159 | C5×#41 | — | 2 | 12 | no | — |
| 160 | C5×#41 | — | 2 | 6 | no | — |
| 161 | C5×#41 | — | 2 | 6 | no | — |
| 162 | C5×#41 | C2×D4 | 1 | 12 | yes | — |
| 163 | C5×#41 | C2×D4 | 1 | 4 | yes | — |
| 164 | C5×#41 | C2×D4 | 1 | 4 | yes | — |
| 165 | C5×#41 | C24 | 1 | 4 | yes | — |
| 166 | C2×C5×Q8 | — | 2 | 4 | no | — |
| 167 | C2×C5×Q8 | C2×D4 | 1 | 6 | yes | — |
| 168 | C2×C5×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C2×C5×D4 | — | 2 | 6 | no | — |
| 170 | C2×C5×D4 | — | 2 | 12 | no | — |
| 171 | C2×C5×D4 | C2×D4 | 1 | 6 | yes | — |
| 172 | C2×C5×D4 | C2×D4 | 1 | 3 | yes | — |
| 173 | C22×C4×C5 | — | 2 | 6 | no | — |
| 174 | C22×C4×C5 | — | 2 | 3 | no | — |
| 175 | C22×C4×C5 | C24 | 1 | 3 | yes | — |
| 176 | C2×C22⋊D5 | — | 2 | 24 | no | — |
| 177 | C2×C22⋊D5 | — | 2 | 12 | no | — |
| 178 | C2×C22⋊D5 | — | 2 | 6 | no | — |
| 179 | C2×C22⋊D5 | — | 2 | 3 | no | — |
| 180 | C2×C22⋊D5 | C2×D4 | 1 | 6 | yes | — |
| 181 | C22×Dic5 | — | 2 | 12 | no | — |
| 182 | C22×Dic5 | — | 2 | 3 | no | — |
| 183 | C22×Dic5 | C2×D4 | 1 | 6 | yes | — |
| 184 | #713 | — | 2 | 12 | no | — |
| 185 | #713 | — | 2 | 4 | no | — |
| 186 | #713 | — | 2 | 4 | no | — |
| 187 | Q8×D5 | — | 2 | 24 | no | — |
| 188 | Q8×D5 | — | 2 | 12 | no | — |
| 189 | Q8×D5 | — | 2 | 4 | no | — |
| 190 | Q8×D5 | — | 2 | 8 | no | — |
| 191 | Q8×D5 | — | 2 | 12 | no | — |
| 192 | Q8×D5 | — | 4 | 4 | no | — |
| 193 | #711 | — | 2 | 48 | no | — |
| 194 | #711 | — | 2 | 24 | no | — |
| 195 | #711 | — | 2 | 24 | no | — |
| 196 | #711 | — | 2 | 12 | no | — |
| 197 | #711 | — | 2 | 12 | no | — |
| 198 | #711 | — | 2 | 24 | no | — |
| 199 | #711 | — | 2 | 12 | no | — |
| 200 | #711 | — | 2 | 24 | no | — |
| 201 | #711 | — | 4 | 12 | no | — |
| 202 | D4×D5 | — | 2 | 24 | no | — |
| 203 | D4×D5 | — | 2 | 12 | no | — |
| 204 | D4×D5 | — | 2 | 8 | no | — |
| 205 | D4×D5 | — | 2 | 12 | no | — |
| 206 | D4×D5 | — | 2 | 4 | no | — |
| 207 | #709 | — | 2 | 24 | no | — |
| 208 | #709 | — | 2 | 24 | no | — |
| 209 | #709 | — | 2 | 24 | no | — |
| 210 | #709 | — | 2 | 6 | no | — |
| 211 | #709 | — | 2 | 6 | no | — |
| 212 | #709 | — | 2 | 6 | no | — |
| 213 | #709 | — | 2 | 6 | no | — |
| 214 | #709 | — | 2 | 12 | no | — |
| 215 | #709 | — | 2 | 6 | no | — |
| 216 | #709 | — | 2 | 6 | no | — |
| 217 | #709 | — | 2 | 4 | no | — |
| 218 | #709 | C2×D4 | 1 | 12 | yes | — |
| 219 | #709 | C24 | 1 | 4 | yes | — |
| 220 | C2×D20 | — | 2 | 4 | no | — |
| 221 | C2×D20 | — | 2 | 2 | no | — |
| 222 | C2×D20 | C2×D4 | 1 | 6 | yes | — |
| 223 | C2×D20 | C24 | 1 | 1 | yes | characteristic |
| 224 | C2×D20 | C24 | 1 | 1 | yes | characteristic |
| 225 | C2×C4×D5 | — | 2 | 12 | no | — |
| 226 | C2×C4×D5 | — | 2 | 24 | no | — |
| 227 | C2×C4×D5 | — | 2 | 6 | no | — |
| 228 | C2×C4×D5 | — | 2 | 3 | no | — |
| 229 | C2×C4×D5 | C2×D4 | 1 | 6 | yes | — |
| 230 | C2×Dic10 | — | 2 | 12 | no | — |
| 231 | C2×Dic10 | — | 2 | 24 | no | — |
| 232 | C2×Dic10 | — | 2 | 6 | no | — |
| 233 | C2×Dic10 | — | 2 | 6 | no | — |
| 234 | C2×Dic10 | — | 2 | 12 | no | — |
| 235 | C2×Dic10 | — | 2 | 6 | no | — |
| 236 | C2×Dic10 | — | 2 | 6 | no | — |
| 237 | C2×Dic10 | — | 2 | 3 | no | — |
| 238 | C2×Dic10 | C2×D4 | 1 | 6 | yes | — |
| 239 | C2×Dic10 | C2×D4 | 1 | 6 | yes | — |
| 240 | C2×Dic10 | C24 | 1 | 3 | yes | — |
| 241 | C2×Dic10 | C24 | 1 | 3 | yes | — |
| 242 | C5×M16 | — | 2 | 6 | no | — |
| 243 | C5×M16 | C24 | 1 | 4 | yes | — |
| 244 | C2×C5×C8 | — | 2 | 6 | no | — |
| 245 | C5×C4⋊C4 | — | 2 | 3 | no | — |
| 246 | C5×C22⋊C4 | — | 2 | 3 | no | — |
| 247 | C42×C5 | — | 2 | 3 | no | — |
| 248 | C42×C5 | C24 | 1 | 1 | yes | characteristic |
| 249 | C42×C5 | C24 | 1 | 3 | yes | — |
| 250 | #689 | — | 2 | 12 | no | — |
| 251 | #688 | — | 2 | 4 | no | — |
| 252 | #687 | — | 2 | 12 | no | — |
| 253 | #686 | — | 2 | 4 | no | — |
| 254 | #685 | — | 2 | 6 | no | — |
| 255 | #685 | — | 2 | 6 | no | — |
| 256 | C4⋊Dic5 | — | 2 | 6 | no | — |
| 257 | C4⋊Dic5 | — | 2 | 12 | no | — |
| 258 | #681 | — | 2 | 6 | no | — |
| 259 | #681 | C24 | 1 | 4 | yes | — |
| 260 | C2×#168 | — | 2 | 6 | no | — |
| 261 | Dic20 | — | 2 | 12 | no | — |
| 262 | D40 | — | 2 | 4 | no | — |
| 263 | #677 | — | 2 | 12 | no | — |
| 264 | #677 | — | 2 | 4 | no | — |
| 265 | #585 | — | 5 | 1 | no | — |
| 266 | #585 | — | 5 | 6 | no | — |
| 267 | #585 | — | 10 | 4 | no | — |
| 268 | #585 | — | 10 | 6 | no | — |
| 269 | #585 | — | 10 | 4 | no | — |
| 270 | #585 | C2×D5 | 1 | 1 | yes | characteristic |
| 271 | C2×2−1+4 | — | 5 | 1 | no | — |
| 272 | C2×2−1+4 | — | 5 | 1 | no | — |
| 273 | C2×2−1+4 | — | 5 | 6 | no | — |
| 274 | C2×2−1+4 | — | 10 | 2 | no | — |
| 275 | C2×2−1+4 | — | 10 | 4 | no | — |
| 276 | C2×2−1+4 | — | 10 | 4 | no | — |
| 277 | #578 | — | 10 | 4 | no | — |
| 278 | #578 | — | 10 | 4 | no | — |
| 279 | #577 | — | 10 | 4 | no | — |
| 280 | #577 | — | 10 | 4 | no | — |
| 281 | #575 | — | 5 | 6 | no | — |
| 282 | #575 | — | 5 | 6 | no | — |
| 283 | C2×#137 | — | 5 | 6 | no | — |
| 284 | C2×#137 | — | 5 | 6 | no | — |
| 285 | #568 | — | 5 | 1 | no | — |
| 286 | #568 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 287 | D4×Q8 | — | 10 | 2 | no | — |
| 288 | #547 | — | 10 | 6 | no | — |
| 289 | #536 | — | 5 | 3 | no | — |
| 290 | #536 | — | 5 | 3 | no | — |
| 291 | #532 | — | 5 | 3 | no | — |
| 292 | C2×C4⋊Q8 | — | 5 | 3 | no | — |
| 293 | C4×#41 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 294 | #456 | — | 5 | 12 | no | — |
| 295 | #456 | — | 5 | 24 | no | — |
| 296 | #455 | — | 5 | 12 | no | — |
| 297 | #454 | — | 5 | 12 | no | — |
| 298 | #453 | — | 5 | 4 | no | — |
| 299 | #421 | — | 5 | 6 | no | — |
| 300 | #421 | C2×D5 | 1 | 6 | yes | complemented |
| 301 | C2×#104 | — | 5 | 6 | no | — |
| 302 | C2×#104 | C2×D5 | 1 | 6 | yes | complemented |
| 303 | #413 | — | 5 | 6 | no | — |
| 304 | C2×#101 | — | 5 | 6 | no | — |
| 305 | C23×C5 | — | 2 | 6 | no | — |
| 306 | C23×C5 | C22×D4 | 1 | 3 | yes | — |
| 307 | C22×D5 | — | 2 | 8 | no | — |
| 308 | C22×D5 | — | 2 | 6 | no | — |
| 309 | C22×D5 | — | 2 | 1 | no | — |
| 310 | C22×D5 | C22×D4 | 1 | 2 | yes | — |
| 311 | C5×Q8 | — | 2 | 6 | no | — |
| 312 | C5×Q8 | #120 | 1 | 4 | yes | — |
| 313 | C5×Q8 | C22×D4 | 1 | 4 | yes | — |
| 314 | C5×D4 | — | 2 | 12 | no | — |
| 315 | C5×D4 | — | 2 | 4 | no | — |
| 316 | C5×D4 | — | 2 | 6 | no | — |
| 317 | C5×D4 | #120 | 1 | 12 | yes | — |
| 318 | C5×D4 | C22×D4 | 1 | 4 | yes | — |
| 319 | C2×C4×C5 | — | 2 | 6 | no | — |
| 320 | C2×C4×C5 | — | 2 | 1 | no | — |
| 321 | C2×C4×C5 | — | 2 | 12 | no | — |
| 322 | C2×C4×C5 | — | 2 | 4 | no | — |
| 323 | C2×C4×C5 | — | 2 | 3 | no | — |
| 324 | C2×C4×C5 | — | 4 | 6 | no | — |
| 325 | C2×C4×C5 | C22×D4 | 1 | 6 | yes | — |
| 326 | C2×C4×C5 | C22×D4 | 1 | 3 | yes | — |
| 327 | C2×C4×C5 | C22×D4 | 1 | 6 | yes | — |
| 328 | C2×C4×C5 | C25 | 1 | 1 | yes | characteristic |
| 329 | C22⋊D5 | — | 2 | 24 | no | — |
| 330 | C22⋊D5 | — | 2 | 8 | no | — |
| 331 | C22⋊D5 | — | 2 | 12 | no | — |
| 332 | C22⋊D5 | — | 2 | 12 | no | — |
| 333 | C22⋊D5 | — | 2 | 4 | no | — |
| 334 | C22⋊D5 | — | 4 | 6 | no | — |
| 335 | C2×Dic5 | — | 2 | 24 | no | — |
| 336 | C2×Dic5 | — | 2 | 12 | no | — |
| 337 | C2×Dic5 | — | 2 | 6 | no | — |
| 338 | C2×Dic5 | — | 2 | 3 | no | — |
| 339 | C2×Dic5 | — | 4 | 6 | no | — |
| 340 | C2×Dic5 | C22×D4 | 1 | 6 | yes | — |
| 341 | D20 | — | 2 | 8 | no | — |
| 342 | D20 | — | 2 | 6 | no | — |
| 343 | D20 | — | 2 | 1 | no | — |
| 344 | D20 | — | 2 | 1 | no | — |
| 345 | D20 | — | 2 | 1 | no | — |
| 346 | D20 | — | 2 | 1 | no | — |
| 347 | D20 | — | 4 | 4 | no | — |
| 348 | D20 | C22×D4 | 1 | 4 | yes | — |
| 349 | C4×D5 | — | 2 | 24 | no | — |
| 350 | C4×D5 | — | 2 | 8 | no | — |
| 351 | C4×D5 | — | 2 | 12 | no | — |
| 352 | C4×D5 | — | 2 | 12 | no | — |
| 353 | C4×D5 | — | 2 | 4 | no | — |
| 354 | C4×D5 | — | 4 | 6 | no | — |
| 355 | Dic10 | — | 2 | 24 | no | — |
| 356 | Dic10 | — | 2 | 12 | no | — |
| 357 | Dic10 | — | 2 | 6 | no | — |
| 358 | Dic10 | — | 2 | 3 | no | — |
| 359 | Dic10 | — | 2 | 3 | no | — |
| 360 | Dic10 | — | 2 | 3 | no | — |
| 361 | Dic10 | — | 2 | 3 | no | — |
| 362 | Dic10 | — | 4 | 6 | no | — |
| 363 | Dic10 | C22×D4 | 1 | 4 | yes | — |
| 364 | C5×C8 | — | 2 | 4 | no | — |
| 365 | #168 | — | 2 | 4 | no | — |
| 366 | 2−1+4 | — | 2 | 1 | no | — |
| 367 | 2−1+4 | — | 5 | 4 | no | — |
| 368 | 2−1+4 | — | 5 | 12 | no | — |
| 369 | 2−1+4 | — | 10 | 8 | no | — |
| 370 | 2−1+4 | — | 10 | 12 | no | — |
| 371 | 2−1+4 | — | 10 | 6 | no | — |
| 372 | 2−1+4 | — | 10 | 12 | no | — |
| 373 | 2−1+4 | — | 10 | 24 | no | — |
| 374 | 2−1+4 | — | 10 | 8 | no | — |
| 375 | 2−1+4 | — | 10 | 12 | no | — |
| 376 | 2−1+4 | — | 10 | 4 | no | — |
| 377 | 2−1+4 | — | 10 | 4 | no | — |
| 378 | 2−1+4 | — | 10 | 6 | no | — |
| 379 | 2−1+4 | — | 10 | 1 | no | — |
| 380 | 2−1+4 | — | 10 | 4 | no | — |
| 381 | 2−1+4 | — | 10 | 4 | no | — |
| 382 | 2−1+4 | D20 | 1 | 4 | yes | complemented |
| 383 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 384 | H(5,𝔽2) | — | 5 | 4 | no | — |
| 385 | H(5,𝔽2) | — | 5 | 4 | no | — |
| 386 | H(5,𝔽2) | — | 10 | 12 | no | — |
| 387 | H(5,𝔽2) | — | 10 | 24 | no | — |
| 388 | H(5,𝔽2) | — | 10 | 6 | no | — |
| 389 | H(5,𝔽2) | — | 10 | 6 | no | — |
| 390 | H(5,𝔽2) | — | 10 | 3 | no | — |
| 391 | H(5,𝔽2) | D20 | 1 | 4 | yes | complemented |
| 392 | C2×#41 | — | 2 | 4 | no | — |
| 393 | C2×#41 | — | 5 | 6 | no | — |
| 394 | C2×#41 | — | 5 | 3 | no | — |
| 395 | C2×#41 | — | 5 | 6 | no | — |
| 396 | C2×#41 | — | 5 | 3 | no | — |
| 397 | C2×#41 | — | 10 | 6 | no | — |
| 398 | C2×#41 | — | 10 | 12 | no | — |
| 399 | C2×#41 | — | 10 | 12 | no | — |
| 400 | C2×#41 | — | 10 | 12 | no | — |
| 401 | C2×#41 | — | 10 | 24 | no | — |
| 402 | C2×#41 | — | 10 | 8 | no | — |
| 403 | C2×#41 | — | 10 | 24 | no | — |
| 404 | C2×#41 | — | 10 | 12 | no | — |
| 405 | C2×#41 | — | 10 | 4 | no | — |
| 406 | C2×#41 | — | 10 | 6 | no | — |
| 407 | C2×#41 | — | 10 | 3 | no | — |
| 408 | C2×#41 | C22×D5 | 1 | 6 | yes | — |
| 409 | C2×#41 | C22×D5 | 1 | 1 | yes | characteristic |
| 410 | C22×Q8 | — | 5 | 2 | no | — |
| 411 | C22×Q8 | — | 5 | 3 | no | — |
| 412 | C22×Q8 | — | 5 | 3 | no | — |
| 413 | C22×Q8 | — | 10 | 6 | no | — |
| 414 | C22×Q8 | — | 10 | 8 | no | — |
| 415 | C22×Q8 | — | 10 | 6 | no | — |
| 416 | C22×Q8 | — | 10 | 1 | no | — |
| 417 | #137 | — | 5 | 12 | no | — |
| 418 | #137 | — | 5 | 12 | no | — |
| 419 | #137 | — | 10 | 6 | no | — |
| 420 | #137 | — | 10 | 12 | no | — |
| 421 | #137 | — | 10 | 12 | no | — |
| 422 | #137 | — | 10 | 6 | no | — |
| 423 | AGL(1,ℤ/8) | — | 5 | 4 | no | — |
| 424 | AGL(1,ℤ/8) | — | 5 | 4 | no | — |
| 425 | AGL(1,ℤ/8) | — | 10 | 6 | no | — |
| 426 | AGL(1,ℤ/8) | — | 10 | 6 | no | — |
| 427 | #135 | — | 10 | 12 | no | — |
| 428 | #135 | — | 10 | 12 | no | — |
| 429 | C2×Q16 | — | 10 | 6 | no | — |
| 430 | C2×Q16 | — | 10 | 6 | no | — |
| 431 | C2×SD16 | — | 10 | 6 | no | — |
| 432 | C2×SD16 | — | 10 | 6 | no | — |
| 433 | #131 | — | 2 | 4 | no | — |
| 434 | #131 | — | 10 | 4 | no | — |
| 435 | C2×M16 | — | 5 | 6 | no | — |
| 436 | C2×M16 | C22×D5 | 1 | 6 | yes | — |
| 437 | C4⋊Q8 | — | 5 | 3 | no | — |
| 438 | C4⋊Q8 | — | 5 | 6 | no | — |
| 439 | C4⋊Q8 | — | 10 | 6 | no | — |
| 440 | #127 | — | 5 | 1 | no | — |
| 441 | #124 | — | 5 | 3 | no | — |
| 442 | #124 | — | 5 | 3 | no | — |
| 443 | #123 | — | 10 | 6 | no | — |
| 444 | #123 | — | 10 | 6 | no | — |
| 445 | C22⋊Q8 | — | 10 | 6 | no | — |
| 446 | C22⋊Q8 | — | 10 | 6 | no | — |
| 447 | #121 | — | 10 | 6 | no | — |
| 448 | C4×Q8 | — | 2 | 1 | no | — |
| 449 | C4×D4 | — | 2 | 3 | no | — |
| 450 | C4×D4 | — | 10 | 6 | no | — |
| 451 | #117 | C22×D5 | 1 | 3 | yes | — |
| 452 | C2×C4⋊C4 | — | 10 | 6 | no | — |
| 453 | C2×C42 | C22×D5 | 1 | 3 | yes | — |
| 454 | #104 | — | 5 | 4 | no | — |
| 455 | #104 | — | 5 | 12 | no | — |
| 456 | #104 | C22×D5 | 1 | 4 | yes | — |
| 457 | #104 | C22×D5 | 1 | 12 | yes | — |
| 458 | #101 | — | 5 | 12 | no | — |
| 459 | #100 | — | 5 | 4 | no | — |
| 460 | C22×C5 | — | 2 | 4 | no | — |
| 461 | C22×C5 | — | 4 | 3 | no | — |
| 462 | C22×C5 | — | 8 | 6 | no | — |
| 463 | C22×C5 | C2×#120 | 1 | 6 | yes | — |
| 464 | C22×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 465 | C2×D5 | — | 2 | 2 | no | — |
| 466 | C2×D5 | — | 2 | 4 | no | — |
| 467 | C2×D5 | — | 4 | 2 | no | — |
| 468 | C2×D5 | — | 4 | 2 | no | — |
| 469 | C2×D5 | — | 4 | 1 | no | — |
| 470 | C2×D5 | — | 8 | 6 | no | — |
| 471 | C2×D5 | — | 8 | 8 | no | — |
| 472 | C4×C5 | — | 2 | 2 | no | — |
| 473 | C4×C5 | — | 2 | 4 | no | — |
| 474 | C4×C5 | — | 4 | 3 | no | — |
| 475 | C4×C5 | C2×#120 | 1 | 6 | yes | — |
| 476 | C4×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 477 | C4×C5 | C23×D4 | 1 | 1 | yes | characteristic |
| 478 | Dic5 | — | 2 | 6 | no | — |
| 479 | Dic5 | — | 2 | 4 | no | — |
| 480 | Dic5 | — | 4 | 3 | no | — |
| 481 | #41 | — | 2 | 4 | no | — |
| 482 | #41 | — | 2 | 12 | no | — |
| 483 | #41 | — | 2 | 6 | no | — |
| 484 | #41 | — | 2 | 6 | no | — |
| 485 | #41 | — | 5 | 12 | no | — |
| 486 | #41 | — | 5 | 4 | no | — |
| 487 | #41 | — | 10 | 12 | no | — |
| 488 | #41 | — | 10 | 4 | no | — |
| 489 | #41 | — | 10 | 24 | no | — |
| 490 | #41 | — | 10 | 24 | no | — |
| 491 | #41 | — | 10 | 24 | no | — |
| 492 | #41 | — | 10 | 24 | no | — |
| 493 | #41 | — | 10 | 48 | no | — |
| 494 | #41 | — | 10 | 24 | no | — |
| 495 | #41 | — | 10 | 12 | no | — |
| 496 | #41 | — | 10 | 24 | no | — |
| 497 | #41 | — | 10 | 12 | no | — |
| 498 | #41 | — | 10 | 4 | no | — |
| 499 | #41 | — | 10 | 4 | no | — |
| 500 | #41 | — | 10 | 12 | no | — |
| 501 | #41 | — | 10 | 24 | no | — |
| 502 | #41 | — | 10 | 12 | no | — |
| 503 | #41 | — | 10 | 6 | no | — |
| 504 | #41 | — | 10 | 6 | no | — |
| 505 | #41 | — | 10 | 6 | no | — |
| 506 | #41 | — | 10 | 6 | no | — |
| 507 | #41 | — | 10 | 6 | no | — |
| 508 | #41 | — | 10 | 6 | no | — |
| 509 | #41 | — | 20 | 12 | no | — |
| 510 | #41 | C2×D20 | 1 | 12 | yes | — |
| 511 | #41 | C2×D20 | 1 | 4 | yes | — |
| 512 | #41 | D4×D5 | 1 | 4 | yes | — |
| 513 | #41 | C23×D5 | 1 | 4 | yes | — |
| 514 | C2×Q8 | — | 2 | 4 | no | — |
| 515 | C2×Q8 | — | 5 | 6 | no | — |
| 516 | C2×Q8 | — | 5 | 3 | no | — |
| 517 | C2×Q8 | — | 5 | 6 | no | — |
| 518 | C2×Q8 | — | 5 | 3 | no | — |
| 519 | C2×Q8 | — | 10 | 12 | no | — |
| 520 | C2×Q8 | — | 10 | 12 | no | — |
| 521 | C2×Q8 | — | 10 | 24 | no | — |
| 522 | C2×Q8 | — | 10 | 12 | no | — |
| 523 | C2×Q8 | — | 10 | 24 | no | — |
| 524 | C2×Q8 | — | 10 | 12 | no | — |
| 525 | C2×Q8 | — | 10 | 8 | no | — |
| 526 | C2×Q8 | — | 10 | 4 | no | — |
| 527 | C2×Q8 | — | 10 | 6 | no | — |
| 528 | C2×Q8 | — | 10 | 6 | no | — |
| 529 | C2×Q8 | — | 10 | 3 | no | — |
| 530 | C2×Q8 | — | 10 | 6 | no | — |
| 531 | C2×Q8 | — | 10 | 6 | no | — |
| 532 | C2×Q8 | — | 20 | 4 | no | — |
| 533 | C2×Q8 | C2×D20 | 1 | 6 | yes | — |
| 534 | C2×Q8 | D4×D5 | 1 | 1 | yes | characteristic |
| 535 | C2×D4 | — | 2 | 6 | no | — |
| 536 | C2×D4 | — | 2 | 12 | no | — |
| 537 | C2×D4 | — | 5 | 6 | no | — |
| 538 | C2×D4 | — | 5 | 6 | no | — |
| 539 | C2×D4 | — | 5 | 1 | no | — |
| 540 | C2×D4 | — | 5 | 1 | no | — |
| 541 | C2×D4 | — | 10 | 4 | no | — |
| 542 | C2×D4 | — | 10 | 2 | no | — |
| 543 | C2×D4 | — | 10 | 8 | no | — |
| 544 | C2×D4 | — | 10 | 24 | no | — |
| 545 | C2×D4 | — | 10 | 12 | no | — |
| 546 | C2×D4 | — | 10 | 24 | no | — |
| 547 | C2×D4 | — | 10 | 12 | no | — |
| 548 | C2×D4 | — | 10 | 6 | no | — |
| 549 | C2×D4 | — | 10 | 4 | no | — |
| 550 | C2×D4 | — | 10 | 12 | no | — |
| 551 | C2×D4 | — | 10 | 3 | no | — |
| 552 | C2×D4 | C2×D20 | 1 | 6 | yes | — |
| 553 | C2×D4 | D4×D5 | 1 | 3 | yes | — |
| 554 | C22×C4 | — | 2 | 6 | no | — |
| 555 | C22×C4 | — | 2 | 3 | no | — |
| 556 | C22×C4 | — | 5 | 6 | no | — |
| 557 | C22×C4 | — | 5 | 6 | no | — |
| 558 | C22×C4 | — | 10 | 12 | no | — |
| 559 | C22×C4 | — | 10 | 24 | no | — |
| 560 | C22×C4 | — | 10 | 12 | no | — |
| 561 | C22×C4 | — | 10 | 6 | no | — |
| 562 | C22×C4 | — | 10 | 3 | no | — |
| 563 | C22×C4 | — | 10 | 3 | no | — |
| 564 | C22×C4 | C23×D5 | 1 | 3 | yes | — |
| 565 | Q16 | — | 10 | 12 | no | — |
| 566 | Q16 | — | 10 | 12 | no | — |
| 567 | SD16 | — | 10 | 12 | no | — |
| 568 | SD16 | — | 10 | 4 | no | — |
| 569 | SD16 | — | 10 | 4 | no | — |
| 570 | SD16 | — | 10 | 12 | no | — |
| 571 | D8 | — | 10 | 4 | no | — |
| 572 | D8 | — | 10 | 4 | no | — |
| 573 | M16 | — | 2 | 6 | no | — |
| 574 | M16 | — | 5 | 4 | no | — |
| 575 | M16 | — | 10 | 6 | no | — |
| 576 | M16 | C23×D5 | 1 | 4 | yes | — |
| 577 | C2×C8 | — | 2 | 6 | no | — |
| 578 | C2×C8 | — | 10 | 6 | no | — |
| 579 | C4⋊C4 | — | 2 | 3 | no | — |
| 580 | C4⋊C4 | — | 10 | 6 | no | — |
| 581 | C4⋊C4 | — | 10 | 12 | no | — |
| 582 | C22⋊C4 | — | 2 | 3 | no | — |
| 583 | C22⋊C4 | — | 10 | 6 | no | — |
| 584 | C22⋊C4 | — | 10 | 6 | no | — |
| 585 | C42 | — | 2 | 3 | no | — |
| 586 | C42 | C23×D5 | 1 | 1 | yes | characteristic |
| 587 | C42 | C23×D5 | 1 | 3 | yes | — |
| 588 | C2×C5 | — | 2 | 1 | no | — |
| 589 | C2×C5 | — | 2 | 6 | no | — |
| 590 | C2×C5 | — | 4 | 4 | no | — |
| 591 | C2×C5 | C22×#120 | 1 | 1 | yes | characteristic |
| 592 | D5 | — | 4 | 2 | no | — |
| 593 | D5 | — | 4 | 4 | no | — |
| 594 | D5 | — | 8 | 1 | no | — |
| 595 | C23 | — | 2 | 6 | no | — |
| 596 | C23 | — | 5 | 2 | no | — |
| 597 | C23 | — | 10 | 8 | no | — |
| 598 | C23 | — | 10 | 6 | no | — |
| 599 | C23 | — | 10 | 1 | no | — |
| 600 | C23 | C2×D4×D5 | 1 | 3 | yes | — |
| 601 | Q8 | — | 2 | 6 | no | — |
| 602 | Q8 | — | 5 | 4 | no | — |
| 603 | Q8 | — | 10 | 24 | no | — |
| 604 | Q8 | — | 10 | 12 | no | — |
| 605 | Q8 | — | 10 | 6 | no | — |
| 606 | Q8 | — | 10 | 3 | no | — |
| 607 | Q8 | — | 10 | 3 | no | — |
| 608 | Q8 | — | 10 | 3 | no | — |
| 609 | Q8 | — | 10 | 3 | no | — |
| 610 | Q8 | — | 20 | 6 | no | — |
| 611 | Q8 | #4028 | 1 | 4 | yes | — |
| 612 | Q8 | C22×D20 | 1 | 4 | yes | — |
| 613 | D4 | — | 2 | 12 | no | — |
| 614 | D4 | — | 2 | 4 | no | — |
| 615 | D4 | — | 2 | 6 | no | — |
| 616 | D4 | — | 5 | 4 | no | — |
| 617 | D4 | — | 10 | 8 | no | — |
| 618 | D4 | — | 10 | 24 | no | — |
| 619 | D4 | — | 10 | 8 | no | — |
| 620 | D4 | — | 10 | 12 | no | — |
| 621 | D4 | — | 10 | 12 | no | — |
| 622 | D4 | — | 10 | 4 | no | — |
| 623 | D4 | — | 10 | 6 | no | — |
| 624 | D4 | — | 10 | 1 | no | — |
| 625 | D4 | — | 10 | 1 | no | — |
| 626 | D4 | — | 10 | 1 | no | — |
| 627 | D4 | — | 10 | 1 | no | — |
| 628 | D4 | — | 20 | 4 | no | — |
| 629 | D4 | — | 20 | 6 | no | — |
| 630 | D4 | #4028 | 1 | 12 | yes | — |
| 631 | D4 | C22×D20 | 1 | 4 | yes | — |
| 632 | C2×C4 | — | 2 | 6 | no | — |
| 633 | C2×C4 | — | 2 | 1 | no | — |
| 634 | C2×C4 | — | 2 | 12 | no | — |
| 635 | C2×C4 | — | 2 | 4 | no | — |
| 636 | C2×C4 | — | 2 | 3 | no | — |
| 637 | C2×C4 | — | 4 | 6 | no | — |
| 638 | C2×C4 | — | 5 | 6 | no | — |
| 639 | C2×C4 | — | 10 | 24 | no | — |
| 640 | C2×C4 | — | 10 | 8 | no | — |
| 641 | C2×C4 | — | 10 | 24 | no | — |
| 642 | C2×C4 | — | 10 | 12 | no | — |
| 643 | C2×C4 | — | 10 | 6 | no | — |
| 644 | C2×C4 | — | 10 | 12 | no | — |
| 645 | C2×C4 | — | 10 | 12 | no | — |
| 646 | C2×C4 | — | 10 | 4 | no | — |
| 647 | C2×C4 | — | 10 | 3 | no | — |
| 648 | C2×C4 | — | 20 | 6 | no | — |
| 649 | C2×C4 | — | 20 | 6 | no | — |
| 650 | C2×C4 | C22×D20 | 1 | 6 | yes | — |
| 651 | C2×C4 | C2×D4×D5 | 1 | 3 | yes | — |
| 652 | C2×C4 | C2×D4×D5 | 1 | 6 | yes | — |
| 653 | C2×C4 | C24×D5 | 1 | 1 | yes | characteristic |
| 654 | C8 | — | 2 | 4 | no | — |
| 655 | C8 | — | 10 | 4 | no | — |
| 656 | C5 | #60391 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 657 | C22 | — | 2 | 4 | no | — |
| 658 | C22 | — | 4 | 3 | no | — |
| 659 | C22 | — | 8 | 6 | no | — |
| 660 | C22 | — | 10 | 4 | no | — |
| 661 | C22 | — | 10 | 2 | no | — |
| 662 | C22 | — | 20 | 2 | no | — |
| 663 | C22 | — | 20 | 2 | no | — |
| 664 | C22 | — | 20 | 1 | no | — |
| 665 | C22 | — | 40 | 6 | no | — |
| 666 | C22 | — | 40 | 8 | no | — |
| 667 | C22 | C2×#4028 | 1 | 6 | yes | — |
| 668 | C22 | C22×D4×D5 | 1 | 1 | yes | characteristic |
| 669 | C4 | — | 2 | 2 | no | — |
| 670 | C4 | — | 2 | 4 | no | — |
| 671 | C4 | — | 4 | 3 | no | — |
| 672 | C4 | — | 10 | 6 | no | — |
| 673 | C4 | — | 10 | 4 | no | — |
| 674 | C4 | — | 20 | 3 | no | — |
| 675 | C4 | C2×#4028 | 1 | 6 | yes | — |
| 676 | C4 | C23×D20 | 1 | 1 | yes | characteristic |
| 677 | C4 | C22×D4×D5 | 1 | 1 | yes | characteristic |
| 678 | C2 | — | 2 | 1 | no | — |
| 679 | C2 | — | 2 | 6 | no | — |
| 680 | C2 | — | 4 | 4 | no | — |
| 681 | C2 | — | 20 | 2 | no | — |
| 682 | C2 | — | 20 | 4 | no | — |
| 683 | C2 | — | 40 | 1 | no | — |
| 684 | C2 | C22×#4028 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10619440 | C2 | semidirect |
| 2. #10619200 | C2 | semidirect |
| 3. #10619069 | C2 | semidirect |
| 4. #10617728 | C2 | semidirect |
| 5. C5×#2901 | C2 | semidirect |
| 6. #10615546 | C2 | semidirect |
| 7. #10614267 | C2 | semidirect |
| 8. #10610727 | C2 | semidirect |
| 9. #10610726 | C2 | semidirect |
| 10. C2×#65115 | C2 | semidirect |
| 11. #10610717 | C2 | semidirect |
| 23. C2×#4150 | C22 | semidirect |
| 24. C5×#568 | C22 | semidirect |
| 25. C4×C5×#41 | C22 | semidirect |
| 28. C2×#4097 | C22 | semidirect |
| 29. #66156 | C22 | semidirect |
| 30. #66153 | C22 | semidirect |
| 33. #66082 | C22 | semidirect |
| 34. C2×#4055 | C22 | semidirect |
| 37. #65860 | C22 | semidirect |
| 38. #65860 | C22 | semidirect |
| 39. #65811 | C22 | semidirect |
| 40. C2×#4015 | C22 | semidirect |
| 41. C5×#421 | C22 | semidirect |
| 42. C2×C5×#104 | C22 | semidirect |
| 43. C2×#3956 | C22 | semidirect |
| 44. #65421 | C22 | semidirect |
| 45. #65294 | C22 | semidirect |
| 46. C2×#3937 | C22 | semidirect |
| 47. #65116 | C22 | semidirect |
| 48. #65115 | C22 | semidirect |
| 49. #65115 | C22 | semidirect |
| 50. #65114 | C22 | semidirect |
| 51. #65111 | C22 | semidirect |
| 54. C5×2−1+4 | D4 | semidirect |
| 56. C5×H(5,𝔽2) | D4 | semidirect |
| 70. #4150 | D4 | semidirect |
| 73. #4149 | D4 | semidirect |
| 156. #2901 | D5 | semidirect |
| 286. #568 | C2×D5 | semidirect |
| 293. C4×#41 | C2×D5 | semidirect |
| 300. #421 | C2×D5 | semidirect |
| 302. C2×#104 | C2×D5 | semidirect |
| 382. 2−1+4 | D20 | semidirect |
| 391. H(5,𝔽2) | D20 | semidirect |
| 656. C5 | #60391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619440 | 2 |
| #10619200 | 2 |
| #10619069 | 2 |
| #10617728 | 2 |
| C5×#2901 | 2 |
| #10615546 | 2 |
| #10614267 | 2 |
| #10610727 | 2 |
| #10610726 | 2 |
| C2×#65115 | 2 |
| #10610717 | 2 |
| #60391 | 5 |