Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
336 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10611687 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10601752 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10600079 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10599874 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C5×#1338 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10598053 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10598007 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #65919 | — | 2 | 1 | no | — |
| 9 | C5×#446 | C22 | 1 | 1 | yes | characteristic |
| 10 | #65316 | — | 2 | 1 | no | — |
| 11 | C2×#3932 | — | 2 | 1 | no | — |
| 12 | C2×D80 | — | 2 | 1 | no | — |
| 13 | C2×D80 | — | 2 | 1 | no | — |
| 14 | #65134 | — | 2 | 1 | no | — |
| 15 | #65133 | — | 2 | 1 | no | — |
| 16 | #65132 | — | 2 | 1 | no | — |
| 17 | #65001 | — | 2 | 1 | no | — |
| 18 | #64999 | — | 2 | 1 | no | — |
| 19 | #64985 | C22 | 1 | 1 | yes | characteristic |
| 20 | #64984 | C22 | 1 | 1 | yes | characteristic |
| 21 | C4×D40 | C22 | 1 | 1 | yes | characteristic |
| 22 | C5×C4⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 23 | C5×#346 | C22 | 1 | 1 | yes | characteristic |
| 24 | #64729 | — | 2 | 1 | no | — |
| 25 | #64705 | — | 2 | 1 | no | — |
| 26 | #64677 | C22 | 1 | 1 | yes | characteristic |
| 27 | #12336 | — | 5 | 1 | no | maximal, Sylow |
| 28 | C4×C5×Q8 | D4 | 1 | 1 | yes | characteristic |
| 29 | #4093 | — | 4 | 1 | no | — |
| 30 | C2×#688 | — | 4 | 1 | no | — |
| 31 | C2×Dic20 | D4 | 1 | 1 | yes | characteristic |
| 32 | C2×D40 | — | 2 | 1 | no | — |
| 33 | C2×D40 | — | 2 | 1 | no | — |
| 34 | C2×D40 | — | 2 | 1 | no | — |
| 35 | C2×D40 | D4 | 1 | 1 | yes | characteristic |
| 36 | C2×D40 | D4 | 1 | 1 | yes | characteristic |
| 37 | C2×#677 | — | 2 | 1 | no | — |
| 38 | C2×#677 | — | 2 | 1 | no | — |
| 39 | #4040 | — | 4 | 1 | no | — |
| 40 | #4040 | — | 4 | 1 | no | — |
| 41 | #4039 | — | 4 | 1 | no | — |
| 42 | #4021 | — | 2 | 1 | no | — |
| 43 | #4021 | — | 2 | 1 | no | — |
| 44 | #4020 | — | 2 | 1 | no | — |
| 45 | #4020 | — | 2 | 1 | no | — |
| 46 | C4×D20 | — | 2 | 1 | no | — |
| 47 | C4×D20 | — | 2 | 1 | no | — |
| 48 | C4×Dic10 | — | 2 | 1 | no | — |
| 49 | C2×C5×C16 | — | 2 | 1 | no | — |
| 50 | C2×C5×C16 | — | 2 | 1 | no | — |
| 51 | C5×C4⋊C8 | — | 2 | 1 | no | — |
| 52 | C5×C4⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 53 | C5×#97 | — | 2 | 1 | no | — |
| 54 | C4×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 55 | #3953 | — | 2 | 1 | no | — |
| 56 | #3953 | — | 2 | 1 | no | — |
| 57 | #3950 | D4 | 1 | 1 | yes | characteristic |
| 58 | #3948 | — | 2 | 1 | no | — |
| 59 | #3941 | — | 4 | 1 | no | — |
| 60 | C4⋊#168 | — | 2 | 1 | no | — |
| 61 | #3932 | — | 4 | 2 | no | — |
| 62 | D80 | — | 4 | 2 | no | — |
| 63 | D80 | — | 4 | 2 | no | — |
| 64 | #3403 | — | 5 | 1 | no | — |
| 65 | #2250 | — | 5 | 1 | no | — |
| 66 | #2206 | — | 5 | 1 | no | — |
| 67 | #1688 | — | 5 | 1 | no | — |
| 68 | #1360 | — | 5 | 1 | no | — |
| 69 | #1338 | D5 | 1 | 1 | yes | characteristic, complemented |
| 70 | #1333 | — | 5 | 1 | no | — |
| 71 | C2×C5×Q8 | D8 | 1 | 1 | yes | characteristic |
| 72 | C2×D20 | — | 2 | 1 | no | — |
| 73 | C2×D20 | — | 2 | 1 | no | — |
| 74 | C2×D20 | — | 4 | 1 | no | — |
| 75 | C2×D20 | — | 4 | 1 | no | — |
| 76 | C2×D20 | — | 4 | 1 | no | — |
| 77 | C2×D20 | — | 4 | 1 | no | — |
| 78 | C2×D20 | — | 4 | 1 | no | — |
| 79 | C2×C4×D5 | — | 4 | 1 | no | — |
| 80 | C2×C4×D5 | — | 4 | 1 | no | — |
| 81 | C2×Dic10 | — | 2 | 1 | no | — |
| 82 | C2×C5×C8 | — | 2 | 1 | no | — |
| 83 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 84 | C2×C5×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 85 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 86 | C5×C4⋊C4 | D8 | 1 | 1 | yes | characteristic |
| 87 | C42×C5 | — | 2 | 1 | no | — |
| 88 | C42×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | #688 | — | 8 | 2 | no | — |
| 90 | #685 | — | 4 | 1 | no | — |
| 91 | #685 | — | 4 | 1 | no | — |
| 92 | #685 | — | 4 | 1 | no | — |
| 93 | #685 | — | 4 | 1 | no | — |
| 94 | #685 | — | 4 | 1 | no | — |
| 95 | #685 | — | 4 | 1 | no | — |
| 96 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 97 | #683 | — | 4 | 1 | no | — |
| 98 | C4×Dic5 | — | 4 | 1 | no | — |
| 99 | C2×#168 | — | 4 | 1 | no | — |
| 100 | Dic20 | — | 4 | 1 | no | — |
| 101 | D40 | — | 2 | 1 | no | — |
| 102 | D40 | — | 2 | 1 | no | — |
| 103 | D40 | — | 4 | 1 | no | — |
| 104 | D40 | — | 4 | 1 | no | — |
| 105 | D40 | — | 4 | 1 | no | — |
| 106 | D40 | — | 4 | 1 | no | — |
| 107 | D40 | — | 4 | 1 | no | — |
| 108 | D40 | — | 8 | 1 | no | — |
| 109 | #677 | — | 4 | 1 | no | — |
| 110 | #677 | — | 4 | 1 | no | — |
| 111 | #677 | — | 8 | 1 | no | — |
| 112 | C5×C16 | — | 2 | 2 | no | — |
| 113 | C5×C16 | — | 4 | 1 | no | — |
| 114 | #559 | — | 10 | 1 | no | — |
| 115 | C2×SD32 | — | 10 | 1 | no | — |
| 116 | C2×D16 | — | 10 | 1 | no | — |
| 117 | C2×D16 | — | 10 | 1 | no | — |
| 118 | #496 | — | 10 | 1 | no | — |
| 119 | #495 | — | 5 | 1 | no | — |
| 120 | #493 | — | 5 | 1 | no | — |
| 121 | #464 | — | 10 | 1 | no | — |
| 122 | #463 | — | 10 | 1 | no | — |
| 123 | #460 | — | 10 | 1 | no | — |
| 124 | #459 | — | 10 | 1 | no | — |
| 125 | #446 | C2×D5 | 1 | 1 | yes | characteristic |
| 126 | #440 | — | 10 | 1 | no | — |
| 127 | C4×D8 | — | 5 | 1 | no | — |
| 128 | C4⋊C16 | C2×D5 | 1 | 1 | yes | characteristic |
| 129 | #357 | — | 10 | 1 | no | — |
| 130 | #346 | C2×D5 | 1 | 1 | yes | characteristic |
| 131 | #334 | — | 5 | 1 | no | — |
| 132 | #331 | — | 10 | 1 | no | — |
| 133 | C22×D5 | — | 4 | 1 | no | — |
| 134 | C22×D5 | — | 4 | 1 | no | — |
| 135 | C22×D5 | — | 8 | 1 | no | — |
| 136 | C5×Q8 | — | 4 | 1 | no | — |
| 137 | C2×C4×C5 | — | 2 | 1 | no | — |
| 138 | C2×C4×C5 | — | 2 | 1 | no | — |
| 139 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 140 | C2×C4×C5 | C2×D8 | 1 | 1 | yes | characteristic |
| 141 | C2×C4×C5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 142 | C2×Dic5 | — | 4 | 1 | no | — |
| 143 | C2×Dic5 | — | 4 | 1 | no | — |
| 144 | D20 | — | 4 | 1 | no | — |
| 145 | D20 | — | 4 | 1 | no | — |
| 146 | D20 | — | 4 | 1 | no | — |
| 147 | D20 | — | 4 | 1 | no | — |
| 148 | D20 | — | 8 | 1 | no | — |
| 149 | D20 | — | 8 | 1 | no | — |
| 150 | D20 | — | 8 | 2 | no | — |
| 151 | D20 | — | 8 | 1 | no | — |
| 152 | D20 | — | 8 | 1 | no | — |
| 153 | D20 | — | 16 | 1 | no | — |
| 154 | D20 | — | 16 | 1 | no | — |
| 155 | C4×D5 | — | 16 | 1 | no | — |
| 156 | C4×D5 | — | 16 | 1 | no | — |
| 157 | Dic10 | — | 4 | 1 | no | — |
| 158 | Dic10 | — | 4 | 1 | no | — |
| 159 | C5×C8 | — | 2 | 1 | no | — |
| 160 | C5×C8 | — | 4 | 1 | no | — |
| 161 | C5×C8 | #135 | 1 | 1 | yes | characteristic |
| 162 | C5×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 163 | #168 | — | 8 | 1 | no | — |
| 164 | C2×Q16 | — | 5 | 1 | no | — |
| 165 | C2×SD16 | — | 10 | 1 | no | — |
| 166 | C2×SD16 | — | 10 | 1 | no | — |
| 167 | C2×SD16 | — | 20 | 1 | no | — |
| 168 | C2×D8 | — | 5 | 1 | no | — |
| 169 | C2×D8 | — | 5 | 1 | no | — |
| 170 | C2×D8 | — | 10 | 1 | no | — |
| 171 | C2×D8 | — | 10 | 1 | no | — |
| 172 | C2×D8 | — | 10 | 1 | no | — |
| 173 | #127 | — | 10 | 1 | no | — |
| 174 | #127 | — | 10 | 1 | no | — |
| 175 | #124 | — | 10 | 1 | no | — |
| 176 | #124 | — | 10 | 1 | no | — |
| 177 | #124 | — | 20 | 1 | no | — |
| 178 | #123 | — | 20 | 1 | no | — |
| 179 | #123 | — | 20 | 1 | no | — |
| 180 | C4×Q8 | — | 10 | 1 | no | — |
| 181 | C4×Q8 | D20 | 1 | 1 | yes | characteristic |
| 182 | C4×D4 | — | 10 | 1 | no | — |
| 183 | C4×D4 | — | 10 | 1 | no | — |
| 184 | C4×D4 | — | 20 | 1 | no | — |
| 185 | SD32 | — | 20 | 2 | no | — |
| 186 | D16 | — | 20 | 2 | no | — |
| 187 | D16 | — | 20 | 2 | no | — |
| 188 | C2×C16 | — | 2 | 1 | no | — |
| 189 | C2×C16 | — | 2 | 1 | no | — |
| 190 | #107 | — | 5 | 1 | no | — |
| 191 | C4⋊C8 | — | 2 | 1 | no | — |
| 192 | C4⋊C8 | — | 10 | 1 | no | — |
| 193 | C4⋊C8 | D20 | 1 | 1 | yes | characteristic |
| 194 | #103 | — | 10 | 1 | no | — |
| 195 | #102 | — | 10 | 1 | no | — |
| 196 | #102 | — | 10 | 1 | no | — |
| 197 | #102 | — | 20 | 1 | no | — |
| 198 | #97 | — | 2 | 1 | no | — |
| 199 | C4×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 200 | C22×C5 | #447 | 1 | 1 | yes | characteristic |
| 201 | C2×D5 | — | 8 | 1 | no | — |
| 202 | C2×D5 | — | 8 | 1 | no | — |
| 203 | C2×D5 | — | 8 | 1 | no | — |
| 204 | C2×D5 | — | 8 | 1 | no | — |
| 205 | C2×D5 | — | 8 | 1 | no | — |
| 206 | C2×D5 | — | 8 | 1 | no | — |
| 207 | C2×D5 | — | 16 | 1 | no | — |
| 208 | C2×D5 | — | 16 | 1 | no | — |
| 209 | C2×D5 | — | 16 | 1 | no | — |
| 210 | C4×C5 | — | 2 | 1 | no | — |
| 211 | C4×C5 | — | 2 | 1 | no | — |
| 212 | C4×C5 | — | 4 | 1 | no | — |
| 213 | C4×C5 | — | 4 | 1 | no | — |
| 214 | C4×C5 | #449 | 1 | 1 | yes | characteristic |
| 215 | C4×C5 | #453 | 1 | 1 | yes | characteristic |
| 216 | Dic5 | — | 8 | 1 | no | — |
| 217 | Dic5 | — | 8 | 1 | no | — |
| 218 | C2×Q8 | — | 10 | 1 | no | — |
| 219 | C2×Q8 | D40 | 1 | 1 | yes | characteristic |
| 220 | C2×D4 | — | 10 | 1 | no | — |
| 221 | C2×D4 | — | 10 | 1 | no | — |
| 222 | C2×D4 | — | 20 | 1 | no | — |
| 223 | C2×D4 | — | 20 | 1 | no | — |
| 224 | C2×D4 | — | 20 | 1 | no | — |
| 225 | C2×D4 | — | 20 | 1 | no | — |
| 226 | C2×D4 | — | 20 | 1 | no | — |
| 227 | C22×C4 | — | 20 | 1 | no | — |
| 228 | C22×C4 | — | 20 | 1 | no | — |
| 229 | Q16 | — | 20 | 1 | no | — |
| 230 | SD16 | — | 20 | 1 | no | — |
| 231 | SD16 | — | 20 | 1 | no | — |
| 232 | SD16 | — | 40 | 1 | no | — |
| 233 | SD16 | — | 40 | 2 | no | — |
| 234 | D8 | — | 10 | 1 | no | — |
| 235 | D8 | — | 10 | 1 | no | — |
| 236 | D8 | — | 20 | 1 | no | — |
| 237 | D8 | — | 20 | 1 | no | — |
| 238 | D8 | — | 20 | 1 | no | — |
| 239 | D8 | — | 20 | 1 | no | — |
| 240 | D8 | — | 20 | 1 | no | — |
| 241 | D8 | — | 40 | 1 | no | — |
| 242 | C2×C8 | — | 2 | 1 | no | — |
| 243 | C2×C8 | — | 20 | 1 | no | — |
| 244 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 245 | C2×C8 | D4×D5 | 1 | 1 | yes | characteristic |
| 246 | C4⋊C4 | — | 2 | 1 | no | — |
| 247 | C4⋊C4 | — | 10 | 1 | no | — |
| 248 | C4⋊C4 | — | 20 | 1 | no | — |
| 249 | C4⋊C4 | D40 | 1 | 1 | yes | characteristic |
| 250 | C22⋊C4 | — | 20 | 1 | no | — |
| 251 | C22⋊C4 | — | 20 | 1 | no | — |
| 252 | C22⋊C4 | — | 20 | 1 | no | — |
| 253 | C22⋊C4 | — | 20 | 1 | no | — |
| 254 | C22⋊C4 | — | 20 | 1 | no | — |
| 255 | C22⋊C4 | — | 20 | 1 | no | — |
| 256 | C42 | — | 2 | 1 | no | — |
| 257 | C42 | — | 20 | 1 | no | — |
| 258 | C42 | C2×D20 | 1 | 1 | yes | characteristic |
| 259 | C16 | — | 2 | 2 | no | — |
| 260 | C16 | — | 4 | 1 | no | — |
| 261 | C2×C5 | #1621 | 1 | 1 | yes | characteristic |
| 262 | C2×C5 | #2190 | 1 | 1 | yes | characteristic |
| 263 | C2×C5 | #2192 | 1 | 1 | yes | characteristic |
| 264 | D5 | — | 16 | 1 | no | — |
| 265 | D5 | — | 16 | 1 | no | — |
| 266 | D5 | — | 32 | 1 | no | — |
| 267 | C23 | — | 20 | 1 | no | — |
| 268 | C23 | — | 20 | 1 | no | — |
| 269 | C23 | — | 40 | 1 | no | — |
| 270 | Q8 | — | 4 | 1 | no | — |
| 271 | Q8 | — | 20 | 1 | no | — |
| 272 | Q8 | — | 20 | 1 | no | — |
| 273 | D4 | — | 20 | 1 | no | — |
| 274 | D4 | — | 20 | 1 | no | — |
| 275 | D4 | — | 20 | 1 | no | — |
| 276 | D4 | — | 20 | 1 | no | — |
| 277 | D4 | — | 40 | 1 | no | — |
| 278 | D4 | — | 40 | 1 | no | — |
| 279 | D4 | — | 40 | 2 | no | — |
| 280 | D4 | — | 40 | 1 | no | — |
| 281 | D4 | — | 40 | 1 | no | — |
| 282 | D4 | — | 80 | 1 | no | — |
| 283 | D4 | — | 80 | 1 | no | — |
| 284 | C2×C4 | — | 2 | 1 | no | — |
| 285 | C2×C4 | — | 2 | 1 | no | — |
| 286 | C2×C4 | — | 20 | 1 | no | — |
| 287 | C2×C4 | — | 20 | 1 | no | — |
| 288 | C2×C4 | — | 80 | 1 | no | — |
| 289 | C2×C4 | — | 80 | 1 | no | — |
| 290 | C2×C4 | #4028 | 1 | 1 | yes | characteristic |
| 291 | C2×C4 | C2×D40 | 1 | 1 | yes | characteristic |
| 292 | C2×C4 | #4054 | 1 | 1 | yes | characteristic |
| 293 | C8 | — | 2 | 1 | no | — |
| 294 | C8 | — | 4 | 1 | no | — |
| 295 | C8 | — | 40 | 1 | no | — |
| 296 | C8 | #4060 | 1 | 1 | yes | characteristic |
| 297 | C8 | #4065 | 1 | 1 | yes | characteristic |
| 298 | C5 | #12336 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 299 | C22 | — | 40 | 1 | no | — |
| 300 | C22 | — | 40 | 1 | no | — |
| 301 | C22 | — | 40 | 1 | no | — |
| 302 | C22 | — | 40 | 1 | no | — |
| 303 | C22 | — | 40 | 1 | no | — |
| 304 | C22 | — | 40 | 1 | no | — |
| 305 | C22 | — | 80 | 1 | no | — |
| 306 | C22 | — | 80 | 1 | no | — |
| 307 | C22 | — | 80 | 1 | no | — |
| 308 | C22 | #65021 | 1 | 1 | yes | characteristic |
| 309 | C4 | — | 2 | 1 | no | — |
| 310 | C4 | — | 2 | 1 | no | — |
| 311 | C4 | — | 4 | 1 | no | — |
| 312 | C4 | — | 4 | 1 | no | — |
| 313 | C4 | — | 40 | 1 | no | — |
| 314 | C4 | — | 40 | 1 | no | — |
| 315 | C4 | #65100 | 1 | 1 | yes | characteristic |
| 316 | C4 | #65111 | 1 | 1 | yes | characteristic |
| 317 | C2 | — | 80 | 1 | no | — |
| 318 | C2 | — | 80 | 1 | no | — |
| 319 | C2 | — | 160 | 1 | no | — |
| 320 | C2 | #10599052 | 1 | 1 | yes | characteristic |
| 321 | C2 | #10599913 | 1 | 1 | yes | characteristic |
| 322 | C2 | #10599919 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10611687 | C2 | semidirect |
| 2. #10601752 | C2 | semidirect |
| 3. #10600079 | C2 | semidirect |
| 4. #10599874 | C2 | semidirect |
| 5. C5×#1338 | C2 | semidirect |
| 6. #10598053 | C2 | semidirect |
| 7. #10598007 | C2 | semidirect |
| 69. #1338 | D5 | semidirect |
| 298. C5 | #12336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611687 | 2 |
| #10601752 | 2 |
| #10600079 | 2 |
| #10599874 | 2 |
| C5×#1338 | 2 |
| #10598053 | 2 |
| #10598007 | 2 |
| #12336 | 5 |