Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
376 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 55 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 | #10610372 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×#2091 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10601516 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10598172 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10597974 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×#4076 | — | 2 | 1 | no | — |
| 7 | C5×#430 | — | 2 | 1 | no | — |
| 8 | C5×#430 | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | C5×#407 | — | 2 | 1 | no | — |
| 10 | C5×#407 | C22 | 1 | 1 | yes | characteristic |
| 11 | #65424 | — | 2 | 1 | no | — |
| 12 | #65424 | C22 | 1 | 2 | yes | — |
| 13 | #65024 | — | 2 | 2 | no | — |
| 14 | #65021 | — | 2 | 2 | no | — |
| 15 | C5×#338 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #64773 | C22 | 1 | 2 | yes | complemented |
| 17 | #64715 | — | 2 | 2 | no | — |
| 18 | #64714 | — | 2 | 2 | no | — |
| 19 | #12298 | — | 5 | 1 | no | maximal, Sylow |
| 20 | C23×C4×C5 | D4 | 1 | 1 | yes | characteristic |
| 21 | C22×C22⋊D5 | — | 4 | 1 | no | — |
| 22 | C22×D20 | — | 2 | 1 | no | — |
| 23 | C2×C5×M16 | — | 2 | 1 | no | — |
| 24 | C2×C5×M16 | — | 2 | 1 | no | — |
| 25 | C2×C5×M16 | D4 | 1 | 1 | yes | characteristic |
| 26 | C2×C5×M16 | C23 | 1 | 1 | yes | characteristic |
| 27 | #4076 | — | 2 | 2 | no | — |
| 28 | #4076 | — | 2 | 2 | no | — |
| 29 | #4076 | — | 4 | 1 | no | — |
| 30 | #4076 | — | 4 | 1 | no | — |
| 31 | C2×#685 | — | 4 | 1 | no | — |
| 32 | C2×C4⋊Dic5 | — | 2 | 1 | no | — |
| 33 | C2×D40 | — | 2 | 1 | no | — |
| 34 | C2×D40 | D4 | 1 | 2 | yes | — |
| 35 | C5×#108 | — | 2 | 2 | no | — |
| 36 | C5×#108 | — | 4 | 2 | no | — |
| 37 | C5×C22⋊C8 | — | 2 | 2 | no | — |
| 38 | C5×C22⋊C8 | — | 4 | 2 | no | — |
| 39 | #3953 | — | 2 | 2 | no | — |
| 40 | #3953 | — | 2 | 2 | no | — |
| 41 | #3949 | — | 2 | 1 | no | — |
| 42 | #3949 | D4 | 1 | 2 | yes | — |
| 43 | #3944 | — | 2 | 2 | no | — |
| 44 | #3192 | — | 5 | 1 | no | — |
| 45 | #2238 | — | 5 | 2 | no | — |
| 46 | #2091 | D5 | 1 | 1 | yes | characteristic, complemented |
| 47 | #1341 | — | 5 | 2 | no | — |
| 48 | #1320 | — | 5 | 1 | no | — |
| 49 | C24×C5 | SD16 | 1 | 1 | yes | characteristic |
| 50 | C23×D5 | — | 4 | 1 | no | — |
| 51 | C22×C4×C5 | — | 2 | 1 | no | — |
| 52 | C22×C4×C5 | — | 2 | 1 | no | — |
| 53 | C22×C4×C5 | — | 4 | 1 | no | — |
| 54 | C22×C4×C5 | — | 4 | 1 | no | — |
| 55 | C22×C4×C5 | SD16 | 1 | 1 | yes | characteristic |
| 56 | C22×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 57 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 58 | C2×C22⋊D5 | — | 4 | 2 | no | — |
| 59 | C2×C22⋊D5 | — | 8 | 4 | no | — |
| 60 | C22×Dic5 | — | 4 | 1 | no | — |
| 61 | C2×D20 | — | 2 | 2 | no | — |
| 62 | C2×D20 | — | 4 | 1 | no | — |
| 63 | C2×D20 | — | 8 | 1 | no | — |
| 64 | C2×D20 | — | 8 | 1 | no | — |
| 65 | C5×M16 | — | 4 | 1 | no | — |
| 66 | C5×M16 | — | 4 | 1 | no | — |
| 67 | C5×M16 | — | 4 | 1 | no | — |
| 68 | C5×M16 | — | 4 | 1 | no | — |
| 69 | C5×M16 | — | 4 | 1 | no | — |
| 70 | C5×M16 | — | 4 | 1 | no | — |
| 71 | C2×C5×C8 | — | 2 | 2 | no | — |
| 72 | C2×C5×C8 | — | 2 | 1 | no | — |
| 73 | C2×C5×C8 | — | 4 | 1 | no | — |
| 74 | C2×C5×C8 | C2×D4 | 1 | 2 | yes | — |
| 75 | #685 | — | 4 | 2 | no | — |
| 76 | #685 | — | 4 | 2 | no | — |
| 77 | C4⋊Dic5 | — | 2 | 2 | no | — |
| 78 | C4⋊Dic5 | — | 4 | 1 | no | — |
| 79 | D40 | — | 4 | 2 | no | — |
| 80 | D40 | — | 8 | 1 | no | — |
| 81 | #672 | — | 4 | 2 | no | — |
| 82 | C2×#121 | — | 10 | 1 | no | — |
| 83 | #481 | — | 10 | 2 | no | — |
| 84 | #469 | — | 5 | 2 | no | — |
| 85 | #469 | — | 10 | 1 | no | — |
| 86 | #447 | — | 10 | 2 | no | — |
| 87 | #430 | — | 2 | 1 | no | — |
| 88 | #430 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 89 | #407 | — | 2 | 1 | no | — |
| 90 | #407 | C2×D5 | 1 | 1 | yes | characteristic |
| 91 | #365 | — | 10 | 2 | no | — |
| 92 | #361 | — | 10 | 2 | no | — |
| 93 | #349 | — | 5 | 2 | no | — |
| 94 | #338 | C2×D5 | 1 | 1 | yes | characteristic, complemented |
| 95 | C23×C5 | — | 2 | 1 | no | — |
| 96 | C23×C5 | — | 4 | 2 | no | — |
| 97 | C23×C5 | — | 4 | 1 | no | — |
| 98 | C23×C5 | C2×SD16 | 1 | 1 | yes | characteristic |
| 99 | C22×D5 | — | 4 | 2 | no | — |
| 100 | C22×D5 | — | 8 | 2 | no | — |
| 101 | C22×D5 | — | 8 | 2 | no | — |
| 102 | C22×D5 | — | 8 | 2 | no | — |
| 103 | C2×C4×C5 | — | 2 | 1 | no | — |
| 104 | C2×C4×C5 | — | 2 | 1 | no | — |
| 105 | C2×C4×C5 | — | 2 | 1 | no | — |
| 106 | C2×C4×C5 | — | 4 | 1 | no | — |
| 107 | C2×C4×C5 | — | 4 | 1 | no | — |
| 108 | C2×C4×C5 | — | 4 | 1 | no | — |
| 109 | C2×C4×C5 | — | 8 | 1 | no | — |
| 110 | C2×C4×C5 | #120 | 1 | 1 | yes | characteristic |
| 111 | C2×C4×C5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 112 | C22⋊D5 | — | 8 | 4 | no | — |
| 113 | C22⋊D5 | — | 8 | 4 | no | — |
| 114 | C2×Dic5 | — | 4 | 2 | no | — |
| 115 | C2×Dic5 | — | 8 | 2 | no | — |
| 116 | D20 | — | 4 | 2 | no | — |
| 117 | D20 | — | 4 | 2 | no | — |
| 118 | D20 | — | 8 | 2 | no | — |
| 119 | C5×C8 | — | 2 | 2 | no | — |
| 120 | C5×C8 | — | 4 | 2 | no | — |
| 121 | C5×C8 | — | 4 | 1 | no | — |
| 122 | C5×C8 | — | 8 | 1 | no | — |
| 123 | C22×D4 | — | 10 | 1 | no | — |
| 124 | C22×D4 | — | 20 | 1 | no | — |
| 125 | C23×C4 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 126 | C2×D8 | — | 5 | 2 | no | — |
| 127 | C2×D8 | — | 10 | 1 | no | — |
| 128 | C2×M16 | — | 2 | 1 | no | — |
| 129 | C2×M16 | — | 2 | 1 | no | — |
| 130 | C2×M16 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 131 | C2×M16 | C22×D5 | 1 | 1 | yes | characteristic |
| 132 | #121 | — | 10 | 2 | no | — |
| 133 | #121 | — | 10 | 2 | no | — |
| 134 | #121 | — | 20 | 1 | no | — |
| 135 | #121 | — | 20 | 1 | no | — |
| 136 | C2×C4⋊C4 | — | 10 | 1 | no | — |
| 137 | C2×C22⋊C4 | — | 20 | 1 | no | — |
| 138 | M32 | — | 10 | 2 | no | — |
| 139 | #108 | — | 2 | 2 | no | — |
| 140 | #108 | — | 4 | 2 | no | — |
| 141 | #106 | — | 5 | 2 | no | — |
| 142 | #106 | — | 10 | 1 | no | — |
| 143 | #102 | — | 10 | 2 | no | — |
| 144 | #102 | — | 10 | 2 | no | — |
| 145 | C22⋊C8 | — | 2 | 2 | no | — |
| 146 | C22⋊C8 | — | 4 | 2 | no | — |
| 147 | C22×C5 | — | 2 | 2 | no | — |
| 148 | C22×C5 | — | 2 | 1 | no | — |
| 149 | C22×C5 | — | 4 | 1 | no | — |
| 150 | C22×C5 | — | 4 | 1 | no | — |
| 151 | C22×C5 | — | 4 | 2 | no | — |
| 152 | C22×C5 | — | 4 | 1 | no | — |
| 153 | C22×C5 | — | 8 | 1 | no | — |
| 154 | C22×C5 | #450 | 1 | 1 | yes | characteristic |
| 155 | C2×D5 | — | 8 | 2 | no | — |
| 156 | C2×D5 | — | 8 | 2 | no | — |
| 157 | C2×D5 | — | 8 | 2 | no | — |
| 158 | C2×D5 | — | 16 | 4 | no | — |
| 159 | C4×C5 | — | 2 | 1 | no | — |
| 160 | C4×C5 | — | 4 | 1 | no | — |
| 161 | C4×C5 | #453 | 1 | 1 | yes | characteristic |
| 162 | C4×C5 | #458 | 1 | 1 | yes | characteristic |
| 163 | Dic5 | — | 8 | 2 | no | — |
| 164 | C24 | — | 20 | 1 | no | — |
| 165 | C24 | #688 | 1 | 1 | yes | characteristic |
| 166 | C2×D4 | — | 10 | 2 | no | — |
| 167 | C2×D4 | — | 20 | 1 | no | — |
| 168 | C2×D4 | — | 20 | 2 | no | — |
| 169 | C2×D4 | — | 20 | 2 | no | — |
| 170 | C2×D4 | — | 40 | 1 | no | — |
| 171 | C2×D4 | — | 40 | 1 | no | — |
| 172 | C2×D4 | — | 40 | 4 | no | — |
| 173 | C22×C4 | — | 2 | 1 | no | — |
| 174 | C22×C4 | — | 2 | 1 | no | — |
| 175 | C22×C4 | — | 4 | 1 | no | — |
| 176 | C22×C4 | — | 4 | 1 | no | — |
| 177 | C22×C4 | — | 20 | 1 | no | — |
| 178 | C22×C4 | #688 | 1 | 1 | yes | characteristic |
| 179 | C22×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 180 | D8 | — | 20 | 2 | no | — |
| 181 | D8 | — | 40 | 1 | no | — |
| 182 | M16 | — | 4 | 1 | no | — |
| 183 | M16 | — | 4 | 1 | no | — |
| 184 | M16 | — | 4 | 1 | no | — |
| 185 | M16 | — | 4 | 1 | no | — |
| 186 | M16 | — | 4 | 1 | no | — |
| 187 | M16 | — | 4 | 1 | no | — |
| 188 | C2×C8 | — | 2 | 2 | no | — |
| 189 | C2×C8 | — | 2 | 1 | no | — |
| 190 | C2×C8 | — | 4 | 1 | no | — |
| 191 | C2×C8 | D4×D5 | 1 | 2 | yes | — |
| 192 | C4⋊C4 | — | 10 | 2 | no | — |
| 193 | C4⋊C4 | — | 20 | 1 | no | — |
| 194 | C22⋊C4 | — | 20 | 2 | no | — |
| 195 | C22⋊C4 | — | 20 | 2 | no | — |
| 196 | C16 | — | 20 | 2 | no | — |
| 197 | C2×C5 | — | 2 | 1 | no | — |
| 198 | C2×C5 | — | 4 | 2 | no | — |
| 199 | C2×C5 | — | 4 | 1 | no | — |
| 200 | C2×C5 | #1613 | 1 | 1 | yes | characteristic |
| 201 | D5 | — | 16 | 2 | no | — |
| 202 | C23 | — | 2 | 1 | no | — |
| 203 | C23 | — | 4 | 1 | no | — |
| 204 | C23 | — | 4 | 2 | no | — |
| 205 | C23 | — | 20 | 2 | no | — |
| 206 | C23 | — | 40 | 2 | no | — |
| 207 | C23 | — | 40 | 2 | no | — |
| 208 | C23 | — | 40 | 2 | no | — |
| 209 | C23 | C2×#688 | 1 | 1 | yes | characteristic |
| 210 | D4 | — | 20 | 2 | no | — |
| 211 | D4 | — | 20 | 2 | no | — |
| 212 | D4 | — | 40 | 2 | no | — |
| 213 | D4 | — | 40 | 4 | no | — |
| 214 | D4 | — | 40 | 4 | no | — |
| 215 | C2×C4 | — | 2 | 1 | no | — |
| 216 | C2×C4 | — | 2 | 1 | no | — |
| 217 | C2×C4 | — | 2 | 1 | no | — |
| 218 | C2×C4 | — | 4 | 1 | no | — |
| 219 | C2×C4 | — | 4 | 1 | no | — |
| 220 | C2×C4 | — | 4 | 1 | no | — |
| 221 | C2×C4 | — | 8 | 1 | no | — |
| 222 | C2×C4 | — | 20 | 2 | no | — |
| 223 | C2×C4 | — | 40 | 2 | no | — |
| 224 | C2×C4 | #4083 | 1 | 1 | yes | characteristic |
| 225 | C2×C4 | #4095 | 1 | 1 | yes | characteristic |
| 226 | C8 | — | 2 | 2 | no | — |
| 227 | C8 | — | 4 | 2 | no | — |
| 228 | C8 | — | 4 | 1 | no | — |
| 229 | C8 | — | 8 | 1 | no | — |
| 230 | C5 | #12298 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 231 | C22 | — | 2 | 2 | no | — |
| 232 | C22 | — | 2 | 1 | no | — |
| 233 | C22 | — | 4 | 1 | no | — |
| 234 | C22 | — | 4 | 1 | no | — |
| 235 | C22 | — | 4 | 2 | no | — |
| 236 | C22 | — | 4 | 1 | no | — |
| 237 | C22 | — | 8 | 1 | no | — |
| 238 | C22 | — | 40 | 2 | no | — |
| 239 | C22 | — | 40 | 2 | no | — |
| 240 | C22 | — | 40 | 2 | no | — |
| 241 | C22 | — | 80 | 4 | no | — |
| 242 | C22 | #65335 | 1 | 1 | yes | characteristic |
| 243 | C4 | — | 2 | 1 | no | — |
| 244 | C4 | — | 4 | 1 | no | — |
| 245 | C4 | — | 40 | 2 | no | — |
| 246 | C4 | #65342 | 1 | 1 | yes | characteristic |
| 247 | C4 | #65366 | 1 | 1 | yes | characteristic |
| 248 | C2 | — | 2 | 1 | no | — |
| 249 | C2 | — | 4 | 2 | no | — |
| 250 | C2 | — | 4 | 1 | no | — |
| 251 | C2 | — | 80 | 2 | no | — |
| 252 | C2 | #10600507 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2091 | C2 | semidirect |
| 3. #10601516 | C2 | semidirect |
| 4. #10598172 | C2 | semidirect |
| 5. #10597974 | C2 | semidirect |
| 8. C5×#430 | C22 | semidirect |
| 15. C5×#338 | C22 | semidirect |
| 16. #64773 | C22 | semidirect |
| 46. #2091 | D5 | semidirect |
| 88. #430 | C2×D5 | semidirect |
| 94. #338 | C2×D5 | semidirect |
| 230. C5 | #12298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610372 | 2 |
| C5×#2091 | 2 |
| #10601516 | 2 |
| #10598172 | 2 |
| #10597974 | 2 |
| #12298 | 5 |