Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
714 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10602332 | C2 | semidirect |
| 3. #10598118 | C2 | semidirect |
| 4. #10598113 | C2 | semidirect |
| 63. C24×C5 | M16 | semidirect |
| 88. C22×C4×C5 | M16 | semidirect |
| 242. C24 | #681 | semidirect |
| 268. C22×C4 | #681 | semidirect |
| 346. C5 | #11502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2308 | 2 |
| #10602332 | 2 |
| #10598118 | 2 |
| #10598113 | 2 |
| #11502 | 5 |