Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
378 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 1. #10604739 | C2 | semidirect |
| 2. M16×#170 | C2 | semidirect |
| 6. #10598793 | C2 | semidirect |
| 7. #10598787 | C2 | semidirect |
| 56. #3955 | C8 | semidirect |
| 308. C5 | #9550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604739 | 2 |
| M16×#170 | 2 |
| #10604270 | 2 |
| C2×#64871 | 2 |
| #10599765 | 2 |
| #10598793 | 2 |
| #10598787 | 2 |
| #9550 | 5 |