Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
324 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 96 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. #10604746 | C2 | semidirect |
| 4. C2×#64886 | C2 | semidirect |
| 6. #10598796 | C2 | semidirect |
| 7. #10598779 | C2 | semidirect |
| 258. C5 | #13125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604746 | 2 |
| C2×#64898 | 2 |
| #10604742 | 2 |
| C2×#64886 | 2 |
| #10599719 | 2 |
| #10598796 | 2 |
| #10598779 | 2 |
| #13125 | 5 |