Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
212 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 62 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. #10604842 | C2 | semidirect |
| 4. #10598807 | C2 | semidirect |
| 6. #10598642 | C2 | semidirect |
| 7. #10598638 | C2 | semidirect |
| 73. C5×C16 | M16 | semidirect |
| 164. C16 | #704 | semidirect |
| 189. C5 | #12087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604842 | 2 |
| #10604796 | 2 |
| #10602267 | 2 |
| #10598807 | 2 |
| #10598799 | 2 |
| #10598642 | 2 |
| #10598638 | 2 |
| #12087 | 5 |