Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
442 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10617365 | C2 | semidirect |
| 3. #10604638 | C2 | semidirect |
| 4. #10604627 | C2 | semidirect |
| 5. #10604595 | C2 | semidirect |
| 6. #10598533 | C2 | semidirect |
| 7. #10598528 | C2 | semidirect |
| 17. C5×#486 | C4 | semidirect |
| 18. #65368 | C4 | semidirect |
| 19. #65362 | C4 | semidirect |
| 22. #64983 | C4 | semidirect |
| 120. #486 | AGL(1,𝔽5) | semidirect |
| 309. C5 | #9417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617365 | 2 |
| #10613291 | 2 |
| #10604638 | 2 |
| #10604627 | 2 |
| #10604595 | 2 |
| #10598533 | 2 |
| #10598528 | 2 |
| #9417 | 5 |