Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 1. C5×#2981 | C2 | semidirect |
| 3. #10602605 | C2 | semidirect |
| 4. #10601625 | C2 | semidirect |
| 5. #10601558 | C2 | semidirect |
| 6. #10598248 | C2 | semidirect |
| 7. #10598228 | C2 | semidirect |
| 16. #65382 | C4 | semidirect |
| 17. #65377 | C4 | semidirect |
| 18. #65365 | C4 | semidirect |
| 19. #65362 | C4 | semidirect |
| 73. #2981 | D5 | semidirect |
| 330. C5 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2981 | 2 |
| #10615035 | 2 |
| #10602605 | 2 |
| #10601625 | 2 |
| #10601558 | 2 |
| #10598248 | 2 |
| #10598228 | 2 |
| #9281 | 5 |