Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
396 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C5×#1531 | C2 | semidirect |
| 3. #10602629 | C2 | semidirect |
| 5. #10601587 | C2 | semidirect |
| 6. #10600599 | C2 | semidirect |
| 12. #65377 | C4 | semidirect |
| 13. #65374 | C4 | semidirect |
| 14. #65370 | C4 | semidirect |
| 15. #65368 | C4 | semidirect |
| 78. #1531 | D5 | semidirect |
| 329. C5 | #9766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615074 | 2 |
| C5×#1531 | 2 |
| #10602629 | 2 |
| #10601625 | 2 |
| #10601587 | 2 |
| #10600599 | 2 |
| #10600591 | 2 |
| #9766 | 5 |