Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
440 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 97 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×#1506 | C2 | semidirect |
| 3. #10602615 | C2 | semidirect |
| 5. #10601587 | C2 | semidirect |
| 6. #10600227 | C2 | semidirect |
| 12. #65377 | C4 | semidirect |
| 13. #65374 | C4 | semidirect |
| 14. #65370 | C4 | semidirect |
| 15. #65368 | C4 | semidirect |
| 82. #1506 | D5 | semidirect |
| 333. C5 | #9761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615074 | 2 |
| C5×#1506 | 2 |
| #10602615 | 2 |
| #10601599 | 2 |
| #10601587 | 2 |
| #10600227 | 2 |
| #10600225 | 2 |
| #9761 | 5 |