Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
360 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #10602531 | C2 | semidirect |
| 5. #10602530 | C2 | semidirect |
| 6. #10601590 | C2 | semidirect |
| 7. #10598241 | C2 | semidirect |
| 313. C5 | #10509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3234 | 2 |
| #10602604 | 2 |
| #10602600 | 2 |
| #10602531 | 2 |
| #10602530 | 2 |
| #10601590 | 2 |
| #10598241 | 2 |
| #10509 | 5 |