Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
392 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 77 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. #10601232 | C2 | semidirect |
| 5. #10601216 | C2 | semidirect |
| 6. #10600264 | C2 | semidirect |
| 7. #10598112 | C2 | semidirect |
| 339. C5 | #10510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614680 | 2 |
| C5×#1983 | 2 |
| #10602513 | 2 |
| #10601232 | 2 |
| #10601216 | 2 |
| #10600264 | 2 |
| #10598112 | 2 |
| #10510 | 5 |