Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
304 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 89 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. #10601546 | C2 | semidirect |
| 5. #10600519 | C2 | semidirect |
| 6. C5×#1278 | C2 | semidirect |
| 7. #10598160 | C2 | semidirect |
| 62. #1278 | D5 | semidirect |
| 264. C5 | #9588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10601566 | 2 |
| #10601546 | 2 |
| #10600646 | 2 |
| #10600528 | 2 |
| #10600519 | 2 |
| C5×#1278 | 2 |
| #10598160 | 2 |
| #9588 | 5 |