Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
304 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 1. C5×#1452 | C2 | semidirect |
| 4. #10601541 | C2 | semidirect |
| 6. #10598234 | C2 | semidirect |
| 7. #10598147 | C2 | semidirect |
| 60. #1452 | 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 |
|---|---|
| C5×#1452 | 2 |
| #10601566 | 2 |
| #10601554 | 2 |
| #10601541 | 2 |
| #10600528 | 2 |
| #10598234 | 2 |
| #10598147 | 2 |
| #9588 | 5 |