Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
574 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 574 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 |
|---|---|---|
| 1. C5×#3206 | C2 | semidirect |
| 3. #10614934 | C2 | semidirect |
| 4. #10602590 | C2 | semidirect |
| 5. #10602583 | C2 | semidirect |
| 6. #10601554 | C2 | semidirect |
| 7. #10598234 | C2 | semidirect |
| 78. #3206 | D5 | semidirect |
| 350. C5 | #10106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3206 | 2 |
| #10615044 | 2 |
| #10614934 | 2 |
| #10602590 | 2 |
| #10602583 | 2 |
| #10601554 | 2 |
| #10598234 | 2 |
| #10106 | 5 |