Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
568 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 85 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×#3165 | C2 | semidirect |
| 4. #10602629 | C2 | semidirect |
| 5. #10602569 | C2 | semidirect |
| 7. #10598156 | C2 | semidirect |
| 79. #3165 | D5 | semidirect |
| 344. C5 | #10102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3165 | 2 |
| #10615088 | 2 |
| #10614995 | 2 |
| #10602629 | 2 |
| #10602569 | 2 |
| #10600653 | 2 |
| #10598156 | 2 |
| #10102 | 5 |