Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
684 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 5. #10602019 | C2 | semidirect |
| 6. #10602013 | C2 | semidirect |
| 7. #10602010 | C2 | semidirect |
| 8. #10602005 | C2 | semidirect |
| 286. C5 | #19751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3139 | 2 |
| #10615079 | 2 |
| #10614938 | 2 |
| #10610271 | 2 |
| #10602019 | 2 |
| #10602013 | 2 |
| #10602010 | 2 |
| #10602005 | 2 |
| #10600642 | 2 |
| #19751 | 5 |