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×#2151 | C2 | semidirect |
| 3. #10602220 | C2 | semidirect |
| 5. #10600694 | C2 | semidirect |
| 7. #10598298 | C2 | semidirect |
| 56. #2151 | D5 | semidirect |
| 254. C5 | #13468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2151 | 2 |
| #10602241 | 2 |
| #10602220 | 2 |
| C2×#64730 | 2 |
| #10600694 | 2 |
| #10600690 | 2 |
| #10598298 | 2 |
| #13468 | 5 |