Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
212 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 57 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. #10602292 | C2 | semidirect |
| 5. C5×#1416 | C2 | semidirect |
| 6. #10598081 | C2 | semidirect |
| 7. #10598069 | C2 | semidirect |
| 48. #1416 | D5 | semidirect |
| 130. Dic5 | SD64 | semidirect |
| 173. C5 | #13687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602292 | 2 |
| C2×#64741 | 2 |
| C2×#64669 | 2 |
| #10600110 | 2 |
| C5×#1416 | 2 |
| #10598081 | 2 |
| #10598069 | 2 |
| #13687 | 5 |