Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
360 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 2. C5×#1989 | C2 | semidirect |
| 3. #10602530 | C2 | semidirect |
| 5. #10601216 | C2 | semidirect |
| 7. #10598112 | C2 | semidirect |
| 72. #1989 | D5 | semidirect |
| 313. C5 | #10509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614750 | 2 |
| C5×#1989 | 2 |
| #10602530 | 2 |
| #10601226 | 2 |
| #10601216 | 2 |
| #10600262 | 2 |
| #10598112 | 2 |
| #10509 | 5 |