Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
464 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 81 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×#3237 | C2 | semidirect |
| 4. #10602633 | C2 | semidirect |
| 5. #10602629 | C2 | semidirect |
| 7. #10598249 | C2 | semidirect |
| 84. #3237 | D5 | semidirect |
| 357. C5 | #10215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3237 | 2 |
| #10615097 | 2 |
| #10615089 | 2 |
| #10602633 | 2 |
| #10602629 | 2 |
| #10601625 | 2 |
| #10598249 | 2 |
| #10215 | 5 |