Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
284 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 83 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. #10599859 | C2 | semidirect |
| 2. #10599858 | C2 | semidirect |
| 5. #10598856 | C2 | semidirect |
| 7. C5×#1312 | C2 | semidirect |
| 53. #1312 | D5 | semidirect |
| 197. C5 | #12530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10599859 | 2 |
| #10599858 | 2 |
| #10599854 | 2 |
| #10599851 | 2 |
| #10598856 | 2 |
| #10598853 | 2 |
| C5×#1312 | 2 |
| #12530 | 5 |