Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
222 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 67 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×#1710 | C2 | semidirect |
| 5. #10598293 | C2 | semidirect |
| 6. #10598292 | C2 | semidirect |
| 7. #10597931 | C2 | semidirect |
| 47. #1710 | D5 | semidirect |
| 190. C5 | #12449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1710 | 2 |
| #10602181 | 2 |
| #10602180 | 2 |
| C8×D40 | 2 |
| #10598293 | 2 |
| #10598292 | 2 |
| #10597931 | 2 |
| #12449 | 5 |