Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
236 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 69 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×#2247 | C2 | semidirect |
| 4. #10598284 | C2 | semidirect |
| 5. #10597991 | C2 | semidirect |
| 35. #2247 | D5 | semidirect |
| 80. D20 | Q32 | semidirect |
| 157. C5 | #12431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2247 | 2 |
| #10602098 | 2 |
| C16×D20 | 2 |
| #10598284 | 2 |
| #10597991 | 2 |
| #12431 | 5 |