Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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×#2546 | C2 | semidirect |
| 4. #10602566 | C2 | semidirect |
| 5. #10602414 | C2 | semidirect |
| 7. #10598111 | C2 | semidirect |
| 82. #2546 | D5 | semidirect |
| 395. C5 | #10243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2546 | 2 |
| #10614946 | 2 |
| #10614172 | 2 |
| #10602566 | 2 |
| #10602414 | 2 |
| #10600262 | 2 |
| #10598111 | 2 |
| #10243 | 5 |