Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. C5×#1531 | C2 | semidirect |
| 3. #10602626 | C2 | semidirect |
| 5. #10600634 | C2 | semidirect |
| 7. #10598249 | C2 | semidirect |
| 68. #1531 | D5 | semidirect |
| 284. C5 | #10527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615097 | 2 |
| C5×#1531 | 2 |
| #10602626 | 2 |
| #10601612 | 2 |
| #10600634 | 2 |
| #10600591 | 2 |
| #10598249 | 2 |
| #10527 | 5 |