Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
568 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 107 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. #10614033 | C2 | semidirect |
| 3. #10602512 | C2 | semidirect |
| 4. #10602396 | C2 | semidirect |
| 5. #10598112 | C2 | semidirect |
| 64. #3935 | D4 | semidirect |
| 369. C5 | #9447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2544 | 2 |
| #10614033 | 2 |
| #10602512 | 2 |
| #10602396 | 2 |
| #10598112 | 2 |
| #9447 | 5 |