Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
478 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #10614178 | C2 | semidirect |
| 5. #10602418 | C2 | semidirect |
| 6. #10601608 | C2 | semidirect |
| 7. #10598247 | C2 | semidirect |
| 353. C5 | #10041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3112 | 2 |
| #10615050 | 2 |
| #10614178 | 2 |
| #10602596 | 2 |
| #10602418 | 2 |
| #10601608 | 2 |
| #10598247 | 2 |
| #10041 | 5 |