Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
464 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 99 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. #10602794 | C2 | semidirect |
| 4. #10602788 | C2 | semidirect |
| 6. #10598109 | C2 | semidirect |
| 7. #10598108 | C2 | semidirect |
| 27. #64758 | C4 | semidirect |
| 28. #64758 | C4 | semidirect |
| 29. #64757 | C4 | semidirect |
| 30. #64757 | C4 | semidirect |
| 399. C5 | #8875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614650 | 2 |
| C5×#1871 | 2 |
| #10602794 | 2 |
| #10602788 | 2 |
| #10602500 | 2 |
| #10598109 | 2 |
| #10598108 | 2 |
| #8875 | 5 |