Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
392 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 96 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. #10603879 | C2 | semidirect |
| 4. #10603862 | C2 | semidirect |
| 6. #10598550 | C2 | semidirect |
| 7. #10598543 | C2 | semidirect |
| 9. #65709 | C4 | semidirect |
| 11. #65705 | C4 | semidirect |
| 13. #65703 | C4 | semidirect |
| 15. #65702 | C4 | semidirect |
| 29. C5×#330 | C4 | semidirect |
| 30. #64763 | C4 | semidirect |
| 31. #64684 | C4 | semidirect |
| 32. #64684 | C4 | semidirect |
| 146. #330 | AGL(1,𝔽5) | semidirect |
| 331. C5 | #8248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617332 | 2 |
| #10604573 | 2 |
| #10603879 | 2 |
| #10603862 | 2 |
| #10599154 | 2 |
| #10598550 | 2 |
| #10598543 | 2 |
| #8248 | 5 |