Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
462 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 108 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. #10604034 | C2 | semidirect |
| 4. #10604012 | C2 | semidirect |
| 6. #10598597 | C2 | semidirect |
| 7. #10598594 | C2 | semidirect |
| 13. #65705 | C4 | semidirect |
| 15. #65702 | C4 | semidirect |
| 26. C5×#332 | C4 | semidirect |
| 27. #64767 | C4 | semidirect |
| 28. #64705 | C4 | semidirect |
| 29. #64705 | C4 | semidirect |
| 139. #332 | AGL(1,𝔽5) | semidirect |
| 335. C5 | #8253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617371 | 2 |
| #10604621 | 2 |
| #10604034 | 2 |
| #10604012 | 2 |
| #10599210 | 2 |
| #10598597 | 2 |
| #10598594 | 2 |
| #8253 | 5 |