Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
458 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 1. #10617202 | C2 | semidirect |
| 5. #10604454 | C2 | semidirect |
| 6. #10598590 | C2 | semidirect |
| 7. #10598585 | C2 | semidirect |
| 20. C5×#477 | C4 | semidirect |
| 21. #65380 | C4 | semidirect |
| 22. #65316 | C4 | semidirect |
| 25. #65137 | C4 | semidirect |
| 145. #477 | AGL(1,𝔽5) | semidirect |
| 379. C5 | #9164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617202 | 2 |
| #10612825 | 2 |
| #10604635 | 2 |
| #10604621 | 2 |
| #10604454 | 2 |
| #10598590 | 2 |
| #10598585 | 2 |
| #9164 | 5 |