Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
532 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 98 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. #10617195 | C2 | semidirect |
| 3. #10604650 | C2 | semidirect |
| 4. #10604621 | C2 | semidirect |
| 5. #10604455 | C2 | semidirect |
| 6. #10598597 | C2 | semidirect |
| 7. #10598589 | C2 | semidirect |
| 21. C5×#462 | C4 | semidirect |
| 23. #65372 | C4 | semidirect |
| 24. #65316 | C4 | semidirect |
| 25. #65132 | C4 | semidirect |
| 159. #462 | AGL(1,𝔽5) | semidirect |
| 426. C5 | #9208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617195 | 2 |
| #10612206 | 2 |
| #10604650 | 2 |
| #10604621 | 2 |
| #10604455 | 2 |
| #10598597 | 2 |
| #10598589 | 2 |
| #9208 | 5 |