Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
466 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 466 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 |
|---|---|---|
| 3. #10604033 | C2 | semidirect |
| 4. #10604030 | C2 | semidirect |
| 6. #10598587 | C2 | semidirect |
| 7. #10598586 | C2 | semidirect |
| 23. C5×#331 | C4 | semidirect |
| 24. #64764 | C4 | semidirect |
| 25. #64705 | C4 | semidirect |
| 26. #64705 | C4 | semidirect |
| 148. #331 | AGL(1,𝔽5) | semidirect |
| 395. C5 | #9563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604616 | 2 |
| #10604613 | 2 |
| #10604033 | 2 |
| #10604030 | 2 |
| D5×#331 | 2 |
| #10598587 | 2 |
| #10598586 | 2 |
| #9563 | 5 |