Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
366 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 4. #10598632 | C2 | semidirect |
| 5. #10598626 | C2 | semidirect |
| 12. C5×#430 | C4 | semidirect |
| 13. #65414 | C4 | semidirect |
| 16. #65182 | C4 | semidirect |
| 102. #430 | AGL(1,𝔽5) | semidirect |
| 246. C5 | #12877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610991 | 2 |
| #10604765 | 2 |
| #10604743 | 2 |
| #10598632 | 2 |
| #10598626 | 2 |
| #12877 | 5 |