Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
662 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 19. C5×#341 | C4 | semidirect |
| 20. #64778 | C4 | semidirect |
| 21. #64772 | C4 | semidirect |
| 123. #341 | AGL(1,𝔽5) | semidirect |
| 293. C5 | #11332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65729 | 2 |
| C22×#3995 | 2 |
| C2×#64902 | 2 |
| #10604717 | 2 |
| D5×#341 | 2 |
| #11332 | 5 |