Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
538 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 9. C5×#338 | C4 | semidirect |
| 10. #64780 | C4 | semidirect |
| 68. #338 | AGL(1,𝔽5) | semidirect |
| 173. C5 | #11312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604767 | 2 |
| C2×#64899 | 2 |
| D5×#338 | 2 |
| #11312 | 5 |