Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
336 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 5. C5×#382 | C4 | semidirect |
| 7. C2×#3935 | C4 | semidirect |
| 9. #64853 | C4 | semidirect |
| 56. #382 | AGL(1,𝔽5) | semidirect |
| 179. C5 | #7504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64853 | 2 |
| #10600346 | 2 |
| #7504 | 5 |