Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
294 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 59 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. C5×#423 | C4 | semidirect |
| 6. C43×C5 | C4 | semidirect |
| 9. #64761 | C4 | semidirect |
| 52. #423 | Dic5 | semidirect |
| 55. C43 | Dic5 | semidirect |
| 153. C5 | #7500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1962 | 2 |
| #10602612 | 2 |
| #7500 | 5 |