Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
364 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 99 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. #10598271 | C2 | semidirect |
| 5. C22×C5×Q16 | C4 | semidirect |
| 8. C5×#470 | C4 | semidirect |
| 12. C5×#427 | C4 | semidirect |
| 99. C22×Q16 | Dic5 | semidirect |
| 103. #470 | Dic5 | semidirect |
| 108. #427 | Dic5 | semidirect |
| 266. C5 | #11869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3059 | 2 |
| #10602805 | 2 |
| #10602800 | 2 |
| #10598271 | 2 |
| #11869 | 5 |