Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
728 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 2. #10602663 | C2 | semidirect |
| 3. #10602659 | C2 | semidirect |
| 7. C5×#563 | C4 | semidirect |
| 8. C5×#559 | C4 | semidirect |
| 142. #563 | Dic5 | semidirect |
| 143. #559 | Dic5 | semidirect |
| 360. C5 | #12771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3550 | 2 |
| #10602663 | 2 |
| #10602659 | 2 |
| #10602613 | 2 |
| #10602610 | 2 |
| #12771 | 5 |