Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
300 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 1. #10604751 | C2 | semidirect |
| 4. C2×#64890 | C2 | semidirect |
| 6. #10598797 | C2 | semidirect |
| 7. #10598780 | C2 | semidirect |
| 258. C5 | #13127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604751 | 2 |
| #10604750 | 2 |
| #10604745 | 2 |
| C2×#64890 | 2 |
| #10599720 | 2 |
| #10598797 | 2 |
| #10598780 | 2 |
| #13127 | 5 |