Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
568 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 107 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. C5×#1740 | C2 | semidirect |
| 3. #10602364 | C2 | semidirect |
| 4. #10597980 | C2 | semidirect |
| 8. C2×#4020 | C4 | semidirect |
| 10. #65280 | C4 | semidirect |
| 14. #65225 | C4 | semidirect |
| 53. #1740 | D5 | semidirect |
| 318. C5 | #11693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614017 | 2 |
| C5×#1740 | 2 |
| #10602364 | 2 |
| #10597980 | 2 |
| #11693 | 5 |