Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
768 conjugacy classes of subgroups.
The subgroup lattice has 606 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10598187 | C2 | semidirect |
| 8. C22×#681 | C4 | semidirect |
| 9. C22×#681 | C4 | semidirect |
| 12. C5×#410 | C4 | semidirect |
| 15. C2×C5×#99 | C4 | semidirect |
| 18. #65529 | C4 | semidirect |
| 22. #65523 | C4 | semidirect |
| 25. C2×#3966 | C4 | semidirect |
| 69. C2×#681 | C2×C4 | semidirect |
| 71. C22×#168 | C2×C4 | semidirect |
| 75. C5×#99 | C2×C4 | semidirect |
| 79. #3966 | C2×C4 | semidirect |
| 194. #410 | Dic5 | semidirect |
| 199. C2×#99 | Dic5 | semidirect |
| 336. #99 | C2×Dic5 | semidirect |
| 560. C5 | #12577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#410 | 2 |
| C2×#65529 | 2 |
| #10615805 | 2 |
| #10598187 | 2 |
| #12577 | 5 |