Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2122 conjugacy classes of subgroups.
The subgroup lattice has 360 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10614246 | C2 | semidirect |
| 4. #10613940 | C2 | semidirect |
| 5. #10613933 | C2 | semidirect |
| 6. #10613780 | C2 | semidirect |
| 7. C2×#65213 | C2 | semidirect |
| 22. #65289 | C22 | semidirect |
| 23. #65286 | C22 | semidirect |
| 24. #65215 | C22 | semidirect |
| 25. #65214 | C22 | semidirect |
| 28. #65213 | C22 | semidirect |
| 29. C2×C4⋊#168 | C22 | semidirect |
| 336. C5 | #60125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×#41 | 2 |
| #10615805 | 2 |
| #10614246 | 2 |
| #10613940 | 2 |
| #10613933 | 2 |
| #10613780 | 2 |
| C2×#65213 | 2 |
| #60125 | 5 |