Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2198 conjugacy classes of subgroups.
The subgroup lattice has 374 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10613941 | C2 | semidirect |
| 4. #10613940 | C2 | semidirect |
| 5. #10613935 | C2 | semidirect |
| 6. #10613933 | C2 | semidirect |
| 7. #10613780 | C2 | semidirect |
| 24. #65289 | C22 | semidirect |
| 25. #65288 | C22 | semidirect |
| 26. #65286 | C22 | semidirect |
| 27. #65215 | C22 | semidirect |
| 28. #65214 | C22 | semidirect |
| 29. #65213 | C22 | semidirect |
| 30. C4×#681 | C22 | semidirect |
| 71. C4⋊#168 | C23 | semidirect |
| 72. #3935 | C23 | semidirect |
| 73. C4×#168 | C23 | semidirect |
| 345. C5 | #60124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#117 | 2 |
| C2×#65496 | 2 |
| #10613941 | 2 |
| #10613940 | 2 |
| #10613935 | 2 |
| #10613933 | 2 |
| #10613780 | 2 |
| #60124 | 5 |