Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2250 conjugacy classes of subgroups.
The subgroup lattice has 294 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10614194 | C2 | semidirect |
| 4. #10614193 | C2 | semidirect |
| 10. C2×C4×C5×Q8 | C4 | semidirect |
| 109. C2×C4×Q8 | Dic5 | semidirect |
| 272. C5 | #34187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×Q8 | 2 |
| #10615793 | 2 |
| #10614194 | 2 |
| #10614193 | 2 |
| #10613886 | 2 |
| #10613875 | 2 |
| #10613793 | 2 |
| #10613791 | 2 |
| #34187 | 5 |