Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
462 conjugacy classes of subgroups.
The subgroup lattice has 320 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. #64748 | C4 | semidirect |
| 20. C2×C5×C4⋊C4 | C8 | semidirect |
| 27. C2×C42×C5 | C8 | semidirect |
| 137. C2×C4⋊C4 | #168 | semidirect |
| 144. C2×C42 | #168 | semidirect |
| 276. C5 | #7189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C4⋊#95 | 2 |
| C2×#64748 | 2 |
| #7189 | 5 |