Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
572 conjugacy classes of subgroups.
The subgroup lattice has 368 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10600182 | C2 | semidirect |
| 4. C4×#3935 | C2 | semidirect |
| 5. #10598121 | C2 | semidirect |
| 21. #64760 | C4 | semidirect |
| 57. #3935 | C2×C4 | semidirect |
| 58. #3935 | C2×C4 | semidirect |
| 333. C5 | #8226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#124 | 2 |
| C2×#64760 | 2 |
| #10600182 | 2 |
| C4×#3935 | 2 |
| #10598121 | 2 |
| #8226 | 5 |