Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2446 conjugacy classes of subgroups.
The subgroup lattice has 380 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. #10605448 | C2 | direct (N × H) |
| 171. C2×C4×C5 | #125 | semidirect |
| 249. C4×C5 | C2×#125 | semidirect |
| 300. C2×C5 | #2552 | semidirect |
| 338. C2×C4 | #4036 | semidirect |
| 348. C5 | C2×#2552 | semidirect |
| 370. C4 | C2×#4036 | semidirect |
| 371. C2 | #10605448 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4036 | 2 |
| C2×C4×C5×C4⋊C4 | 2 |
| C2×#65274 | 2 |
| C2×#65217 | 2 |
| C2×#65224 | 2 |
| C2×C4×C4⋊Dic5 | 2 |
| #10605448 | 2 |
| C2×#64950 | 2 |
| C2×#2552 | 5 |