Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2942 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 |
|---|---|---|
| 5. #10602362 | C2 | direct (N × H) |
| 12. C22×C5×C4⋊C4 | C4 | semidirect |
| 48. C2×C5×C4⋊C4 | C2×C4 | semidirect |
| 111. C22×C4⋊C4 | Dic5 | semidirect |
| 193. C2×C4⋊C4 | C2×Dic5 | semidirect |
| 273. C2×C5 | #1445 | semidirect |
| 329. C5 | C2×#1445 | semidirect |
| 358. C2 | #10602362 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×C4⋊C4 | 2 |
| C22×#3963 | 2 |
| #10602362 | 2 |
| C2×#1445 | 5 |