Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3630 conjugacy classes of subgroups.
The subgroup lattice has 296 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10613954 | C2 | semidirect |
| 4. Dic5×#117 | C2 | semidirect |
| 5. #10613875 | C2 | semidirect |
| 7. C4×#4072 | C2 | semidirect |
| 9. C2×C5×#117 | C4 | semidirect |
| 16. C2×#4072 | C4 | semidirect |
| 24. C4⋊C4×Dic5 | C22 | semidirect |
| 26. C4×C4⋊Dic5 | C22 | semidirect |
| 27. #65221 | C22 | semidirect |
| 28. C42×Dic5 | C22 | semidirect |
| 39. C5×#117 | C2×C4 | semidirect |
| 40. C5×#117 | C2×C4 | semidirect |
| 41. C2×C5×C4⋊C4 | C2×C4 | semidirect |
| 45. C2×C42×C5 | C2×C4 | semidirect |
| 51. #4072 | C2×C4 | semidirect |
| 52. #4072 | C2×C4 | semidirect |
| 53. #4072 | C2×C4 | semidirect |
| 54. #4072 | C2×C4 | semidirect |
| 55. C2×C4⋊Dic5 | C2×C4 | semidirect |
| 58. C2×C4×Dic5 | C2×C4 | semidirect |
| 76. C22×C4×C5 | C42 | semidirect |
| 112. C2×#117 | Dic5 | semidirect |
| 168. #117 | C2×Dic5 | semidirect |
| 169. #117 | C2×Dic5 | semidirect |
| 173. C2×C4⋊C4 | C2×Dic5 | semidirect |
| 184. C2×C42 | C2×Dic5 | semidirect |
| 213. C22×C4 | C4×Dic5 | semidirect |
| 273. C5 | #33996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#117 | 2 |
| C22×#4072 | 2 |
| #10613954 | 2 |
| Dic5×#117 | 2 |
| #10613875 | 2 |
| #10613814 | 2 |
| C4×#4072 | 2 |
| #33996 | 5 |