Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3350 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 3350 conjugacy classes of subgroups — too many to draw. Only its 827 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×C4⋊Q8 | C2 | semidirect |
| 2. C23×#689 | C2 | semidirect |
| 5. C2×#65375 | C2 | direct (N × H) |
| 6. C22×#3935 | C2 | semidirect |
| 11. C2×C5×C4⋊Q8 | C22 | semidirect |
| 15. C22×#689 | C22 | semidirect |
| 22. #65375 | C22 | direct (N × H) |
| 23. C2×#3935 | C22 | semidirect |
| 41. C5×C4⋊Q8 | C23 | semidirect |
| 46. C2×#689 | C23 | semidirect |
| 54. #3935 | C23 | semidirect |
| 57. C22×C4⋊Q8 | D5 | semidirect |
| 104. C2×C4⋊Q8 | C2×D5 | semidirect |
| 159. C4⋊Q8 | C22×D5 | semidirect |
| 167. C22×C5 | #497 | semidirect |
| 213. C2×C5 | C2×#497 | semidirect |
| 242. C5 | C22×#497 | semidirect |
| 246. C22 | #65375 | direct (N × H) |
| 256. C2 | C2×#65375 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C4⋊Q8 | 2 |
| C23×#689 | 2 |
| C23×#688 | 2 |
| C22×#4021 | 2 |
| C2×#65375 | 2 |
| C22×#3935 | 2 |
| C22×#497 | 5 |