Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1974 conjugacy classes of subgroups.
The subgroup lattice has 314 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10614168 | C2 | semidirect |
| 3. #10614167 | C2 | semidirect |
| 4. #10614166 | C2 | semidirect |
| 5. Q8×#681 | C2 | semidirect |
| 19. #65313 | C22 | semidirect |
| 20. Q8×#168 | C22 | semidirect |
| 74. C2×C5×Q8 | M16 | semidirect |
| 217. C2×Q8 | #681 | semidirect |
| 287. C5 | #60248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×Q8 | 2 |
| #10614168 | 2 |
| #10614167 | 2 |
| #10614166 | 2 |
| Q8×#681 | 2 |
| #10613780 | 2 |
| #60248 | 5 |