Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1882 conjugacy classes of subgroups.
The subgroup lattice has 262 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10615061 | C2 | semidirect |
| 3. #10615059 | C2 | semidirect |
| 6. Q8×#681 | C2 | semidirect |
| 7. C2×Q8×#168 | C2 | semidirect |
| 52. #4094 | Q8 | direct (N × H) |
| 96. #681 | C2×Q8 | semidirect |
| 98. C2×#168 | C2×Q8 | semidirect |
| 130. C5×Q8 | #131 | semidirect |
| 229. Q8 | #4094 | direct (N × H) |
| 245. C5 | Q8×#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×#41 | 2 |
| #10615061 | 2 |
| #10615059 | 2 |
| #10614243 | 2 |
| C4×#4094 | 2 |
| Q8×#681 | 2 |
| C2×Q8×#168 | 2 |
| Q8×#131 | 5 |