Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2154 conjugacy classes of subgroups.
The subgroup lattice has 288 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×#681 | C2 | direct (N × H) |
| 3. C2×#65313 | C2 | semidirect |
| 4. C2×Q8×#168 | C2 | semidirect |
| 18. #65313 | C22 | semidirect |
| 19. Q8×#168 | C22 | semidirect |
| 51. C2×#681 | Q8 | direct (N × H) |
| 69. C2×C5×Q8 | M16 | semidirect |
| 96. #681 | C2×Q8 | direct (N × H) |
| 98. C2×#168 | C2×Q8 | semidirect |
| 126. C5×Q8 | C2×M16 | semidirect |
| 147. #168 | C22×Q8 | semidirect |
| 200. C2×Q8 | #681 | direct (N × H) |
| 233. C2×C5 | Q8×M16 | semidirect |
| 243. Q8 | C2×#681 | direct (N × H) |
| 265. C5 | C2×Q8×M16 | semidirect |
| 283. C2 | Q8×#681 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×Q8 | 2 |
| Q8×#681 | 2 |
| C2×#65313 | 2 |
| C2×Q8×#168 | 2 |
| C2×#65213 | 2 |
| C2×C4×#681 | 2 |
| C2×Q8×M16 | 5 |