Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2230 conjugacy classes of subgroups.
The subgroup lattice has 276 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10614250 | C2 | direct (N × H) |
| 3. C2×Q8×#168 | C2 | semidirect |
| 4. C2×#65301 | C2 | semidirect |
| 5. C2×#65215 | C2 | semidirect |
| 6. C2×C4×#681 | C2 | semidirect |
| 18. Q8×#168 | C22 | semidirect |
| 19. #65301 | C22 | semidirect |
| 20. #65215 | C22 | semidirect |
| 22. C4×#681 | C22 | semidirect |
| 67. C2×C5×Q8 | M16 | semidirect |
| 95. C2×#168 | #41 | semidirect |
| 122. C5×Q8 | C2×M16 | semidirect |
| 142. #168 | C2×#41 | semidirect |
| 192. C2×Q8 | #681 | semidirect |
| 224. C2×C5 | #2971 | semidirect |
| 233. Q8 | C2×#681 | semidirect |
| 254. C5 | C2×#2971 | semidirect |
| 271. C2 | #10614250 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×#41 | 2 |
| #10614250 | 2 |
| C2×Q8×#168 | 2 |
| C2×#65301 | 2 |
| C2×#65215 | 2 |
| C2×C4×#681 | 2 |
| C2×#2971 | 5 |