Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2118 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 2118 conjugacy classes of subgroups — too many to draw. Only its 587 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×#4065 | C2 | semidirect |
| 2. C22×C5×Q32 | C2 | semidirect |
| 3. C22×#3960 | C2 | semidirect |
| 4. C2×#65208 | C2 | direct (N × H) |
| 5. C22×D80 | C2 | semidirect |
| 6. C22×D5×C16 | C2 | semidirect |
| 11. C2×#4065 | C22 | semidirect |
| 14. C2×C5×Q32 | C22 | semidirect |
| 16. C2×#3960 | C22 | semidirect |
| 18. #65208 | C22 | direct (N × H) |
| 19. C2×D80 | C22 | semidirect |
| 20. C2×D5×C16 | C22 | semidirect |
| 35. #4065 | C23 | semidirect |
| 40. C5×Q32 | C23 | semidirect |
| 42. #3960 | C23 | semidirect |
| 44. D80 | C23 | semidirect |
| 45. D5×C16 | C23 | semidirect |
| 48. C22×Q32 | D5 | semidirect |
| 87. C2×Q32 | C2×D5 | semidirect |
| 131. Q32 | C22×D5 | semidirect |
| 137. C22×C5 | #508 | semidirect |
| 174. C2×C5 | C2×#508 | semidirect |
| 198. C5 | C22×#508 | semidirect |
| 203. C22 | #65208 | direct (N × H) |
| 211. C2 | C2×#65208 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4065 | 2 |
| C22×C5×Q32 | 2 |
| C22×#3960 | 2 |
| C2×#65208 | 2 |
| C22×D80 | 2 |
| C22×D5×C16 | 2 |
| C22×#508 | 5 |