Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
876 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 876 conjugacy classes of subgroups — too many to draw. Only its 306 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. C32×C5×#41 | C2 | semidirect |
| 2. C5×Q8×C3⋊D3 | C2 | semidirect |
| 3. C5×#3830 | C2 | semidirect |
| 4. C5×#3828 | C2 | semidirect |
| 5. C2×C5×#634 | C2 | semidirect |
| 16. #64367 | C5 | direct (N × H) |
| 17. C3×C5×#41 | D3 | semidirect |
| 28. C32×#41 | C2×C5 | semidirect |
| 29. Q8×C3⋊D3 | C2×C5 | semidirect |
| 30. #3830 | C2×C5 | semidirect |
| 31. #3828 | C2×C5 | semidirect |
| 32. C2×#634 | C2×C5 | semidirect |
| 48. C5×#41 | C3⋊D3 | semidirect |
| 65. C3×#41 | C5×D3 | semidirect |
| 70. C32×C5 | 2−1+4 | semidirect |
| 108. #41 | C5×C3⋊D3 | semidirect |
| 111. C3×C5 | #1010 | semidirect |
| 120. C32 | C5×2−1+4 | semidirect |
| 133. C5 | #64367 | direct (N × H) |
| 139. C3 | C5×#1010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×#41 | 2 |
| C5×Q8×C3⋊D3 | 2 |
| C5×#3830 | 2 |
| C5×#3828 | 2 |
| C2×C5×#634 | 2 |
| C5×#1010 | 3 |
| #64367 | 5 |