Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
372 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 130 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×#3828 | C2 | semidirect |
| 3. C5×#3756 | C2 | semidirect |
| 4. C5×#3755 | C2 | semidirect |
| 5. C5×#3754 | C2 | semidirect |
| 6. C5×#3753 | C2 | semidirect |
| 7. C2×C5×C3⋊(C3⋊C8) | C2 | semidirect |
| 20. #64159 | C5 | direct (N × H) |
| 21. C3×C5×#41 | D3 | semidirect |
| 36. C32×#41 | C2×C5 | semidirect |
| 37. #3828 | C2×C5 | semidirect |
| 38. #3756 | C2×C5 | semidirect |
| 39. #3755 | C2×C5 | semidirect |
| 40. #3754 | C2×C5 | semidirect |
| 41. #3753 | C2×C5 | semidirect |
| 42. C2×C3⋊(C3⋊C8) | C2×C5 | semidirect |
| 60. C5×#41 | C3⋊D3 | semidirect |
| 84. C3×#41 | C5×D3 | semidirect |
| 91. C32×C5 | #135 | semidirect |
| 138. #41 | C5×C3⋊D3 | semidirect |
| 144. C3×C5 | #950 | semidirect |
| 156. C32 | C5×#135 | semidirect |
| 172. C5 | #64159 | direct (N × H) |
| 180. C3 | C5×#950 | 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×#3828 | 2 |
| C5×#3756 | 2 |
| C5×#3755 | 2 |
| C5×#3754 | 2 |
| C5×#3753 | 2 |
| C2×C5×C3⋊(C3⋊C8) | 2 |
| C5×#950 | 3 |
| #64159 | 5 |