Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
334 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 2. C2×C3×C5×Dic6 | C2 | semidirect |
| 3. C32×C42×C5 | C2 | semidirect |
| 4. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C5×#875 | C3 | direct (N × H) |
| 13. C3×#875 | C5 | direct (N × H) |
| 17. C2×C5×Dic6 | C2×C3 | semidirect |
| 20. C3×C42×C5 | D3 | semidirect |
| 21. C3×C42×C5 | C2×C3 | semidirect |
| 22. C5×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 31. C2×C3×Dic6 | C2×C5 | semidirect |
| 32. C32×C42 | C2×C5 | semidirect |
| 33. C3×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 49. #875 | C3×C5 | direct (N × H) |
| 56. C42×C5 | C3×D3 | semidirect |
| 81. C2×Dic6 | C2×C3×C5 | semidirect |
| 84. C3×C42 | C5×D3 | semidirect |
| 85. C3×C42 | C2×C3×C5 | semidirect |
| 86. (C2×D3)⋊C4 | C2×C3×C5 | semidirect |
| 87. C32×C5 | #124 | semidirect |
| 135. C42 | C3×C5×D3 | semidirect |
| 137. C3×C5 | #875 | direct (N × H) |
| 138. C3×C5 | C3×#124 | semidirect |
| 157. C32 | C5×#124 | semidirect |
| 172. C5 | C3×#875 | direct (N × H) |
| 180. C3 | C5×#875 | direct (N × H) |
| 181. C3 | C3×C5×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D12 | 2 |
| C2×C3×C5×Dic6 | 2 |
| C32×C42×C5 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| C3×C5×#124 | 3 |
| C5×#875 | 3 |
| C3×#875 | 5 |