Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
486 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 3. C3×C4×Dic15 | C2 | semidirect |
| 4. #10623828 | C2 | semidirect |
| 9. C4×C5×C3⋊D3 | C4 | semidirect |
| 11. #67155 | C4 | direct (N × H) |
| 16. C4×Dic15 | D3 | semidirect |
| 22. C32×C4×C5 | C2×C4 | semidirect |
| 23. C5×C3⋊Dic3 | C2×C4 | semidirect |
| 24. C3×Dic15 | C2×C4 | semidirect |
| 44. C5×C3⋊D3 | C42 | semidirect |
| 52. C4×C3⋊D3 | Dic5 | semidirect |
| 62. C3×C4×C5 | C4×D3 | semidirect |
| 63. Dic15 | C4×D3 | semidirect |
| 73. C32×C5 | C2×C42 | semidirect |
| 83. C32×C4 | C2×Dic5 | semidirect |
| 84. C3⋊Dic3 | C2×Dic5 | semidirect |
| 108. C4×C5 | #624 | semidirect |
| 112. C3⋊D3 | C4×Dic5 | semidirect |
| 118. C3×C5 | C42×D3 | semidirect |
| 127. C3×C4 | D3×Dic5 | semidirect |
| 134. C32 | C2×C4×Dic5 | semidirect |
| 147. C5 | C4×#624 | semidirect |
| 153. C4 | #67155 | direct (N × H) |
| 155. C3 | C4×D3×Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C3⋊D3 | 2 |
| C2×#67155 | 2 |
| C3×C4×Dic15 | 2 |
| #10623828 | 2 |
| C4×D3×Dic5 | 3 |
| C4×#624 | 5 |