Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 156 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⋊D3×Dic5 | C2 | semidirect |
| 3. C4⋊(C3⋊Dic15) | C2 | semidirect |
| 4. C32×C4×Dic5 | C2 | semidirect |
| 5. #10623771 | C2 | semidirect |
| 10. C5×C4⋊(C3⋊D3) | C4 | semidirect |
| 18. C3×C4×Dic5 | D3 | semidirect |
| 23. C2×C5×C3⋊D3 | C2×C4 | semidirect |
| 24. C32×C4×C5 | C2×C4 | semidirect |
| 27. C32×Dic5 | D4 | semidirect |
| 50. C4×Dic5 | C3⋊D3 | semidirect |
| 56. C4⋊(C3⋊D3) | Dic5 | direct (N × H) |
| 62. C3×C4×C5 | C4×D3 | semidirect |
| 65. C3×Dic5 | D12 | semidirect |
| 71. C32×C5 | C4×D4 | semidirect |
| 82. C2×C3⋊D3 | C2×Dic5 | semidirect |
| 85. C32×C4 | C2×Dic5 | semidirect |
| 103. C4×C5 | C4×C3⋊D3 | semidirect |
| 106. Dic5 | C4⋊(C3⋊D3) | direct (N × H) |
| 116. C3×C5 | C4×D12 | semidirect |
| 123. C3×C4 | D3×Dic5 | semidirect |
| 129. C32 | D4×Dic5 | semidirect |
| 141. C5 | C4×C4⋊(C3⋊D3) | semidirect |
| 149. C4 | C3⋊D3×Dic5 | semidirect |
| 150. C3 | Dic5×D12 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×C3⋊D3×Dic5 | 2 |
| C4⋊(C3⋊Dic15) | 2 |
| C32×C4×Dic5 | 2 |
| #10623771 | 2 |
| Dic5×D12 | 3 |
| C4×C4⋊(C3⋊D3) | 5 |