Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
780 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 162 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. C23×C5×C3⋊D3 | C2 | semidirect |
| 2. C2×C5×#638 | C2 | semidirect |
| 3. C2×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 4. C32×C5×C22⋊C4 | C2 | semidirect |
| 5. C5×#3752 | C2 | semidirect |
| 11. C22×C5×C3⋊D3 | C22 | semidirect |
| 12. C2×C32×C4×C5 | C22 | semidirect |
| 14. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 16. #64091 | C5 | direct (N × H) |
| 20. C3×C5×C22⋊C4 | D3 | semidirect |
| 23. C22×C32×C5 | D4 | semidirect |
| 30. C2×C5×C3⋊D3 | D4 | semidirect |
| 34. C23×C3⋊D3 | C2×C5 | semidirect |
| 35. C2×#638 | C2×C5 | semidirect |
| 36. C2×C4⋊(C3⋊D3) | C2×C5 | semidirect |
| 37. C32×C22⋊C4 | C2×C5 | semidirect |
| 38. #3752 | C2×C5 | semidirect |
| 44. C2×C3×C4×C5 | C2×D3 | semidirect |
| 58. C5×C22⋊C4 | C3⋊D3 | semidirect |
| 63. C22×C3⋊D3 | C22×C5 | semidirect |
| 64. C2×C32×C4 | C22×C5 | semidirect |
| 66. C2×C3⋊Dic3 | C22×C5 | semidirect |
| 69. C22×C3×C5 | D12 | semidirect |
| 82. C3×C22⋊C4 | C5×D3 | semidirect |
| 84. C32×C5 | #120 | semidirect |
| 93. C2×C4×C5 | C2×C3⋊D3 | semidirect |
| 95. C22×C32 | C5×D4 | semidirect |
| 102. C2×C3⋊D3 | C5×D4 | semidirect |
| 116. C2×C3×C4 | C2×C5×D3 | semidirect |
| 127. C22×C5 | C4⋊(C3⋊D3) | semidirect |
| 140. C22⋊C4 | C5×C3⋊D3 | semidirect |
| 141. C3×C5 | #882 | semidirect |
| 143. C22×C3 | C5×D12 | semidirect |
| 158. C32 | C5×#120 | semidirect |
| 167. C2×C4 | C2×C5×C3⋊D3 | semidirect |
| 173. C5 | #64091 | direct (N × H) |
| 181. C22 | C5×C4⋊(C3⋊D3) | semidirect |
| 185. C3 | C5×#882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×C3⋊D3 | 2 |
| C2×C5×#638 | 2 |
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C32×C5×C22⋊C4 | 2 |
| C5×#3752 | 2 |
| C5×#882 | 3 |
| #64091 | 5 |