Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
462 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 164 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. C2×C3×C5×D12 | C2 | semidirect |
| 2. C32×C42×C5 | C2 | semidirect |
| 4. C5×#874 | C3 | direct (N × H) |
| 8. C3×#874 | C5 | direct (N × H) |
| 10. C2×C5×D12 | C2×C3 | semidirect |
| 12. C3×C42×C5 | D3 | semidirect |
| 13. C3×C42×C5 | C2×C3 | semidirect |
| 16. C32×C4×C5 | D4 | semidirect |
| 18. C2×C3×D12 | C2×C5 | semidirect |
| 19. C32×C42 | C2×C5 | semidirect |
| 28. #874 | C3×C5 | direct (N × H) |
| 32. C42×C5 | C3×D3 | semidirect |
| 42. C3×C4×C5 | D12 | semidirect |
| 43. C3×C4×C5 | C3×D4 | semidirect |
| 45. C2×D12 | C2×C3×C5 | semidirect |
| 47. C3×C42 | C5×D3 | semidirect |
| 48. C3×C42 | C2×C3×C5 | semidirect |
| 49. C32×C5 | #127 | semidirect |
| 55. C32×C4 | C5×D4 | semidirect |
| 71. C4×C5 | C3×D12 | semidirect |
| 75. C42 | C3×C5×D3 | semidirect |
| 77. C3×C5 | #874 | direct (N × H) |
| 78. C3×C5 | C3×#127 | semidirect |
| 85. C3×C4 | C5×D12 | semidirect |
| 86. C3×C4 | C3×C5×D4 | semidirect |
| 89. C32 | C5×#127 | semidirect |
| 98. C5 | C3×#874 | direct (N × H) |
| 101. C4 | C3×C5×D12 | semidirect |
| 103. C3 | C5×#874 | direct (N × H) |
| 104. C3 | C3×C5×#127 | 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 |
| C32×C42×C5 | 2 |
| C3×C5×#127 | 3 |
| C5×#874 | 3 |
| C3×#874 | 5 |