Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
360 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 130 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. C32×C5×C4⋊C4 | C2 | semidirect |
| 5. C5×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 6. C5×#3750 | C2 | semidirect |
| 7. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 16. #64107 | C5 | direct (N × H) |
| 17. C3×C5×C4⋊C4 | D3 | semidirect |
| 35. C32×C4⋊C4 | C2×C5 | semidirect |
| 39. C4⋊(C3⋊Dic3) | C2×C5 | semidirect |
| 40. #3750 | C2×C5 | semidirect |
| 41. C4×C3⋊Dic3 | C2×C5 | semidirect |
| 56. C5×C4⋊C4 | C3⋊D3 | semidirect |
| 78. C3×C4⋊C4 | C5×D3 | semidirect |
| 85. C32×C5 | #126 | semidirect |
| 131. C4⋊C4 | C5×C3⋊D3 | semidirect |
| 136. C3×C5 | #898 | semidirect |
| 151. C32 | C5×#126 | semidirect |
| 163. C5 | #64107 | direct (N × H) |
| 174. C3 | C5×#898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×C4⋊C4 | 2 |
| C5×#3752 | 2 |
| C5×C4⋊(C3⋊Dic3) | 2 |
| C5×#3750 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C5×#898 | 3 |
| #64107 | 5 |