Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 136 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. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 3. C32×C4×Dic5 | C2 | semidirect |
| 4. #10623774 | C2 | semidirect |
| 10. C4×C3⋊D15 | C4 | semidirect |
| 16. C3×C4×Dic5 | D3 | semidirect |
| 31. C4×C3⋊Dic3 | D5 | semidirect |
| 46. C4×Dic5 | C3⋊D3 | semidirect |
| 65. C32×C5 | #117 | semidirect |
| 104. C3×C5 | #872 | semidirect |
| 115. C32 | #4018 | semidirect |
| 125. C5 | #64081 | semidirect |
| 133. C3 | #91386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊D15 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C32×C4×Dic5 | 2 |
| #10623774 | 2 |
| #10623772 | 2 |
| #91386 | 3 |
| #64081 | 5 |