Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 170 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. C32×C5×C4⋊C4 | C2 | semidirect |
| 4. C5×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 5. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 12. C4×C5×C3⋊D3 | C4 | semidirect |
| 13. #64101 | C5 | direct (N × H) |
| 15. C3×C5×C4⋊C4 | D3 | semidirect |
| 29. C32×C4⋊C4 | C2×C5 | semidirect |
| 31. C4⋊(C3⋊Dic3) | C2×C5 | semidirect |
| 32. C4×C3⋊Dic3 | C2×C5 | semidirect |
| 46. C5×C4⋊C4 | C3⋊D3 | semidirect |
| 54. C4×C3⋊D3 | C4×C5 | semidirect |
| 64. C3×C4⋊C4 | C5×D3 | semidirect |
| 68. C32×C5 | #117 | semidirect |
| 108. C4⋊C4 | C5×C3⋊D3 | semidirect |
| 111. C3×C5 | #892 | semidirect |
| 124. C32 | C5×#117 | semidirect |
| 135. C5 | #64101 | direct (N × H) |
| 144. C3 | C5×#892 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C3⋊D3 | 2 |
| C32×C5×C4⋊C4 | 2 |
| C5×#3752 | 2 |
| C5×C4⋊(C3⋊Dic3) | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C5×#892 | 3 |
| #64101 | 5 |