Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
358 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 120 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. C3×C5×C4⋊Dic3 | C2 | semidirect |
| 4. C5×Dic32 | C2 | semidirect |
| 9. C4×C5×C3⋊D3 | C4 | semidirect |
| 11. #63849 | C5 | direct (N × H) |
| 16. C5×C4⋊Dic3 | D3 | semidirect |
| 26. C3×C4⋊Dic3 | C2×C5 | semidirect |
| 28. Dic32 | C2×C5 | semidirect |
| 50. C4×C3⋊D3 | C4×C5 | semidirect |
| 69. C4⋊Dic3 | C5×D3 | semidirect |
| 71. C32×C5 | #117 | semidirect |
| 115. C3×C5 | #892 | semidirect |
| 132. C32 | C5×#117 | semidirect |
| 145. C5 | #63849 | direct (N × H) |
| 153. 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 |
| C3×C5×C4⋊Dic3 | 2 |
| C5×#3722 | 2 |
| C5×Dic32 | 2 |
| C5×#892 | 3 |
| #63849 | 5 |