Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 250 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 |
|---|---|---|
| 3. C5×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 4. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 7. C2×C32×C4×C5 | C4 | semidirect |
| 11. #64135 | C5 | direct (N × H) |
| 25. C4⋊(C3⋊Dic3) | C2×C5 | semidirect |
| 26. C4×C3⋊Dic3 | C2×C5 | semidirect |
| 28. C2×C3×C4×C5 | Dic3 | semidirect |
| 41. C2×C32×C4 | C4×C5 | semidirect |
| 55. C32×C5 | #117 | semidirect |
| 58. C2×C4×C5 | C3⋊Dic3 | semidirect |
| 72. C2×C3×C4 | C5×Dic3 | semidirect |
| 89. C3×C5 | #926 | semidirect |
| 99. C32 | C5×#117 | semidirect |
| 102. C2×C4 | C5×C3⋊Dic3 | semidirect |
| 108. C5 | #64135 | direct (N × H) |
| 115. C3 | C5×#926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4×C5 | 2 |
| C5×#3757 | 2 |
| C5×C4⋊(C3⋊Dic3) | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C5×#926 | 3 |
| #64135 | 5 |