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 |
|---|---|---|
| 4. C5×#3750 | C2 | semidirect |
| 5. C4×C5×C3⋊Dic3 | C2 | semidirect |
| 9. C2×C5×C3⋊Dic3 | C4 | semidirect |
| 13. #64086 | C5 | direct (N × H) |
| 30. #3750 | C2×C5 | semidirect |
| 31. C4×C3⋊Dic3 | C2×C5 | semidirect |
| 49. C2×C3⋊Dic3 | C4×C5 | semidirect |
| 65. C32×C5 | #117 | semidirect |
| 104. C3×C5 | #877 | semidirect |
| 115. C32 | C5×#117 | semidirect |
| 125. C5 | #64086 | direct (N × H) |
| 133. C3 | C5×#877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C3⋊Dic3 | 2 |
| C32×C5×C22⋊C4 | 2 |
| C5×#3757 | 2 |
| C5×#3750 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C5×#877 | 3 |
| #64086 | 5 |