Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
468 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 1. C22×C5×C3⋊Dic3 | C2 | semidirect |
| 3. #10623913 | C2 | semidirect |
| 4. #10623774 | C2 | semidirect |
| 5. #10623770 | C2 | semidirect |
| 30. C22×C3⋊Dic3 | D5 | semidirect |
| 71. C32×C5 | #123 | semidirect |
| 116. C3×C5 | #935 | semidirect |
| 129. C32 | #4075 | semidirect |
| 141. C5 | #64144 | semidirect |
| 150. C3 | #91536 | 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 |
| C2×C32×C22⋊D5 | 2 |
| #10623913 | 2 |
| #10623774 | 2 |
| #10623770 | 2 |
| #91536 | 3 |
| #64144 | 5 |