Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
360 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 104 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. #10623775 | C2 | semidirect |
| 5. #10623774 | C2 | semidirect |
| 6. #10623773 | C2 | semidirect |
| 7. Dic5×C3⋊Dic3 | C2 | semidirect |
| 85. C32×C5 | #126 | semidirect |
| 136. C3×C5 | #879 | semidirect |
| 151. C32 | #4025 | semidirect |
| 163. C5 | #64088 | semidirect |
| 174. C3 | #91531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623913 | 2 |
| C5×#3757 | 2 |
| C32×C22⋊Dic5 | 2 |
| #10623775 | 2 |
| #10623774 | 2 |
| #10623773 | 2 |
| Dic5×C3⋊Dic3 | 2 |
| #91531 | 3 |
| #64088 | 5 |