Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
312 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 66 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. #10624098 | C2 | semidirect |
| 3. C32×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. C22×C3⋊D15 | C4 | semidirect |
| 9. C2×C5×C3⋊Dic3 | C4 | semidirect |
| 15. C3×C22⋊AGL(1,𝔽5) | D3 | semidirect |
| 44. C22⋊AGL(1,𝔽5) | C3⋊D3 | semidirect |
| 51. C2×C3⋊Dic3 | AGL(1,𝔽5) | semidirect |
| 64. C32×C5 | #99 | semidirect |
| 111. C3×C5 | #806 | semidirect |
| 126. C32 | #3999 | semidirect |
| 139. C5 | #63633 | semidirect |
| 149. C3 | #91173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67139 | 2 |
| #10624098 | 2 |
| C32×C22⋊AGL(1,𝔽5) | 2 |
| #91173 | 3 |
| #63633 | 5 |