Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
274 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D32×D5 |
| commutator, Fitting, socle, cosocle | C22×C32×C5 | C23 |
| prime radical | C22×C5×C3⋊D3 | C22 |
| hypocenter | C32×C5 | #126 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Dic3⋊Dic15 | C2 | semidirect |
| 3. #10623815 | C2 | semidirect |
| 6. C3×#6669 | C2 | semidirect |
| 7. C3×Dic3×Dic5 | C2 | semidirect |
| 26. #6669 | D3 | semidirect |
| 32. Dic3×Dic5 | D3 | semidirect |
| 129. C32×C5 | #126 | semidirect |
| 199. C3×C5 | #876 | semidirect |
| 200. C3×C5 | #898 | semidirect |
| 231. C32 | #4025 | semidirect |
| 251. C5 | #63868 | semidirect |
| 263. C3 | #91342 | semidirect |
| 264. C3 | #91372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623830 | 2 |
| Dic3⋊Dic15 | 2 |
| #10623815 | 2 |
| C5×#3722 | 2 |
| #10623771 | 2 |
| C3×#6669 | 2 |
| C3×Dic3×Dic5 | 2 |
| #91372 | 3 |
| #91342 | 3 |
| #63868 | 5 |