Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
338 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 78 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 | C2×C5×#626 | C2 |
| hypocenter | C32×C5 | #124 |
| 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 |
|---|---|---|
| 1. C2×#67153 | C2 | semidirect |
| 3. #10623830 | C2 | semidirect |
| 4. (C2×D3)⋊Dic15 | C2 | semidirect |
| 5. #10623771 | C2 | semidirect |
| 6. C3×(C2×D3)⋊Dic5 | C2 | semidirect |
| 7. C3×Dic3×Dic5 | C2 | semidirect |
| 33. (C2×D3)⋊Dic5 | D3 | semidirect |
| 34. Dic3×Dic5 | D3 | semidirect |
| 144. C32×C5 | #124 | semidirect |
| 227. C3×C5 | #875 | semidirect |
| 228. C3×C5 | #885 | semidirect |
| 264. C32 | #4082 | semidirect |
| 288. C5 | #63852 | semidirect |
| 302. C3 | #91373 | semidirect |
| 303. C3 | #91525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67153 | 2 |
| C2×C5×#626 | 2 |
| #10623830 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| #10623771 | 2 |
| C3×(C2×D3)⋊Dic5 | 2 |
| C3×Dic3×Dic5 | 2 |
| #91525 | 3 |
| #91373 | 3 |
| #63852 | 5 |