Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
342 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 74 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×#625 | 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 |
|---|---|---|
| 2. C2×#67141 | C2 | semidirect |
| 3. #10623828 | C2 | semidirect |
| 4. (C2×D3)⋊Dic15 | C2 | semidirect |
| 5. C3×(C2×D3)⋊Dic5 | C2 | semidirect |
| 21. (C2×D3)⋊Dic5 | D3 | semidirect |
| 90. C32×C5 | #124 | semidirect |
| 144. C3×C5 | #885 | semidirect |
| 164. C32 | #4082 | semidirect |
| 179. C5 | #63913 | semidirect |
| 189. C3 | #91525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#625 | 2 |
| C2×#67141 | 2 |
| #10623828 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| C3×(C2×D3)⋊Dic5 | 2 |
| #91525 | 3 |
| #63913 | 5 |