Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
462 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D3×D15 |
| commutator, socle, cosocle | C22×C32×C5 | C23 |
| Fitting | C2×C32×C4×C5 | C22 |
| hypercenter | C2×C4 | D3×D15 |
| hypocenter | C32×C5 | #127 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×D60 | C2 | semidirect |
| 2. C2×C3×C5×D12 | C2 | semidirect |
| 3. C2×#67150 | C2 | semidirect |
| 4. C4×C3⋊Dic15 | C2 | semidirect |
| 17. C2×D60 | D3 | semidirect |
| 18. C2×C5×D12 | D3 | semidirect |
| 29. C32×C4×C5 | D4 | semidirect |
| 30. C3⋊Dic15 | D4 | semidirect |
| 33. C2×C3×D12 | D5 | semidirect |
| 81. C3×C4×C5 | #67 | semidirect |
| 82. C3×C4×C5 | #67 | semidirect |
| 91. C2×D12 | D15 | semidirect |
| 95. C32×C5 | #127 | semidirect |
| 108. C32×C4 | C22⋊D5 | semidirect |
| 142. C4×C5 | #625 | semidirect |
| 153. C3×C5 | #940 | semidirect |
| 154. C3×C5 | #940 | semidirect |
| 167. C3×C4 | #1201 | semidirect |
| 168. C3×C4 | #1220 | semidirect |
| 176. C32 | #4086 | semidirect |
| 194. C5 | #63914 | semidirect |
| 201. C4 | #67150 | semidirect |
| 203. C3 | #91463 | semidirect |
| 204. C3 | #91829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D60 | 2 |
| C2×C3×C5×D12 | 2 |
| C2×#67150 | 2 |
| C4×C3⋊Dic15 | 2 |
| #91829 | 3 |
| #91463 | 3 |
| #63914 | 5 |