Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
134 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 46 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 | C8 | D3×D15 |
| commutator, hypocenter | C32×C5 | C2×C16 |
| Fitting, cosocle | C32×C5×C8 | C22 |
| socle | C2×C32×C5 | C2×C8 |
| prime radical | C2×C3⋊D15 | C8 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C3⋊#672 | C2 | semidirect |
| 3. C3×C5×C3⋊C16 | C2 | semidirect |
| 14. C3⋊#672 | D3 | semidirect |
| 16. C5×C3⋊C16 | D3 | semidirect |
| 23. C3×C3⋊C16 | D5 | semidirect |
| 36. C3⋊D15 | C16 | semidirect |
| 58. C3⋊C16 | D15 | semidirect |
| 59. C32×C5 | C2×C16 | semidirect |
| 91. C3×C5 | D3×C16 | semidirect |
| 92. C3×C5 | D3×C16 | semidirect |
| 104. C32 | D5×C16 | semidirect |
| 114. C5 | #63542 | semidirect |
| 119. C3 | #90933 | semidirect |
| 120. C3 | C16×D15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C3⋊D15 | 2 |
| C3×C3⋊#672 | 2 |
| C3×C5×C3⋊C16 | 2 |
| C16×D15 | 3 |
| #90933 | 3 |
| #63542 | 5 |