Finite Group DatabasebetaFinite Group Databasebeta← C22×C5×((C3⋊D3)⋊C3)⋊C2 #72219435
Order 2160.
1002 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | ((C3⋊D3)⋊C3)⋊C2 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C24×C5 |
| Frattini | C3 | C22×C5×D32 |
| Fitting | C22×C5×H(3,𝔽3) | C22 |
| socle | C22×C3×C5 | D32 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C22×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#272 | 2 |
| C22×C5×(C3⋊D3)⋊C3 | 2 |
| C2×C5×((C3⋊D3)⋊C3)⋊C2 | 2 |
| C22×C5×D32 | 3 |
| C22×((C3⋊D3)⋊C3)⋊C2 | 5 |