Finite Group DatabasebetaFinite Group Databasebeta← ((C5⋊D5)⋊C3)⋊(C11⋊D11) #49137583
Order 36300.
420 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 73 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 | C1 | G |
| commutator, cosocle, hypocenter | C112×C52⋊C3 | C22 |
| Fitting, socle | C52×C112 | C2×D3 |
| LCS | G ▷ C112×C52⋊C3 | |
| UCS | C1 | |
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 |
|---|---|
| C112×(C5⋊D5)⋊C3 | 2 |
| C11⋊(C11⋊#3874) | 2 |
| (C5⋊D5)⋊(C11⋊D11) | 3 |
| ((C5⋊D5)⋊C3)⋊D11 | 11 |
| C2×C3⋊(C11⋊D11) | 25 |