Finite Group DatabasebetaFinite Group Databasebeta← ((C11⋊D11)⋊C3)⋊(C5⋊D5) #49137615
Order 36300.
256 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 43 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 | C52×C112⋊C3 | C22 |
| Fitting, socle | C52×C112 | C2×D3 |
| LCS | G ▷ C52×C112⋊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 |
|---|---|
| C5⋊(C5⋊#10624391) | 2 |
| C52×(C11⋊D11)⋊C3 | 2 |
| #27130989 | 3 |
| ((C11⋊D11)⋊C3)⋊D5 | 5 |
| C2×C3⋊(C5⋊D5) | 121 |