Finite Group DatabasebetaFinite Group DatabasebetaOrder 36300.
292 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 35 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, Fitting, socle, cosocle, hypocenter | C3×C5×C112 | C22×C5 |
| LCS | G ▷ C3×C5×C112 | |
| 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 |
|---|---|
| C3⋊(C5⋊#11925895) | 2 |
| C5×C3⋊#11925895 | 2 |
| C3×C5⋊#11925892 | 2 |
| #11925895⋊D5 | 3 |
| D33⋊D55 | 5 |
| #20300008 | 5 |
| D15⋊AGL(1,𝔽11) | 11 |
| D3×C5⋊AGL(1,𝔽11) | 11 |