Finite Group DatabasebetaFinite Group DatabasebetaOrder 36300.
200 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #27130915 |
| commutator, cosocle, hypocenter | C5×C112 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C112 | C22×C5 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C3 | |
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⋊#11925896 | 2 |
| C3×C5×#11925893 | 2 |
| #27130915 | 3 |
| C3×D55⋊D11 | 5 |
| C3×#11925896⋊C2 | 5 |
| C3×D5×AGL(1,𝔽11) | 11 |