Finite Group DatabasebetaFinite Group DatabasebetaOrder 36300.
448 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 122 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 | C2 | C3⋊(C5⋊#11925892) |
| commutator, hypocenter | C3×C5×C112 | C4×C5 |
| Fitting, socle, cosocle | C2×C3×C5×C112 | C2×C5 |
| prime radical | C2×C3×C5×#10597243 | C2 |
| LCS | G ▷ C3×C5×C112 | |
| UCS | C1 ◁ C2 | |
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 |
|---|---|
| C2×C3×C5×#10597243 | 2 |
| #27130851 | 3 |
| C3⋊(C11⋊Dic55) | 5 |
| C3⋊#14559051 | 5 |
| C3⋊((C11⋊C5)⋊Dic5) | 11 |