Finite Group DatabasebetaFinite Group DatabasebetaOrder 36900.
128 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D3×(C5⋊D5)⋊C3 |
| commutator, cosocle, hypocenter | C3×C52 | C22×C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C22×C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C41 | |
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 |
|---|---|
| D3×C41×C52⋊C3 | 2 |
| C41×C3⋊((C5⋊D5)⋊C3) | 2 |
| C3×C41×(C5⋊D5)⋊C3 | 2 |
| D3×C41×C5⋊D5 | 3 |
| C2×C41×(C5⋊D5)⋊C3 | 3 |
| C2×C3×D3×C41 | 25 |
| D3×(C5⋊D5)⋊C3 | 41 |