Finite Group DatabasebetaFinite Group DatabasebetaOrder 30420.
704 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 170 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 | D15⋊(C13⋊D13) |
| commutator, cosocle, hypocenter | C3×C5×C132 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C132 | C22 |
| LCS | G ▷ C3×C5×C132 | |
| 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 |
|---|---|
| C32×C5⋊(C13⋊D13) | 2 |
| C3×C5×C3⋊(C13⋊D13) | 2 |
| C3×C132×D15 | 2 |
| D15⋊(C13⋊D13) | 3 |
| C3×D5×C13⋊D13 | 3 |
| C3×D3×C13⋊D13 | 5 |
| C3×D15⋊D13 | 13 |