Finite Group DatabasebetaFinite Group DatabasebetaOrder 30420.
256 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×#11759816 |
| commutator, cosocle, hypocenter | C3×C132 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C132 | C22×C3 |
| LCS | G ▷ C3×C132 | |
| UCS | C1 ◁ C5 | |
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 |
|---|---|
| C5×D3×#92789 | 2 |
| C5×C3⋊#11759816 | 2 |
| C3×C5×#11759816 | 2 |
| C5×D3×C13⋊D13 | 3 |
| C2×C5×#11759816 | 3 |
| D3×#11759816 | 5 |
| C5×D3×D13⋊C3 | 13 |