Finite Group DatabasebetaFinite Group Databasebeta← C2×C3×C5⋊#11759818 #44478162
Order 30420.
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C5⋊#11759818 |
| commutator, cosocle, hypocenter | C5×C132 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C132 | C2×C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C2×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 |
|---|---|
| C2×C3×C5×#92789 | 2 |
| C3×C5⋊#11759818 | 2 |
| C2×C3×C13×D65 | 3 |
| C2×C5⋊#11759818 | 3 |
| C2×C3×#11759818 | 5 |
| C2×C3×D5×C13⋊C3 | 13 |
| C2×C3×C5⋊(D13⋊C3) | 13 |