Finite Group DatabasebetaFinite Group Databasebeta← C2×C3⋊D15×ΓL(1,𝔽32) #42124832
Order 27900.
288 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 81 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⋊D15×ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C32×C5×C31 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C5×C31 | C2×C5 |
| LCS | G ▷ C32×C5×C31 | |
| 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×C32×C5×ΓL(1,𝔽32) | 2 |
| C3⋊D15×ΓL(1,𝔽32) | 2 |
| C2×D15×ΓL(1,𝔽32) | 3 |
| C2×C31×C3⋊D15 | 5 |
| C2×C3⋊D3×ΓL(1,𝔽32) | 5 |
| C2×C5×C3⋊D15 | 31 |