Finite Group DatabasebetaFinite Group Databasebeta← C2×C5×ΓL(1,𝔽16)⋊D3 #72231212
Order 3600.
526 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 118 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×C5 | ΓL(1,𝔽16)⋊D3 |
| commutator, hypocenter | C32×C5 | C22×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52 | C2×C4 |
| prime radical | C2×C5×D5×C3⋊D3 | C2 |
| cosocle | C32×D5 | C23×C5 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2×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 |
|---|---|
| C2×C5×D5×C3⋊D3 | 2 |
| C2×C3×C5×ΓL(1,𝔽16) | 2 |
| C5×ΓL(1,𝔽16)⋊D3 | 2 |
| C2×C5×D3×AGL(1,𝔽5) | 3 |
| C2×ΓL(1,𝔽16)⋊D3 | 5 |
| C2×C5×#624 | 5 |