Finite Group DatabasebetaFinite Group Databasebeta← C2×D5⋊(C3⋊ΓL(1,𝔽16)) #72229714
Order 3600.
744 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 179 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 | D5⋊(C3⋊ΓL(1,𝔽16)) |
| commutator, hypocenter | C32×C52 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52 | C2×C4 |
| prime radical | C2×C32×D52 | C2 |
| cosocle | C32×C5⋊D5 | C23 |
| LCS | G ▷ C32×C52 | |
| 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×D52 | 2 |
| C2×C3⋊(C3⋊#1044) | 2 |
| C2×C3⋊(C3⋊#1043) | 2 |
| D5⋊(C3⋊ΓL(1,𝔽16)) | 2 |
| C2×D5⋊ΓL(1,𝔽16) | 3 |
| C22×C3⋊ΓL(1,𝔽16) | 5 |