Finite Group DatabasebetaFinite Group Databasebeta← C2×C3⋊(C5⋊AGL(1,𝔽31)) #42124696
Order 27900.
224 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 52 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⋊AGL(1,𝔽31)) |
| commutator, cosocle, hypocenter | C3×C5×C31 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C31 | C2×C3×C5 |
| LCS | G ▷ C3×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×C3×C5×(C31⋊C3)⋊C5 | 2 |
| C3⋊(C5⋊AGL(1,𝔽31)) | 2 |
| C2×C3⋊(C5⋊(D31⋊C5)) | 3 |
| C2×C5⋊AGL(1,𝔽31) | 3 |
| C2×C3⋊(C5⋊(D31⋊C3)) | 5 |
| C2×C3⋊AGL(1,𝔽31) | 5 |
| C2×C3×C5×D15 | 31 |