Finite Group DatabasebetaFinite Group Databasebeta← D3×C5⋊(C5⋊(D31⋊C3)) #42124815
Order 27900.
352 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C31 | C22×C3 |
| LCS | G ▷ C3×C52×C31 | |
| UCS | C1 | |
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 |
|---|---|
| C3⋊(C5⋊(C5⋊(D31⋊C3))) | 2 |
| C52×D3×C31⋊C3 | 2 |
| C3×C5⋊(C5⋊(D31⋊C3)) | 2 |
| D3×C5⋊D155 | 3 |
| C2×C5⋊(C5⋊(D31⋊C3)) | 3 |
| D3×C5⋊(D31⋊C3) | 5 |
| C3×D3×C5⋊D5 | 31 |