Finite Group DatabasebetaFinite Group DatabasebetaOrder 32340.
240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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, hypocenter | C5×C72×C11 | C3×C4 |
| prime radical | D5×C11×#3861 | C2 |
| cosocle | C72×D5×C11 | C2×C3 |
| LCS | G ▷ C5×C72×C11 | |
| 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 |
|---|---|
| D5×C11×#3861 | 2 |
| C7⋊(C7⋊(C11⋊AGL(1,𝔽5))) | 3 |
| C11⋊#10596874 | 5 |
| C11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5)) | 7 |
| #15668765 | 11 |