Finite Group DatabasebetaFinite Group Databasebeta← (C11⋊AGL(1,𝔽7))⋊(C5⋊D5) #37528544
Order 23100.
320 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 73 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 | C52×C7×C11 | C22×C3 |
| LCS | G ▷ C52×C7×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 |
|---|---|
| ΓL(1,𝔽8)×C5⋊D55 | 2 |
| C11×C5⋊(C5⋊AGL(1,𝔽7)) | 2 |
| C52×C11⋊AGL(1,𝔽7) | 2 |
| D77⋊(C5⋊D5) | 3 |
| D55⋊AGL(1,𝔽7) | 5 |
| C3×D11×C5⋊D5 | 7 |
| AGL(1,𝔽7)×C5⋊D5 | 11 |