Finite Group DatabasebetaFinite Group DatabasebetaOrder 23100.
320 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D21×AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C3×C7×C11 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C11 | C22×C5 |
| LCS | G ▷ C3×C7×C11 | |
| UCS | C1 ◁ C5 | |
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 |
|---|---|
| C5×D21×C11⋊C5 | 2 |
| C5×C3⋊(C7⋊AGL(1,𝔽11)) | 2 |
| C3×C5×C7×AGL(1,𝔽11) | 2 |
| C5×D7×AGL(1,𝔽11) | 3 |
| C5×D11×D21 | 5 |
| D21×AGL(1,𝔽11) | 5 |
| C5×D3×AGL(1,𝔽11) | 7 |
| C2×C52×D21 | 11 |