Finite Group DatabasebetaFinite Group DatabasebetaOrder 4800.
5920 conjugacy classes of subgroups; only the 997 normal subgroups are shown.
This group has 5920 conjugacy classes of subgroups — too many to draw. Only its 997 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #10597182 |
| commutator, hypocenter | C3×C52 | C24×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C52 | C2×C4 |
| prime radical | C23×D15⋊D5 | C2 |
| cosocle | C3×C5⋊D5 | C25 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C23 | |
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 |
|---|---|
| C23×C3⋊#1044 | 2 |
| C23×D15⋊D5 | 2 |
| C22×#10597182 | 2 |
| C23×C3×#1043 | 2 |
| C23×D5⋊AGL(1,𝔽5) | 3 |
| C23×D3×AGL(1,𝔽5) | 5 |