Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
236 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 53 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 | C4 | #10597183 |
| commutator, hypocenter | C3×C52 | C4×C8 |
| Fitting | C3×C4×C52 | C2×C4 |
| socle | C2×C3×C52 | C42 |
| prime radical | C2×C3×C5⋊D5 | C2×C4 |
| cosocle | C3×C4×C5⋊D5 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C3×#6034 | C4 | semidirect |
| 8. C5×C3⋊#168 | C4 | semidirect |
| 14. C3⋊#1043 | C8 | semidirect |
| 23. #6034 | Dic3 | semidirect |
| 33. C3⋊#168 | AGL(1,𝔽5) | semidirect |
| 44. C3×C52 | C4×C8 | semidirect |
| 70. C52 | C8×Dic3 | semidirect |
| 87. C3×C5 | C8×AGL(1,𝔽5) | semidirect |
| 103. C5 | ΓL(1,𝔽16)⋊C8 | semidirect |
| 108. C3 | #11716761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C3⋊#1043 | 2 |
| C3×#87862 | 2 |
| #11925150 | 2 |
| #11716761 | 3 |
| ΓL(1,𝔽16)⋊C8 | 5 |