Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
608 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 122 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 | C22 | D3×#1043 |
| commutator | C2×C3×C52 | C42 |
| Fitting, socle | C22×C3×C52 | C2×C4 |
| prime radical, cosocle | C22×C3×C5⋊D5 | C22 |
| hypocenter | C3×C52 | #95 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C2×C3⋊#1043 | C4 | semidirect |
| 11. C2×C3×#1043 | C4 | semidirect |
| 12. C2×C3⋊#1039 | C4 | semidirect |
| 13. C2×C52×Dic3 | C4 | semidirect |
| 40. C2×#1043 | Dic3 | semidirect |
| 61. C2×C5×Dic3 | AGL(1,𝔽5) | semidirect |
| 79. C3×C52 | #95 | semidirect |
| 120. C52 | C3⋊#95 | semidirect |
| 131. C2×Dic3 | #1043 | semidirect |
| 146. C3×C5 | (C2×AGL(1,𝔽5))⋊C4 | semidirect |
| 183. C5 | (C2×AGL(1,𝔽5))⋊Dic3 | semidirect |
| 195. C3 | #11716874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊#1043 | 2 |
| C22×C3×#1043 | 2 |
| C2×Dic3×C5⋊D5 | 2 |
| #11716874 | 3 |
| (C2×AGL(1,𝔽5))⋊Dic3 | 5 |