Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
356 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 64 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 | C2 | D3×D5⋊AGL(1,𝔽5) |
| commutator, Fitting, socle | C2×C3×C52 | C22×C4 |
| prime radical | C2×D15⋊D5 | C22 |
| cosocle | C2×C3×C5⋊D5 | C23 |
| hypocenter | C3×C52 | #117 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11925349 | C2 | semidirect |
| 5. Dic3⋊#1044 | C2 | semidirect |
| 6. Dic3⋊#1043 | C2 | semidirect |
| 7. C3×#87830 | C2 | semidirect |
| 14. Dic5×D15 | C4 | semidirect |
| 16. C5×#1200 | C4 | semidirect |
| 25. #87830 | D3 | semidirect |
| 69. #1200 | AGL(1,𝔽5) | semidirect |
| 93. C3×C52 | #117 | semidirect |
| 146. C52 | #872 | semidirect |
| 182. C3×C5 | #4130 | semidirect |
| 216. C5 | #91909 | semidirect |
| 228. C3 | #11717354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11925416 | 2 |
| #11925360 | 2 |
| #11925355 | 2 |
| #11925349 | 2 |
| Dic3⋊#1044 | 2 |
| Dic3⋊#1043 | 2 |
| C3×#87830 | 2 |
| #11717354 | 3 |
| #91909 | 5 |