Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
342 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 48 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 | D52×A4 |
| commutator, hypocenter | C22×C52 | C2×C3×C4 |
| Fitting, socle, cosocle | C23×C52 | C22×C3 |
| prime radical | C2×A4×C5⋊D5 | C2 |
| LCS | G ▷ C22×C52 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×A4×Dic5 | C2 | semidirect |
| 3. C22×#6036 | C3 | semidirect |
| 5. A4×C5⋊D5 | C4 | semidirect |
| 9. C22×C5×Dic5 | C2×C3 | semidirect |
| 14. C52×A4 | C2×C4 | semidirect |
| 19. A4×Dic5 | D5 | semidirect |
| 24. C22×C5⋊D5 | C3×C4 | semidirect |
| 30. #6036 | A4 | direct (N × H) |
| 41. C22×C52 | C2×C3×C4 | semidirect |
| 49. C5×Dic5 | C2×A4 | semidirect |
| 54. C22×Dic5 | C3×D5 | semidirect |
| 63. C5×A4 | C4×D5 | semidirect |
| 70. C5⋊D5 | C4×A4 | semidirect |
| 97. C52 | C2×C4×A4 | semidirect |
| 106. C22×C5 | C3×C4×D5 | semidirect |
| 122. Dic5 | D5×A4 | semidirect |
| 131. A4 | #6036 | direct (N × H) |
| 157. C5 | C4×D5×A4 | semidirect |
| 166. C22 | C3×#6036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×A4×C5⋊D5 | 2 |
| C5×A4×Dic5 | 2 |
| C22×#6036 | 3 |
| C3×#6036 | 4 |
| C4×D5×A4 | 5 |