Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
504 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C5 | C23×D3 |
| commutator, cosocle | C22×C3 | C24×C5 |
| Frattini | C22 | C23×C5×D3 |
| Fitting | C3×C5×#126 | C2 |
| socle | C22×C3×C5 | C24 |
| hypercenter | C5×#126 | D3 |
| hypocenter | C3 | C5×#560 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22×C5 ◁ C5×#126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#126 | C2 | semidirect |
| 2. C5×#895 | C2 | semidirect |
| 3. C5×#894 | C2 | semidirect |
| 4. C5×#884 | C2 | semidirect |
| 5. C5×#882 | C2 | semidirect |
| 6. C5×#876 | C2 | semidirect |
| 7. C5×#874 | C2 | semidirect |
| 13. C2×C5×D12 | C22 | semidirect |
| 14. C2×C4×C5×D3 | C22 | semidirect |
| 15. C3×C5×C4⋊C4 | C22 | semidirect |
| 17. C3×C42×C5 | C22 | semidirect |
| 20. C5×(C2×D3)⋊C4 | C22 | semidirect |
| 21. C5×Dic3⋊C4 | C22 | semidirect |
| 22. #5711 | C5 | direct (N × H) |
| 25. C5×#126 | D3 | semidirect |
| 43. C3×#126 | C2×C5 | semidirect |
| 44. #895 | C2×C5 | semidirect |
| 45. #894 | C2×C5 | semidirect |
| 46. #884 | C2×C5 | semidirect |
| 47. #882 | C2×C5 | semidirect |
| 48. #876 | C2×C5 | semidirect |
| 49. #874 | C2×C5 | semidirect |
| 57. C5×C4⋊C4 | C2×D3 | semidirect |
| 62. C42×C5 | C2×D3 | semidirect |
| 79. C2×D12 | C22×C5 | semidirect |
| 80. C2×C4×D3 | C22×C5 | semidirect |
| 81. C3×C4⋊C4 | C22×C5 | semidirect |
| 83. C3×C42 | C22×C5 | semidirect |
| 86. (C2×D3)⋊C4 | C22×C5 | semidirect |
| 87. Dic3⋊C4 | C22×C5 | semidirect |
| 103. #126 | C5×D3 | semidirect |
| 144. C4⋊C4 | C2×C5×D3 | semidirect |
| 149. C42 | C2×C5×D3 | semidirect |
| 150. C3×C5 | #560 | semidirect |
| 185. C5 | #5711 | direct (N × H) |
| 197. C3 | C5×#560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#126 | 2 |
| C5×#895 | 2 |
| C5×#894 | 2 |
| C5×#884 | 2 |
| C5×#882 | 2 |
| C5×#876 | 2 |
| C5×#874 | 2 |
| C5×#560 | 3 |
| #5711 | 5 |