Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
620 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C3 | C23×D5 |
| commutator, cosocle | C22×C5 | C24×C3 |
| Frattini | C22 | C23×C3×D5 |
| Fitting | C3×C5×#127 | C2 |
| socle | C22×C3×C5 | C24 |
| hypercenter | C3×#127 | D5 |
| hypocenter | C5 | C3×#532 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C3 ◁ C3×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#711 | C2 | semidirect |
| 2. C3×C5×#127 | C2 | semidirect |
| 3. C3×#4084 | C2 | semidirect |
| 4. C3×#4082 | C2 | semidirect |
| 5. C3×D4×Dic5 | C2 | semidirect |
| 6. C3×C42×D5 | C2 | semidirect |
| 7. C3×#4015 | C2 | semidirect |
| 8. #66050 | C3 | direct (N × H) |
| 23. C2×#711 | C2×C3 | semidirect |
| 24. C5×#127 | C2×C3 | semidirect |
| 25. #4084 | C2×C3 | semidirect |
| 26. #4082 | C2×C3 | semidirect |
| 27. D4×Dic5 | C2×C3 | semidirect |
| 28. C42×D5 | C2×C3 | semidirect |
| 29. #4015 | C2×C3 | semidirect |
| 42. C3×C4×D5 | D4 | semidirect |
| 46. C3×#127 | D5 | semidirect |
| 71. C3×C4×C5 | #41 | semidirect |
| 100. C4×D5 | C3×D4 | semidirect |
| 104. #127 | C3×D5 | semidirect |
| 133. C4×C5 | C3×#41 | semidirect |
| 150. C3×C5 | #532 | semidirect |
| 160. C3×C4 | #711 | semidirect |
| 183. C5 | C3×#532 | semidirect |
| 193. C4 | C3×#711 | semidirect |
| 194. C3 | #66050 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#711 | 2 |
| C3×C5×#127 | 2 |
| C3×#4084 | 2 |
| C3×#4082 | 2 |
| C3×D4×Dic5 | 2 |
| C3×C42×D5 | 2 |
| C3×#4015 | 2 |
| #66050 | 3 |
| C3×#532 | 5 |