Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#135 | C2 | semidirect |
| 2. C3×#4050 | C2 | semidirect |
| 3. C3×#3961 | C2 | semidirect |
| 4. C3×#3960 | C2 | semidirect |
| 5. C3×#3959 | C2 | semidirect |
| 6. C3×#3958 | C2 | semidirect |
| 7. C2×C3×#672 | C2 | semidirect |
| 8. #65483 | C3 | direct (N × H) |
| 21. C5×#135 | C2×C3 | semidirect |
| 22. #4050 | C2×C3 | semidirect |
| 23. #3961 | C2×C3 | semidirect |
| 24. #3960 | C2×C3 | semidirect |
| 25. #3959 | C2×C3 | semidirect |
| 26. #3958 | C2×C3 | semidirect |
| 27. C2×#672 | C2×C3 | semidirect |
| 40. C3×#135 | D5 | semidirect |
| 88. #135 | C3×D5 | semidirect |
| 127. C3×C5 | #508 | semidirect |
| 154. C5 | C3×#508 | semidirect |
| 162. C3 | #65483 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#135 | 2 |
| C3×#4050 | 2 |
| C3×#3961 | 2 |
| C3×#3960 | 2 |
| C3×#3959 | 2 |
| C3×#3958 | 2 |
| C2×C3×#672 | 2 |
| #65483 | 3 |
| C3×#508 | 5 |