Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
260 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 86 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×#124 | C2 | semidirect |
| 2. C2×C3×#689 | C2 | semidirect |
| 3. C2×C3×#688 | C2 | semidirect |
| 4. C2×C3×#687 | C2 | semidirect |
| 6. C3×#4021 | C2 | semidirect |
| 7. C3×C4×#168 | C2 | semidirect |
| 8. #65348 | C3 | direct (N × H) |
| 23. C5×#124 | C2×C3 | semidirect |
| 24. C2×#689 | C2×C3 | semidirect |
| 25. C2×#688 | C2×C3 | semidirect |
| 26. C2×#687 | C2×C3 | semidirect |
| 28. #4021 | C2×C3 | semidirect |
| 29. C4×#168 | C2×C3 | semidirect |
| 51. C3×#124 | D5 | semidirect |
| 111. #124 | C3×D5 | semidirect |
| 156. C3×C5 | #495 | semidirect |
| 191. C5 | C3×#495 | semidirect |
| 202. C3 | #65348 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#124 | 2 |
| C2×C3×#689 | 2 |
| C2×C3×#688 | 2 |
| C2×C3×#687 | 2 |
| C2×C3×#686 | 2 |
| C3×#4021 | 2 |
| C3×C4×#168 | 2 |
| #65348 | 3 |
| C3×#495 | 5 |