Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
196 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 66 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. C5×D3×D8 | C2 | semidirect |
| 2. C3×C5×D16 | C2 | semidirect |
| 3. C5×#826 | C2 | semidirect |
| 4. C5×D48 | C2 | semidirect |
| 5. C5×D3×C16 | C2 | semidirect |
| 8. C3×C5×D8 | C22 | semidirect |
| 10. C5×D24 | C22 | semidirect |
| 12. C3×C5×C16 | C22 | semidirect |
| 13. C5×C3⋊C16 | C22 | semidirect |
| 14. D3×D16 | C5 | direct (N × H) |
| 18. C5×D16 | D3 | direct (N × H) |
| 27. D3×D8 | C2×C5 | semidirect |
| 28. C3×D16 | C2×C5 | semidirect |
| 29. #826 | C2×C5 | semidirect |
| 30. D48 | C2×C5 | semidirect |
| 31. D3×C16 | C2×C5 | semidirect |
| 35. C5×D8 | C2×D3 | semidirect |
| 38. C5×C16 | C2×D3 | semidirect |
| 47. C3×D8 | C22×C5 | semidirect |
| 49. D24 | C22×C5 | semidirect |
| 51. C3×C16 | C22×C5 | semidirect |
| 52. C3⋊C16 | C22×C5 | semidirect |
| 63. D16 | C5×D3 | direct (N × H) |
| 68. C5×D3 | D16 | direct (N × H) |
| 85. D8 | C2×C5×D3 | semidirect |
| 88. C16 | C2×C5×D3 | semidirect |
| 89. C3×C5 | C2×D16 | semidirect |
| 110. D3 | C5×D16 | direct (N × H) |
| 111. C5 | D3×D16 | direct (N × H) |
| 118. C3 | C2×C5×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×D8 | 2 |
| C3×C5×D16 | 2 |
| C5×#826 | 2 |
| C5×D48 | 2 |
| C5×D3×C16 | 2 |
| C2×C5×D16 | 3 |
| D3×D16 | 5 |