Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
196 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 78 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. C2×C3×C5×D8 | C2 | semidirect |
| 2. C2×C5×D24 | C2 | semidirect |
| 3. C5×#826 | C2 | direct (N × H) |
| 4. C2×C5×C3⋊C16 | C2 | semidirect |
| 9. C3×C5×D8 | C22 | semidirect |
| 12. C5×D24 | C22 | semidirect |
| 13. C5×C3⋊C16 | C22 | semidirect |
| 14. C2×#826 | C5 | direct (N × H) |
| 16. C2×C5×D8 | D3 | semidirect |
| 28. C2×C3×D8 | C2×C5 | semidirect |
| 29. C2×D24 | C2×C5 | semidirect |
| 30. #826 | C2×C5 | direct (N × H) |
| 31. C2×C3⋊C16 | C2×C5 | semidirect |
| 37. C5×D8 | C2×D3 | semidirect |
| 51. C3×D8 | C22×C5 | semidirect |
| 54. D24 | C22×C5 | semidirect |
| 55. C3⋊C16 | C22×C5 | semidirect |
| 66. C2×D8 | C5×D3 | semidirect |
| 70. C2×C3×C5 | D16 | semidirect |
| 94. D8 | C2×C5×D3 | semidirect |
| 97. C3×C5 | C2×D16 | semidirect |
| 107. C2×C5 | #826 | direct (N × H) |
| 119. C2×C3 | C5×D16 | semidirect |
| 122. C5 | C2×#826 | direct (N × H) |
| 130. C3 | C2×C5×D16 | semidirect |
| 133. C2 | C5×#826 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D8 | 2 |
| C2×C5×D24 | 2 |
| C5×#826 | 2 |
| C2×C5×C3⋊C16 | 2 |
| C2×C5×D16 | 3 |
| C2×#826 | 5 |