Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
244 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 110 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×C4×C5×Q8 | C2 | semidirect |
| 4. C5×#835 | C2 | semidirect |
| 6. C5×#808 | C2 | semidirect |
| 7. C4×C5×C3⋊C8 | C2 | semidirect |
| 16. C5×#215 | C4 | direct (N × H) |
| 21. C4×#215 | C5 | direct (N × H) |
| 23. C4×C5×Q8 | D3 | semidirect |
| 31. C3×C5×Q8 | C2×C4 | semidirect |
| 42. C5×C3⋊C8 | C2×C4 | semidirect |
| 43. C3×C4×Q8 | C2×C5 | semidirect |
| 46. #835 | C2×C5 | semidirect |
| 48. #808 | C2×C5 | semidirect |
| 49. C4×C3⋊C8 | C2×C5 | semidirect |
| 70. C3×C4×C5 | SD16 | semidirect |
| 81. #215 | C4×C5 | direct (N × H) |
| 88. C5×Q8 | C4×D3 | semidirect |
| 101. C4×Q8 | C5×D3 | semidirect |
| 113. C3×Q8 | C2×C4×C5 | semidirect |
| 124. C3⋊C8 | C2×C4×C5 | semidirect |
| 133. C4×C5 | #215 | direct (N × H) |
| 148. C3×C5 | C4×SD16 | semidirect |
| 156. C3×C4 | C5×SD16 | semidirect |
| 166. Q8 | C4×C5×D3 | semidirect |
| 182. C5 | C4×#215 | direct (N × H) |
| 191. C4 | C5×#215 | direct (N × H) |
| 194. C3 | C4×C5×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×Q8 | 2 |
| C2×C5×#215 | 2 |
| C4×C5×D12 | 2 |
| C5×#835 | 2 |
| C5×#809 | 2 |
| C5×#808 | 2 |
| C4×C5×C3⋊C8 | 2 |
| C4×C5×SD16 | 3 |
| C4×#215 | 5 |