Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
560 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 246 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×C5×D3×Q8 | C2 | semidirect |
| 2. C3×C4×C5×Q8 | C2 | semidirect |
| 3. C5×#897 | C2 | semidirect |
| 5. C5×#869 | C2 | semidirect |
| 17. Q8×D12 | C5 | direct (N × H) |
| 21. C4×C5×Q8 | D3 | semidirect |
| 24. C3×C5×Q8 | D4 | semidirect |
| 29. C5×D12 | Q8 | direct (N × H) |
| 32. C2×D3×Q8 | C2×C5 | semidirect |
| 33. C3×C4×Q8 | C2×C5 | semidirect |
| 34. #897 | C2×C5 | semidirect |
| 36. #869 | C2×C5 | semidirect |
| 51. C2×C5×D3 | C2×Q8 | semidirect |
| 54. C3×C4×C5 | C2×Q8 | semidirect |
| 68. C5×Q8 | D12 | direct (N × H) |
| 78. C4×Q8 | C5×D3 | semidirect |
| 85. C3×Q8 | C5×D4 | semidirect |
| 90. D12 | C5×Q8 | direct (N × H) |
| 100. C4×C5 | D3×Q8 | semidirect |
| 111. C3×C5 | D4×Q8 | semidirect |
| 115. C2×D3 | C2×C5×Q8 | semidirect |
| 118. C3×C4 | C2×C5×Q8 | semidirect |
| 126. Q8 | C5×D12 | direct (N × H) |
| 137. C5 | Q8×D12 | direct (N × H) |
| 145. C4 | C5×D3×Q8 | semidirect |
| 146. C3 | C5×D4×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×Q8 | 2 |
| C3×C4×C5×Q8 | 2 |
| C5×#897 | 2 |
| C4×C5×D12 | 2 |
| C5×#869 | 2 |
| C5×D4×Q8 | 3 |
| Q8×D12 | 5 |