Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 180 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×Q16 | C2 | semidirect |
| 3. C3×C5×SD32 | C2 | semidirect |
| 4. C5×#828 | C2 | semidirect |
| 5. C5×#827 | C2 | semidirect |
| 6. C5×#800 | C2 | semidirect |
| 7. C5×D3×C16 | C2 | semidirect |
| 11. C3×C5×Q16 | C22 | semidirect |
| 15. C5×Dic12 | C22 | semidirect |
| 18. C3×C5×C16 | C22 | semidirect |
| 19. C5×C3⋊C16 | C22 | semidirect |
| 20. D3×SD32 | C5 | direct (N × H) |
| 26. C5×SD32 | D3 | direct (N × H) |
| 39. D3×Q16 | C2×C5 | semidirect |
| 41. C3×SD32 | C2×C5 | semidirect |
| 42. #828 | C2×C5 | semidirect |
| 43. #827 | C2×C5 | semidirect |
| 44. #800 | C2×C5 | semidirect |
| 45. D3×C16 | C2×C5 | semidirect |
| 50. C5×Q16 | C2×D3 | semidirect |
| 56. C5×C16 | C2×D3 | semidirect |
| 68. C3×Q16 | C22×C5 | semidirect |
| 72. Dic12 | C22×C5 | semidirect |
| 75. C3×C16 | C22×C5 | semidirect |
| 76. C3⋊C16 | C22×C5 | semidirect |
| 93. SD32 | C5×D3 | direct (N × H) |
| 98. C5×D3 | SD32 | direct (N × H) |
| 122. Q16 | C2×C5×D3 | semidirect |
| 128. C16 | C2×C5×D3 | semidirect |
| 129. C3×C5 | C2×SD32 | semidirect |
| 156. D3 | C5×SD32 | direct (N × H) |
| 157. C5 | D3×SD32 | direct (N × H) |
| 166. C3 | C2×C5×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×Q16 | 2 |
| C5×D3×D8 | 2 |
| C3×C5×SD32 | 2 |
| C5×#828 | 2 |
| C5×#827 | 2 |
| C5×#800 | 2 |
| C5×D3×C16 | 2 |
| C2×C5×SD32 | 3 |
| D3×SD32 | 5 |