Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
660 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 160 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×Q8×D5 | C2 | semidirect |
| 3. #91836 | C2 | semidirect |
| 4. C5×#947 | C2 | semidirect |
| 5. D5×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C4×D5×Dic3 | C2 | semidirect |
| 7. #91374 | C2 | semidirect |
| 8. #91370 | C2 | semidirect |
| 9. #91326 | C2 | semidirect |
| 12. C2×C3×C5×Q8 | C22 | semidirect |
| 18. C2×C3×Dic10 | C22 | semidirect |
| 19. C2×C3×Dic10 | C22 | semidirect |
| 23. #6714 | C22 | semidirect |
| 24. C4×Dic15 | C22 | semidirect |
| 25. C5×(C2×D3)⋊C4 | C22 | semidirect |
| 26. C4×C5×Dic3 | C22 | semidirect |
| 27. #6667 | C22 | semidirect |
| 28. (C2×D3)⋊Dic5 | C22 | semidirect |
| 29. Dic3×Dic5 | C22 | semidirect |
| 31. C2×Q8×D5 | D3 | semidirect |
| 66. #947 | D5 | direct (N × H) |
| 70. C2×C5×Q8 | C2×D3 | semidirect |
| 79. C2×Dic10 | C2×D3 | semidirect |
| 80. C2×Dic10 | C2×D3 | semidirect |
| 107. C2×C3×Q8 | C2×D5 | semidirect |
| 118. (C2×D3)⋊C4 | C2×D5 | semidirect |
| 121. C4×Dic3 | C2×D5 | semidirect |
| 154. C3×D5 | #124 | semidirect |
| 194. C2×Q8 | D3×D5 | semidirect |
| 209. C3×C5 | C2×#124 | semidirect |
| 228. D5 | #947 | direct (N × H) |
| 254. C5 | C2×#947 | semidirect |
| 269. C3 | D5×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×D5 | 2 |
| C2×D5×D12 | 2 |
| #91836 | 2 |
| C5×#947 | 2 |
| D5×(C2×D3)⋊C4 | 2 |
| C4×D5×Dic3 | 2 |
| #91374 | 2 |
| #91370 | 2 |
| #91326 | 2 |
| D5×#124 | 3 |
| C2×#947 | 5 |