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×C5×D3×Q8 | C2 | semidirect |
| 3. #91836 | C2 | semidirect |
| 4. C3×#4093 | C2 | semidirect |
| 5. D3×#685 | C2 | semidirect |
| 6. #91455 | C2 | semidirect |
| 7. C4×D3×Dic5 | C2 | semidirect |
| 8. #91375 | C2 | semidirect |
| 9. #91368 | C2 | semidirect |
| 12. C2×C3×C5×Q8 | C22 | semidirect |
| 17. C2×C5×Dic6 | C22 | semidirect |
| 18. C2×C5×Dic6 | C22 | semidirect |
| 23. #6714 | C22 | semidirect |
| 24. C4×Dic15 | C22 | semidirect |
| 25. C3×#685 | C22 | semidirect |
| 26. C3×C4×Dic5 | C22 | semidirect |
| 27. #6667 | C22 | semidirect |
| 28. #6665 | C22 | semidirect |
| 29. Dic3×Dic5 | C22 | semidirect |
| 37. #4093 | D3 | direct (N × H) |
| 60. C2×D3×Q8 | D5 | semidirect |
| 73. C2×C5×Q8 | C2×D3 | semidirect |
| 84. #685 | C2×D3 | semidirect |
| 87. C4×Dic5 | C2×D3 | semidirect |
| 104. C2×C3×Q8 | C2×D5 | semidirect |
| 113. C2×Dic6 | C2×D5 | semidirect |
| 114. C2×Dic6 | C2×D5 | semidirect |
| 155. C5×D3 | #124 | semidirect |
| 194. C2×Q8 | D3×D5 | semidirect |
| 209. C3×C5 | C2×#124 | semidirect |
| 253. D3 | #4093 | direct (N × H) |
| 254. C5 | D3×#124 | semidirect |
| 269. C3 | C2×#4093 | 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 |
| C2×D3×D20 | 2 |
| #91836 | 2 |
| C3×#4093 | 2 |
| D3×#685 | 2 |
| #91455 | 2 |
| C4×D3×Dic5 | 2 |
| #91375 | 2 |
| #91368 | 2 |
| C2×#4093 | 3 |
| D3×#124 | 5 |