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 |
|---|---|---|
| 2. C2×D5×Dic6 | C2 | semidirect |
| 3. #91825 | C2 | semidirect |
| 4. C5×#936 | C2 | semidirect |
| 5. D5×#217 | C2 | semidirect |
| 6. #91534 | C2 | semidirect |
| 7. C4×D5×Dic3 | C2 | semidirect |
| 8. #91368 | C2 | semidirect |
| 9. #91364 | C2 | semidirect |
| 13. C2×Dic30 | C22 | semidirect |
| 14. C2×C5×Dic6 | C22 | semidirect |
| 19. C2×#1204 | C22 | semidirect |
| 23. #6719 | C22 | semidirect |
| 24. C4×Dic15 | C22 | semidirect |
| 25. C5×#217 | C22 | semidirect |
| 26. C4×C5×Dic3 | C22 | semidirect |
| 27. #6665 | C22 | semidirect |
| 28. #6665 | C22 | semidirect |
| 29. Dic3×Dic5 | C22 | semidirect |
| 67. #936 | D5 | direct (N × H) |
| 114. C2×Dic6 | C2×D5 | semidirect |
| 118. #217 | C2×D5 | semidirect |
| 121. C4×Dic3 | C2×D5 | semidirect |
| 155. C3×D5 | #124 | semidirect |
| 209. C3×C5 | C2×#124 | semidirect |
| 228. D5 | #936 | direct (N × H) |
| 254. C5 | C2×#936 | 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×D4×D5 | 2 |
| C2×D5×Dic6 | 2 |
| #91825 | 2 |
| C5×#936 | 2 |
| D5×#217 | 2 |
| #91534 | 2 |
| C4×D5×Dic3 | 2 |
| #91368 | 2 |
| #91364 | 2 |
| D5×#124 | 3 |
| C2×#936 | 5 |