Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
572 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 96 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. D3×#3966 | C2 | semidirect |
| 3. #11746366 | C2 | semidirect |
| 4. C3×#64765 | C2 | semidirect |
| 5. #11746010 | C2 | semidirect |
| 7. C2×C5×#237 | C4 | semidirect |
| 10. C5×#940 | C4 | semidirect |
| 14. C5×#875 | C4 | semidirect |
| 15. C5×#872 | C4 | semidirect |
| 24. #64765 | D3 | semidirect |
| 28. C2×C3×C5×D4 | C2×C4 | semidirect |
| 38. C2×C5×Dic6 | C2×C4 | semidirect |
| 40. C3×C42×C5 | C2×C4 | semidirect |
| 46. C4×C5×Dic3 | C2×C4 | semidirect |
| 93. C2×#237 | Dic5 | semidirect |
| 96. #940 | Dic5 | semidirect |
| 101. #875 | Dic5 | semidirect |
| 102. #872 | Dic5 | semidirect |
| 115. C2×C5×D4 | C4×D3 | semidirect |
| 125. C42×C5 | C4×D3 | semidirect |
| 154. C2×C3×D4 | C2×Dic5 | semidirect |
| 165. C2×Dic6 | C2×Dic5 | semidirect |
| 167. C3×C42 | C2×Dic5 | semidirect |
| 174. C4×Dic3 | C2×Dic5 | semidirect |
| 271. C2×D4 | D3×Dic5 | semidirect |
| 284. C42 | D3×Dic5 | semidirect |
| 285. C3×C5 | #2127 | semidirect |
| 341. C5 | #69150 | semidirect |
| 360. C3 | #10602653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5715 | 2 |
| D3×#3966 | 2 |
| #11746366 | 2 |
| C3×#64765 | 2 |
| #11746010 | 2 |
| #10602653 | 3 |
| #69150 | 5 |