Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
640 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 140 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×C3×#4008 | C2 | semidirect |
| 3. C3×#65686 | C2 | semidirect |
| 4. C3×#65682 | C2 | semidirect |
| 5. #10604612 | C3 | direct (N × H) |
| 9. C3×C5×#127 | C4 | semidirect |
| 11. C3×#4082 | C4 | semidirect |
| 14. C3×#4015 | C4 | semidirect |
| 20. C2×#4008 | C2×C3 | semidirect |
| 21. #65686 | C2×C3 | semidirect |
| 22. #65682 | C2×C3 | semidirect |
| 35. C3×C4×AGL(1,𝔽5) | D4 | semidirect |
| 49. C5×#127 | C3×C4 | semidirect |
| 51. #4082 | C3×C4 | semidirect |
| 54. #4015 | C3×C4 | semidirect |
| 81. C3×#127 | AGL(1,𝔽5) | semidirect |
| 102. C4×AGL(1,𝔽5) | C3×D4 | semidirect |
| 166. #127 | C3×AGL(1,𝔽5) | semidirect |
| 229. C3×C5 | #1963 | semidirect |
| 269. C5 | C3×#1963 | semidirect |
| 282. C3 | #10604612 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66050 | 2 |
| C2×C3×#4008 | 2 |
| C3×#65686 | 2 |
| C3×#65682 | 2 |
| #10604612 | 3 |
| C3×#1963 | 5 |