Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
544 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 11. C3×#4002 | C4 | semidirect |
| 12. #91087 | C4 | semidirect |
| 13. C5×#803 | C4 | semidirect |
| 14. #90952 | C4 | semidirect |
| 42. #4002 | Dic3 | semidirect |
| 68. #803 | AGL(1,𝔽5) | semidirect |
| 166. C3×C5 | #1745 | semidirect |
| 194. C5 | #69805 | semidirect |
| 203. C3 | #10603878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×ΓL(1,𝔽16) | 2 |
| C3×#65676 | 2 |
| D5×#803 | 2 |
| #11746517 | 2 |
| #10603878 | 3 |
| #69805 | 5 |