Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
168 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 37 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 |
|---|---|---|
| 5. C3×C5×#125 | C4 | semidirect |
| 11. C3×C4×#168 | C4 | semidirect |
| 28. C5×#125 | Dic3 | semidirect |
| 34. C4×#168 | Dic3 | semidirect |
| 46. C3×#125 | AGL(1,𝔽5) | semidirect |
| 92. #125 | ΓL(1,𝔽16) | semidirect |
| 129. C3×C5 | #1414 | semidirect |
| 154. C5 | #67782 | semidirect |
| 163. C3 | #10598741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65357 | 2 |
| #11746727 | 2 |
| #11746725 | 2 |
| #10598741 | 3 |
| #67782 | 5 |