Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
352 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 6. #10602131 | C3 | direct (N × H) |
| 148. C3×C5 | #1716 | semidirect |
| 169. C5 | C3×#1716 | semidirect |
| 176. C3 | #10602131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#498 | 2 |
| C3×#65370 | 2 |
| C3×#65368 | 2 |
| C3×#64988 | 2 |
| C3×#64675 | 2 |
| #10602131 | 3 |
| C3×#1716 | 5 |