Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
200 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 12. #67781 | C5 | direct (N × H) |
| 151. C3×C5 | #1342 | semidirect |
| 178. C5 | #67781 | direct (N × H) |
| 187. C3 | C5×#1342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#470 | 2 |
| C5×C3⋊#338 | 2 |
| C5×#4553 | 2 |
| C5×#1342 | 3 |
| #67781 | 5 |