Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
188 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 9. #67718 | C5 | direct (N × H) |
| 109. C3×C5 | #1323 | semidirect |
| 131. C5 | #67718 | direct (N × H) |
| 139. C3 | C5×#1323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#424 | 2 |
| C5×#4549 | 2 |
| C5×#1323 | 3 |
| #67718 | 5 |