Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
172 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 90 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. #67802 | C5 | direct (N × H) |
| 116. C3×C5 | #1365 | semidirect |
| 139. C5 | #67802 | direct (N × H) |
| 147. C3 | C5×#1365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#500 | 2 |
| C5×C4⋊(C3⋊C16) | 2 |
| C5×#4458 | 2 |
| C5×#1365 | 3 |
| #67802 | 5 |