Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
344 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 344 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 |
|---|---|---|
| 18. #71252 | C5 | direct (N × H) |
| 171. C3×C5 | #1663 | semidirect |
| 192. C5 | #71252 | direct (N × H) |
| 200. C3 | C5×#1663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C3⋊#564 | 2 |
| C3×C5×#491 | 2 |
| C5×#5081 | 2 |
| C5×#4543 | 2 |
| C5×#4465 | 2 |
| C5×#1663 | 3 |
| #71252 | 5 |