Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
328 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 22. #68096 | C5 | direct (N × H) |
| 209. C3×C5 | #1718 | semidirect |
| 238. C5 | #68096 | direct (N × H) |
| 247. C3 | C5×#1718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4682 | 2 |
| C5×#4681 | 2 |
| C5×#4680 | 2 |
| C3×C5×#322 | 2 |
| C5×#1718 | 3 |
| #68096 | 5 |