Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
328 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 114 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. #71220 | C5 | direct (N × H) |
| 209. C3×C5 | #1718 | semidirect |
| 238. C5 | #71220 | 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 |
|---|---|
| C3×C5×#487 | 2 |
| C5×#5093 | 2 |
| C5×#5080 | 2 |
| C5×#5079 | 2 |
| C5×#5078 | 2 |
| C5×#4681 | 2 |
| C5×#4455 | 2 |
| C5×#1718 | 3 |
| #71220 | 5 |