Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
372 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 4. C5×#4682 | C2 | semidirect |
| 5. C5×#4681 | C2 | semidirect |
| 6. C5×#4681 | C2 | semidirect |
| 7. C3×C5×#322 | C2 | semidirect |
| 22. #68093 | C5 | direct (N × H) |
| 29. C5×#322 | D3 | semidirect |
| 50. #4682 | C2×C5 | semidirect |
| 51. #4681 | C2×C5 | semidirect |
| 52. #4681 | C2×C5 | semidirect |
| 53. C3×#322 | C2×C5 | semidirect |
| 120. #322 | C5×D3 | semidirect |
| 224. C3×C5 | #1719 | semidirect |
| 259. C5 | #68093 | direct (N × H) |
| 270. C3 | C5×#1719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4694 | 2 |
| C5×#4693 | 2 |
| C5×#4682 | 2 |
| C5×#4681 | 2 |
| C3×C5×#322 | 2 |
| C5×#1719 | 3 |
| #68093 | 5 |