Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
668 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 2. C5×#568⋊C3 | C2 | semidirect |
| 3. C2×C5×#131⋊C3 | C2 | semidirect |
| 4. C5×#3573 | C3 | semidirect |
| 9. C5×#131⋊C3 | C22 | semidirect |
| 10. C5×#131⋊C3 | C22 | semidirect |
| 11. #85629 | C5 | direct (N × H) |
| 15. C5×#568 | C2×C3 | semidirect |
| 18. C2×C5×#131 | C2×C3 | semidirect |
| 26. #568⋊C3 | C2×C5 | semidirect |
| 27. C2×#131⋊C3 | C2×C5 | semidirect |
| 51. #3573 | C3×C5 | semidirect |
| 62. #131⋊C3 | C22×C5 | semidirect |
| 63. #131⋊C3 | C22×C5 | semidirect |
| 99. #568 | C2×C3×C5 | semidirect |
| 102. C2×#131 | C2×C3×C5 | semidirect |
| 240. C5 | #85629 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5945 | 2 |
| C5×#568⋊C3 | 2 |
| C2×C5×#131⋊C3 | 2 |
| C5×#3573 | 3 |
| C3×C5×#131 | 4 |
| #85629 | 5 |