Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
694 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. C2×C5⋊#994 | C2 | semidirect |
| 2. C2×C5×#131⋊C3 | C2 | semidirect |
| 3. #66086⋊C3 | C2 | direct (N × H) |
| 4. C2×#66086 | C3 | semidirect |
| 7. C5⋊#994 | C22 | semidirect |
| 10. C5×#131⋊C3 | C22 | semidirect |
| 15. #66086 | C2×C3 | semidirect |
| 28. C2×#131⋊C3 | D5 | semidirect |
| 64. #131⋊C3 | C2×D5 | semidirect |
| 235. C2×C5 | #576⋊C3 | semidirect |
| 269. C5 | C2×#576⋊C3 | semidirect |
| 287. C2 | #66086⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5⋊#994 | 2 |
| C2×C5×#131⋊C3 | 2 |
| #66086⋊C3 | 2 |
| C2×#66086 | 3 |
| C2×C3×Dic20 | 4 |
| C2×#576⋊C3 | 5 |