Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
542 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 76 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×#986 | C2 | semidirect |
| 2. C2×C5×#131⋊C3 | C2 | semidirect |
| 3. C5×#5407 | C2 | direct (N × H) |
| 7. C5×#986 | C22 | semidirect |
| 10. C5×#131⋊C3 | C22 | semidirect |
| 11. C2×#5407 | C5 | direct (N × H) |
| 14. C2×C5×#131 | D3 | semidirect |
| 26. C2×#986 | C2×C5 | semidirect |
| 27. C2×#131⋊C3 | C2×C5 | semidirect |
| 28. #5407 | C2×C5 | direct (N × H) |
| 42. C5×#131 | C2×D3 | semidirect |
| 57. #986 | C22×C5 | semidirect |
| 60. #131⋊C3 | C22×C5 | semidirect |
| 92. C2×#131 | C5×D3 | semidirect |
| 145. #131 | C2×C5×D3 | semidirect |
| 210. C2×C5 | #5407 | direct (N × H) |
| 238. C5 | C2×#5407 | direct (N × H) |
| 255. C2 | C5×#5407 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#986 | 2 |
| C2×C5×#131⋊C3 | 2 |
| C5×#5407 | 2 |
| C2×C5×#472 | 3 |
| C2×C5×D24 | 4 |
| C2×#5407 | 5 |