Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
718 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 184 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. C2×C5×#131⋊C3 | C2 | direct (N × H) |
| 3. C22×C5×#131 | C3 | semidirect |
| 8. C5×#131⋊C3 | C22 | direct (N × H) |
| 9. C22×#131⋊C3 | C5 | direct (N × H) |
| 12. C2×C5×#131 | C2×C3 | semidirect |
| 21. C2×#131⋊C3 | C2×C5 | direct (N × H) |
| 31. C5×#131 | C22×C3 | semidirect |
| 38. C22×#131 | C3×C5 | semidirect |
| 48. #131⋊C3 | C22×C5 | direct (N × H) |
| 76. C2×#131 | C2×C3×C5 | semidirect |
| 119. #131 | C22×C3×C5 | semidirect |
| 137. C22×C5 | #131⋊C3 | direct (N × H) |
| 175. C2×C5 | C2×#131⋊C3 | direct (N × H) |
| 201. C5 | C22×#131⋊C3 | direct (N × H) |
| 206. C22 | C5×#131⋊C3 | direct (N × H) |
| 215. C2 | C2×C5×#131⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#41⋊C3 | 2 |
| C2×C5×#131⋊C3 | 2 |
| C22×C5×#131 | 3 |
| C22×C3×C5×C8 | 4 |
| C22×#131⋊C3 | 5 |