Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
314 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 3. C4×C5×#131 | C3 | semidirect |
| 5. C5×#131⋊C3 | C4 | direct (N × H) |
| 8. C4×#131⋊C3 | C5 | direct (N × H) |
| 22. C5×#131 | C3×C4 | semidirect |
| 33. C4×#131 | C3×C5 | semidirect |
| 39. #131⋊C3 | C4×C5 | direct (N × H) |
| 87. #131 | C3×C4×C5 | semidirect |
| 110. C4×C5 | #131⋊C3 | direct (N × H) |
| 152. C5 | C4×#131⋊C3 | direct (N × H) |
| 159. C4 | 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 |
|---|---|
| C2×C5×#131⋊C3 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C4×C5×#131 | 3 |
| C3×C4×C5×C8 | 4 |
| C4×#131⋊C3 | 5 |