Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
302 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 4. #10617415 | C3 | semidirect |
| 7. #4133⋊C3 | C4 | semidirect |
| 8. C5×#131⋊C3 | C4 | semidirect |
| 10. #4094⋊C3 | C4 | semidirect |
| 30. #4133 | C3×C4 | semidirect |
| 37. C5×#131 | C3×C4 | semidirect |
| 38. #4094 | C3×C4 | semidirect |
| 58. #131⋊C3 | AGL(1,𝔽5) | semidirect |
| 133. #131 | C3×AGL(1,𝔽5) | semidirect |
| 225. C5 | #2875⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| AGL(1,𝔽5)×#41⋊C3 | 2 |
| D5⋊(#131⋊C3) | 2 |
| D5×#131⋊C3 | 2 |
| #10617415 | 3 |
| C3×#3992 | 4 |
| #2875⋊C3 | 5 |