Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
244 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 8. C5×GU(2,𝔽3) | C4 | semidirect |
| 9. C5×GU(2,𝔽3) | C4 | semidirect |
| 11. #73129 | C5 | direct (N × H) |
| 56. GU(2,𝔽3) | C4×C5 | semidirect |
| 57. GU(2,𝔽3) | C4×C5 | semidirect |
| 218. C5 | #73129 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#568⋊C3 | 2 |
| C5×#5423 | 2 |
| C2×C5×GU(2,𝔽3) | 2 |
| C5×#1861 | 3 |
| C5×#822 | 4 |
| #73129 | 5 |