Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
434 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 64 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×GU(2,𝔽3) | C2 | semidirect |
| 5. C2×C5×#41⋊C3 | C4 | semidirect |
| 7. C22×C5×SL(2,𝔽3) | C4 | semidirect |
| 10. #73149 | C5 | direct (N × H) |
| 23. C2×GU(2,𝔽3) | C2×C5 | semidirect |
| 47. C5×SL(2,𝔽3) | C22⋊C4 | semidirect |
| 50. C2×#41⋊C3 | C4×C5 | semidirect |
| 52. C22×SL(2,𝔽3) | C4×C5 | semidirect |
| 163. SL(2,𝔽3) | C5×C22⋊C4 | semidirect |
| 174. C22×C5 | GU(2,𝔽3) | semidirect |
| 264. C5 | #73149 | direct (N × H) |
| 274. C22 | C5×GU(2,𝔽3) | semidirect |
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×GU(2,𝔽3) | 2 |
| C5×#1789 | 3 |
| C5×#830 | 4 |
| #73149 | 5 |