Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
346 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 5. #91885 | C4 | direct (N × H) |
| 6. C4×C5×SL(2,𝔽3) | C4 | semidirect |
| 8. Dic5×SL(2,𝔽3) | C4 | semidirect |
| 40. C5×SL(2,𝔽3) | C42 | semidirect |
| 44. C4×SL(2,𝔽3) | AGL(1,𝔽5) | semidirect |
| 122. SL(2,𝔽3) | C4×AGL(1,𝔽5) | semidirect |
| 132. C4×C5 | GU(2,𝔽3) | semidirect |
| 134. Dic5 | GU(2,𝔽3) | semidirect |
| 189. C5 | C4×GU(2,𝔽3) | semidirect |
| 201. C4 | #91885 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91885 | 2 |
| C4×C5⋊(#41⋊C3) | 2 |
| C4×#4010 | 3 |
| C4×C3⋊#170 | 4 |
| C4×GU(2,𝔽3) | 5 |