Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
718 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 96 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×#91885 | C2 | direct (N × H) |
| 4. C22×C5×SL(2,𝔽3) | C4 | semidirect |
| 6. C2×C5⋊(#41⋊C3) | C4 | semidirect |
| 8. #91885 | C22 | direct (N × H) |
| 16. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 18. C5⋊(#41⋊C3) | C2×C4 | semidirect |
| 41. C5×SL(2,𝔽3) | C22×C4 | semidirect |
| 45. C22×SL(2,𝔽3) | AGL(1,𝔽5) | semidirect |
| 86. C2×SL(2,𝔽3) | C2×AGL(1,𝔽5) | semidirect |
| 131. SL(2,𝔽3) | C22×AGL(1,𝔽5) | semidirect |
| 133. C22×C5 | GU(2,𝔽3) | semidirect |
| 175. C2×C5 | C2×GU(2,𝔽3) | semidirect |
| 204. C5 | C22×GU(2,𝔽3) | semidirect |
| 209. C22 | #91885 | direct (N × H) |
| 219. C2 | C2×#91885 | direct (N × H) |
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×#91885 | 2 |
| C22×#4010 | 3 |
| C22×C3⋊#170 | 4 |
| C22×GU(2,𝔽3) | 5 |