Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
626 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 80 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. #11756720 | C2 | direct (N × H) |
| 3. C2×#91885 | C2 | semidirect |
| 5. C22×C5×SL(2,𝔽3) | C4 | semidirect |
| 7. C2×C5⋊(#41⋊C3) | C4 | semidirect |
| 8. C2×C5⋊(#41⋊C3) | C4 | semidirect |
| 11. #91885 | C22 | semidirect |
| 22. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 26. C5⋊(#41⋊C3) | C2×C4 | semidirect |
| 67. C22×SL(2,𝔽3) | AGL(1,𝔽5) | semidirect |
| 132. C2×SL(2,𝔽3) | C2×AGL(1,𝔽5) | semidirect |
| 276. C2×C5 | #5423 | semidirect |
| 322. C5 | C2×#5423 | semidirect |
| 345. C2 | #11756720 | 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 |
| #11756720 | 2 |
| C2×#91885 | 2 |
| C2×#65784 | 3 |
| C2×#6762 | 4 |
| C2×#5423 | 5 |