Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
244 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 50 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. SL(2,𝔽3)×#170 | C2 | semidirect |
| 3. #10617203 | C3 | semidirect |
| 16. C5⋊(#41⋊C3) | C8 | semidirect |
| 37. C5×SL(2,𝔽3) | C2×C8 | semidirect |
| 45. #713 | C3×C8 | semidirect |
| 111. SL(2,𝔽3) | D5⋊C8 | semidirect |
| 173. C5 | #2988⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5⋊(#41⋊C3) | 2 |
| SL(2,𝔽3)×#170 | 2 |
| #10617203 | 3 |
| C3×#4004 | 4 |
| #2988⋊C3 | 5 |