Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
224 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 48 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. C5×C8×SL(2,𝔽3) | C2 | semidirect |
| 3. C5×SL(2,𝔽3)⋊C8 | C2 | semidirect |
| 9. GL(2,𝔽3)⋊C8 | C5 | direct (N × H) |
| 10. C5×C8×Q8 | D3 | semidirect |
| 19. C5×GL(2,𝔽3) | C8 | semidirect |
| 23. C8×SL(2,𝔽3) | C2×C5 | semidirect |
| 24. SL(2,𝔽3)⋊C8 | C2×C5 | semidirect |
| 44. C5×SL(2,𝔽3) | C2×C8 | semidirect |
| 67. C8×Q8 | C5×D3 | semidirect |
| 83. GL(2,𝔽3) | C5×C8 | semidirect |
| 125. SL(2,𝔽3) | C2×C5×C8 | semidirect |
| 187. C5 | GL(2,𝔽3)⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×GL(2,𝔽3) | 2 |
| C5×C8×SL(2,𝔽3) | 2 |
| C5×SL(2,𝔽3)⋊C8 | 2 |
| C5×SD16⋊C8 | 3 |
| C5×(C2×D3)⋊C8 | 4 |
| GL(2,𝔽3)⋊C8 | 5 |