Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
254 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 254 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 |
|---|---|---|
| 2. C5×C8×SL(2,𝔽3) | C2 | semidirect |
| 3. C5×SL(2,𝔽3)⋊C8 | C2 | semidirect |
| 9. C8×GL(2,𝔽3) | C5 | direct (N × H) |
| 10. C5×C8×Q8 | D3 | semidirect |
| 19. C5×GL(2,𝔽3) | C8 | direct (N × H) |
| 24. C8×SL(2,𝔽3) | C2×C5 | semidirect |
| 25. SL(2,𝔽3)⋊C8 | C2×C5 | semidirect |
| 45. C5×SL(2,𝔽3) | C2×C8 | semidirect |
| 68. C8×Q8 | C5×D3 | semidirect |
| 84. GL(2,𝔽3) | C5×C8 | direct (N × H) |
| 90. C5×Q8 | D3×C8 | semidirect |
| 104. C5×C8 | GL(2,𝔽3) | direct (N × H) |
| 127. SL(2,𝔽3) | C2×C5×C8 | semidirect |
| 170. Q8 | C5×D3×C8 | semidirect |
| 184. C8 | C5×GL(2,𝔽3) | direct (N × H) |
| 189. C5 | C8×GL(2,𝔽3) | 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×C8×SD16 | 3 |
| C2×C5×D3×C8 | 4 |
| C8×GL(2,𝔽3) | 5 |