Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
276 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 276 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. C5×C8×SL(2,𝔽3) | C2 | semidirect |
| 3. C5×Q8×M16 | C3 | semidirect |
| 8. M16×SL(2,𝔽3) | C5 | direct (N × H) |
| 11. C5×C8×Q8 | C2×C3 | semidirect |
| 20. C8×SL(2,𝔽3) | C2×C5 | semidirect |
| 34. Q8×M16 | C3×C5 | semidirect |
| 40. C5×SL(2,𝔽3) | M16 | direct (N × H) |
| 54. C5×M16 | SL(2,𝔽3) | direct (N × H) |
| 66. C8×Q8 | C2×C3×C5 | semidirect |
| 85. C5×Q8 | C3×M16 | semidirect |
| 98. C5×C8 | C2×SL(2,𝔽3) | semidirect |
| 121. SL(2,𝔽3) | C5×M16 | direct (N × H) |
| 143. M16 | C5×SL(2,𝔽3) | direct (N × H) |
| 169. Q8 | C3×C5×M16 | semidirect |
| 182. C8 | C2×C5×SL(2,𝔽3) | semidirect |
| 187. C5 | M16×SL(2,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×SL(2,𝔽3) | 2 |
| C5×C8×SL(2,𝔽3) | 2 |
| C5×Q8×M16 | 3 |
| C2×C3×C5×M16 | 4 |
| M16×SL(2,𝔽3) | 5 |