Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1038 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1038 conjugacy classes of subgroups — too many to draw. Only its 271 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. C2×Dic5×SL(2,𝔽3) | C2 | direct (N × H) |
| 3. C22×Q8×Dic5 | C3 | semidirect |
| 5. C22×C5×SL(2,𝔽3) | C4 | semidirect |
| 7. Dic5×SL(2,𝔽3) | C22 | direct (N × H) |
| 11. C2×Q8×Dic5 | C2×C3 | semidirect |
| 17. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 23. C22×C5×Q8 | C3×C4 | semidirect |
| 30. Q8×Dic5 | C22×C3 | semidirect |
| 42. C5×SL(2,𝔽3) | C22×C4 | semidirect |
| 44. C22×SL(2,𝔽3) | Dic5 | direct (N × H) |
| 53. C2×C5×Q8 | C2×C3×C4 | semidirect |
| 61. C22×Dic5 | SL(2,𝔽3) | direct (N × H) |
| 81. C2×SL(2,𝔽3) | C2×Dic5 | direct (N × H) |
| 91. C5×Q8 | C22×C3×C4 | semidirect |
| 99. C2×Dic5 | C2×SL(2,𝔽3) | direct (N × H) |
| 103. C22×Q8 | C3×Dic5 | semidirect |
| 125. SL(2,𝔽3) | C22×Dic5 | direct (N × H) |
| 126. C22×C5 | C4×SL(2,𝔽3) | semidirect |
| 135. Dic5 | C22×SL(2,𝔽3) | direct (N × H) |
| 142. C2×Q8 | C2×C3×Dic5 | semidirect |
| 163. C2×C5 | C2×C4×SL(2,𝔽3) | semidirect |
| 175. Q8 | C22×C3×Dic5 | semidirect |
| 189. C5 | C22×C4×SL(2,𝔽3) | semidirect |
| 190. C22 | Dic5×SL(2,𝔽3) | direct (N × H) |
| 201. C2 | C2×Dic5×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 |
|---|---|
| C23×C5×SL(2,𝔽3) | 2 |
| C2×Dic5×SL(2,𝔽3) | 2 |
| C22×Q8×Dic5 | 3 |
| C23×C3×Dic5 | 4 |
| C22×C4×SL(2,𝔽3) | 5 |