Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
744 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 137 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. #66161⋊C3 | C2 | semidirect |
| 3. Dic5×#41⋊C3 | C2 | semidirect |
| 4. #66146⋊C3 | C2 | semidirect |
| 5. C2×Dic5×SL(2,𝔽3) | C2 | semidirect |
| 6. Dic5×2−1+4 | C3 | semidirect |
| 7. C5×2−1+4⋊C3 | C4 | semidirect |
| 18. #66161 | C2×C3 | semidirect |
| 21. #41×Dic5 | C2×C3 | semidirect |
| 23. #66146 | C2×C3 | semidirect |
| 25. C2×Q8×Dic5 | C2×C3 | semidirect |
| 28. C5×#41⋊C3 | C2×C4 | semidirect |
| 29. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 40. C5×2−1+4 | C3×C4 | semidirect |
| 84. 2−1+4⋊C3 | Dic5 | direct (N × H) |
| 96. C5×#41 | C2×C3×C4 | semidirect |
| 102. C2×C5×Q8 | C2×C3×C4 | semidirect |
| 156. #41⋊C3 | C2×Dic5 | semidirect |
| 157. C2×SL(2,𝔽3) | C2×Dic5 | semidirect |
| 193. 2−1+4 | C3×Dic5 | semidirect |
| 256. Dic5 | 2−1+4⋊C3 | direct (N × H) |
| 262. #41 | C2×C3×Dic5 | semidirect |
| 268. C2×Q8 | C2×C3×Dic5 | semidirect |
| 349. C5 | C4×2−1+4⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×2−1+4⋊C3 | 2 |
| #66161⋊C3 | 2 |
| Dic5×#41⋊C3 | 2 |
| #66146⋊C3 | 2 |
| C2×Dic5×SL(2,𝔽3) | 2 |
| Dic5×2−1+4 | 3 |
| C3×D4×Dic5 | 4 |
| C4×2−1+4⋊C3 | 5 |