Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 104 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. C3×D8×Dic5 | C2 | semidirect |
| 3. Dic5×D24 | C2 | semidirect |
| 4. #11746383 | C2 | semidirect |
| 5. #11745941 | C2 | semidirect |
| 6. #11745893 | C2 | semidirect |
| 7. Dic5×C3⋊C16 | C2 | semidirect |
| 15. C5×#826 | C4 | semidirect |
| 24. D8×Dic5 | D3 | semidirect |
| 34. C3×C5×D8 | C2×C4 | semidirect |
| 38. C5×D24 | C2×C4 | semidirect |
| 45. C5×C3⋊C16 | C2×C4 | semidirect |
| 89. #826 | Dic5 | direct (N × H) |
| 101. C5×D8 | C4×D3 | semidirect |
| 130. C3×Dic5 | D16 | semidirect |
| 136. C3×D8 | C2×Dic5 | semidirect |
| 145. D24 | C2×Dic5 | semidirect |
| 147. C3⋊C16 | C2×Dic5 | semidirect |
| 209. Dic5 | #826 | direct (N × H) |
| 217. D8 | D3×Dic5 | semidirect |
| 227. C3×C5 | C4×D16 | semidirect |
| 267. C5 | C4×#826 | semidirect |
| 281. C3 | Dic5×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#826 | 2 |
| C3×D8×Dic5 | 2 |
| Dic5×D24 | 2 |
| #11746383 | 2 |
| #11745941 | 2 |
| #11745893 | 2 |
| Dic5×C3⋊C16 | 2 |
| Dic5×D16 | 3 |
| C4×#826 | 5 |