Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
372 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 1. C3×#65440 | C2 | semidirect |
| 2. C2×C3×#3958 | C2 | semidirect |
| 3. C2×C3×D80 | C2 | semidirect |
| 4. C3×#65161 | C2 | semidirect |
| 5. C3×C5×#357 | C2 | semidirect |
| 6. C3×#64721 | C2 | semidirect |
| 7. C3×#64711 | C2 | semidirect |
| 8. #10599995 | C3 | direct (N × H) |
| 23. #65440 | C2×C3 | semidirect |
| 24. C2×#3958 | C2×C3 | semidirect |
| 25. C2×D80 | C2×C3 | semidirect |
| 26. #65161 | C2×C3 | semidirect |
| 27. C5×#357 | C2×C3 | semidirect |
| 28. #64721 | C2×C3 | semidirect |
| 29. #64711 | C2×C3 | semidirect |
| 47. C3×D40 | D4 | semidirect |
| 56. C3×#357 | D5 | semidirect |
| 120. D40 | C3×D4 | semidirect |
| 129. #357 | C3×D5 | semidirect |
| 144. C3×Dic5 | D16 | semidirect |
| 236. Dic5 | C3×D16 | semidirect |
| 257. C3×C5 | #2206 | semidirect |
| 304. C5 | C3×#2206 | semidirect |
| 320. C3 | #10599995 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65440 | 2 |
| C2×C3×#3958 | 2 |
| C2×C3×D80 | 2 |
| C3×#65161 | 2 |
| C3×C5×#357 | 2 |
| C3×#64721 | 2 |
| C3×#64711 | 2 |
| #10599995 | 3 |
| C3×#2206 | 5 |