Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 102 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×#65163 | C2 | semidirect |
| 3. C3×C5×#357 | C2 | semidirect |
| 4. C3×#64782 | C2 | semidirect |
| 5. C3×#64729 | C2 | semidirect |
| 6. C3×C16×Dic5 | C2 | semidirect |
| 7. C3×#64711 | C2 | semidirect |
| 8. #10599976 | C3 | direct (N × H) |
| 22. #65163 | C2×C3 | semidirect |
| 23. C5×#357 | C2×C3 | semidirect |
| 24. #64782 | C2×C3 | semidirect |
| 25. #64729 | C2×C3 | semidirect |
| 26. C16×Dic5 | C2×C3 | semidirect |
| 27. #64711 | C2×C3 | semidirect |
| 51. C3×#357 | D5 | semidirect |
| 116. #357 | C3×D5 | semidirect |
| 230. C3×C5 | #2240 | semidirect |
| 271. C5 | C3×#2240 | semidirect |
| 285. C3 | #10599976 | 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 |
| C3×#65163 | 2 |
| C3×C5×#357 | 2 |
| C3×#64782 | 2 |
| C3×#64729 | 2 |
| C3×C16×Dic5 | 2 |
| C3×#64711 | 2 |
| #10599976 | 3 |
| C3×#2240 | 5 |