Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
540 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 146 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×#65529 | C2 | semidirect |
| 3. C3×#64765 | C2 | semidirect |
| 4. #10602654 | C3 | direct (N × H) |
| 6. C22×C3×C5×D4 | C4 | semidirect |
| 8. C3×C5×#124 | C4 | semidirect |
| 11. C3×C5×#117 | C4 | semidirect |
| 14. C3×#3966 | C22 | semidirect |
| 17. #65529 | C2×C3 | semidirect |
| 18. #64765 | C2×C3 | semidirect |
| 41. C22×C5×D4 | C3×C4 | semidirect |
| 43. C5×#124 | C3×C4 | semidirect |
| 46. C5×#117 | C3×C4 | semidirect |
| 49. #3966 | C22×C3 | semidirect |
| 71. C22×C3×D4 | Dic5 | semidirect |
| 73. C3×#124 | Dic5 | semidirect |
| 77. C3×#117 | Dic5 | semidirect |
| 152. C22×D4 | C3×Dic5 | semidirect |
| 154. #124 | C3×Dic5 | semidirect |
| 158. #117 | C3×Dic5 | semidirect |
| 216. C3×C5 | #2128 | semidirect |
| 259. C5 | C3×#2128 | semidirect |
| 273. C3 | #10602654 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#535 | 2 |
| C3×#65529 | 2 |
| C3×#64765 | 2 |
| #10602654 | 3 |
| C3×#2128 | 5 |