Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
148 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 62 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×C5×#367 | C2 | semidirect |
| 3. C3×#64719 | C2 | semidirect |
| 4. #10598071 | C3 | direct (N × H) |
| 8. C3×Dic40 | C4 | semidirect |
| 10. C3×D80 | C4 | semidirect |
| 14. C5×#367 | C2×C3 | semidirect |
| 15. #64719 | C2×C3 | semidirect |
| 26. C3×#367 | D5 | semidirect |
| 30. Dic40 | C3×C4 | semidirect |
| 32. D80 | C3×C4 | semidirect |
| 60. #367 | C3×D5 | semidirect |
| 115. C3×C5 | #1418 | semidirect |
| 136. C5 | C3×#1418 | semidirect |
| 143. C3 | #10598071 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65193 | 2 |
| C3×C5×#367 | 2 |
| C3×#64719 | 2 |
| #10598071 | 3 |
| C3×#1418 | 5 |