Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 118 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×#65161 | C2 | semidirect |
| 3. C3×C5×#366 | C2 | semidirect |
| 4. C3×C16×Dic5 | C2 | semidirect |
| 5. C3×#64711 | C2 | semidirect |
| 6. #10600110 | C3 | direct (N × H) |
| 14. C3×D80 | C4 | semidirect |
| 17. #65161 | C2×C3 | semidirect |
| 18. C5×#366 | C2×C3 | semidirect |
| 19. C16×Dic5 | C2×C3 | semidirect |
| 20. #64711 | C2×C3 | semidirect |
| 29. C3×D40 | C2×C4 | semidirect |
| 30. C3×C5×C16 | C2×C4 | semidirect |
| 34. C3×#366 | D5 | semidirect |
| 44. D80 | C3×C4 | semidirect |
| 73. D40 | C2×C3×C4 | semidirect |
| 74. C5×C16 | C2×C3×C4 | semidirect |
| 78. #366 | C3×D5 | semidirect |
| 89. C3×Dic5 | D16 | semidirect |
| 100. C3×C16 | C4×D5 | semidirect |
| 143. Dic5 | C3×D16 | semidirect |
| 154. C16 | C3×C4×D5 | semidirect |
| 155. C3×C5 | C4×D16 | semidirect |
| 184. C5 | C3×C4×D16 | semidirect |
| 194. C3 | #10600110 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D80 | 2 |
| C3×#65161 | 2 |
| C3×C5×#366 | 2 |
| C3×C16×Dic5 | 2 |
| C3×#64711 | 2 |
| #10600110 | 3 |
| C3×C4×D16 | 5 |