Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
800 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 298 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. C22×C5×Dic12 | C2 | semidirect |
| 3. C22×C3×C5×C16 | C2 | semidirect |
| 4. C2×C5×#800 | C2 | direct (N × H) |
| 10. C2×C5×Dic12 | C22 | semidirect |
| 13. C2×C3×C5×C16 | C22 | semidirect |
| 14. C5×#800 | C22 | direct (N × H) |
| 15. C22×#800 | C5 | direct (N × H) |
| 19. C22×C5×C16 | D3 | semidirect |
| 30. C5×Dic12 | C23 | semidirect |
| 33. C3×C5×C16 | C23 | semidirect |
| 34. C22×Dic12 | C2×C5 | semidirect |
| 36. C22×C3×C16 | C2×C5 | semidirect |
| 37. C2×#800 | C2×C5 | direct (N × H) |
| 46. C2×C5×C16 | C2×D3 | semidirect |
| 64. C2×Dic12 | C22×C5 | semidirect |
| 67. C2×C3×C16 | C22×C5 | semidirect |
| 68. #800 | C22×C5 | direct (N × H) |
| 82. C5×C16 | C22×D3 | semidirect |
| 86. C22×C16 | C5×D3 | semidirect |
| 87. C22×C3×C5 | SD32 | semidirect |
| 104. Dic12 | C23×C5 | semidirect |
| 107. C3×C16 | C23×C5 | semidirect |
| 128. C2×C16 | C2×C5×D3 | semidirect |
| 129. C2×C3×C5 | C2×SD32 | semidirect |
| 146. C22×C5 | #800 | direct (N × H) |
| 164. C16 | C22×C5×D3 | semidirect |
| 165. C3×C5 | C22×SD32 | semidirect |
| 166. C22×C3 | C5×SD32 | semidirect |
| 174. C2×C5 | C2×#800 | direct (N × H) |
| 188. C2×C3 | C2×C5×SD32 | semidirect |
| 191. C5 | C22×#800 | direct (N × H) |
| 194. C22 | C5×#800 | direct (N × H) |
| 199. C3 | C22×C5×SD32 | semidirect |
| 201. C2 | C2×C5×#800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic12 | 2 |
| C22×C5×D24 | 2 |
| C22×C3×C5×C16 | 2 |
| C2×C5×#800 | 2 |
| C22×C5×SD32 | 3 |
| C22×#800 | 5 |