Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11748063 | C2 | semidirect |
| 3. #11747775 | C2 | semidirect |
| 4. #11746334 | C2 | semidirect |
| 5. C3×#64732 | C2 | semidirect |
| 6. #11745918 | C2 | semidirect |
| 7. #11745912 | C2 | semidirect |
| 16. C5×#800 | C4 | semidirect |
| 17. C5×D48 | C4 | semidirect |
| 29. #64732 | D3 | semidirect |
| 36. C5×Dic12 | C2×C4 | semidirect |
| 39. C5×D24 | C2×C4 | semidirect |
| 46. C3×C5×C16 | C2×C4 | semidirect |
| 95. #800 | Dic5 | semidirect |
| 96. D48 | Dic5 | semidirect |
| 113. C5×C16 | C4×D3 | semidirect |
| 141. Dic12 | C2×Dic5 | semidirect |
| 144. D24 | C2×Dic5 | semidirect |
| 149. C3×C16 | C2×Dic5 | semidirect |
| 224. C16 | D3×Dic5 | semidirect |
| 225. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 259. C5 | #69091 | semidirect |
| 270. C3 | #10602308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4908 | 2 |
| #11748063 | 2 |
| #11747775 | 2 |
| #11746334 | 2 |
| C3×#64732 | 2 |
| #11745918 | 2 |
| #11745912 | 2 |
| #10602308 | 3 |
| #69091 | 5 |