Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 86 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. #11751253 | C2 | semidirect |
| 3. #11748073 | C2 | semidirect |
| 4. C3×#64783 | C2 | semidirect |
| 5. #11745938 | C2 | semidirect |
| 6. #11745912 | C2 | semidirect |
| 7. #11745878 | C2 | semidirect |
| 16. C5×#827 | C4 | semidirect |
| 17. C5×#826 | C4 | semidirect |
| 27. #64783 | D3 | semidirect |
| 40. C5×Dic12 | C2×C4 | semidirect |
| 41. C5×D24 | C2×C4 | semidirect |
| 47. C5×C3⋊C16 | C2×C4 | semidirect |
| 91. #827 | Dic5 | semidirect |
| 92. #826 | Dic5 | semidirect |
| 143. Dic12 | C2×Dic5 | semidirect |
| 144. D24 | C2×Dic5 | semidirect |
| 149. C3⋊C16 | C2×Dic5 | semidirect |
| 225. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 259. C5 | #69254 | semidirect |
| 270. C3 | #10602308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751253 | 2 |
| C5×#5147 | 2 |
| #11748073 | 2 |
| C3×#64783 | 2 |
| #11745938 | 2 |
| #11745912 | 2 |
| #11745878 | 2 |
| #10602308 | 3 |
| #69254 | 5 |