Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
252 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 72 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. #11748027 | C2 | semidirect |
| 3. #11746315 | C2 | semidirect |
| 4. C3×#64714 | C2 | semidirect |
| 5. #11745932 | C2 | semidirect |
| 26. #64714 | D3 | semidirect |
| 35. C5×Dic12 | Q8 | semidirect |
| 36. C5×D24 | Q8 | semidirect |
| 128. Dic12 | Dic10 | semidirect |
| 129. D24 | Dic10 | semidirect |
| 201. C3×C5 | #2230 | semidirect |
| 230. C5 | #69315 | semidirect |
| 239. C3 | #10601712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4895 | 2 |
| #11748027 | 2 |
| #11746315 | 2 |
| C3×#64714 | 2 |
| #11745932 | 2 |
| #11745912 | 2 |
| #11745911 | 2 |
| #10601712 | 3 |
| #69315 | 5 |