Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
256 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 78 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. #11746760 | C2 | semidirect |
| 3. C3×#64889 | C2 | semidirect |
| 5. #11746545 | C2 | semidirect |
| 21. #64889 | D3 | semidirect |
| 174. C3×C5 | #2165 | semidirect |
| 202. C5 | #69298 | semidirect |
| 211. C3 | #10604752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic5×ΓL(1,𝔽25) | 2 |
| #11746760 | 2 |
| C3×#64889 | 2 |
| #11746548 | 2 |
| #11746545 | 2 |
| #10604752 | 3 |
| #69298 | 5 |