Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11748018 | C2 | semidirect |
| 5. C5×#4503 | C2 | semidirect |
| 6. C3×#64721 | C2 | semidirect |
| 7. #11745902 | C2 | semidirect |
| 28. #64721 | D3 | semidirect |
| 56. #4503 | D5 | semidirect |
| 136. C3×Dic5 | SD32 | semidirect |
| 220. Dic5 | #800 | semidirect |
| 241. C3×C5 | #2208 | semidirect |
| 278. C5 | #69287 | semidirect |
| 290. C3 | #10600027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91084 | 2 |
| #11748018 | 2 |
| #11747766 | 2 |
| C2×#90945 | 2 |
| C5×#4503 | 2 |
| C3×#64721 | 2 |
| #11745902 | 2 |
| #10600027 | 3 |
| #69287 | 5 |