Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 76 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. C2×C5×#800 | C2 | semidirect |
| 2. #11747980 | C2 | semidirect |
| 3. #11747810 | C2 | semidirect |
| 5. #11746322 | C2 | semidirect |
| 6. C3×#64729 | C2 | semidirect |
| 7. #11745899 | C2 | semidirect |
| 28. #64729 | D3 | semidirect |
| 52. C2×#800 | D5 | semidirect |
| 246. C3×C5 | #2210 | semidirect |
| 287. C5 | #69203 | semidirect |
| 301. C3 | #10602270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#800 | 2 |
| #11747980 | 2 |
| #11747810 | 2 |
| C2×#90937 | 2 |
| #11746322 | 2 |
| C3×#64729 | 2 |
| #11745899 | 2 |
| #10602270 | 3 |
| #69203 | 5 |