Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
156 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 66 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. C5×#4506 | C2 | semidirect |
| 3. C5×#4499 | C2 | semidirect |
| 11. #67825 | C5 | direct (N × H) |
| 23. #4506 | C2×C5 | semidirect |
| 24. #4499 | C2×C5 | semidirect |
| 102. C3×C5 | #1419 | semidirect |
| 121. C5 | #67825 | direct (N × H) |
| 127. C3 | C5×#1419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D16 | 2 |
| C5×#4506 | 2 |
| C5×#4499 | 2 |
| C5×#1419 | 3 |
| #67825 | 5 |