Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 3. C5×#4543 | C2 | semidirect |
| 14. #71821 | C5 | direct (N × H) |
| 33. #4543 | C2×C5 | semidirect |
| 153. C3×C5 | #1526 | semidirect |
| 178. C5 | #71821 | direct (N × H) |
| 187. C3 | C5×#1526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#533 | 2 |
| C4×C5×#208 | 2 |
| C5×#4543 | 2 |
| C5×#1526 | 3 |
| #71821 | 5 |