Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
558 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 50 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×#3573 | C3 | semidirect |
| 6. #85666 | C5 | direct (N × H) |
| 24. C5×#131 | A4 | semidirect |
| 31. C22×C5×C8 | A4 | semidirect |
| 32. #3573 | C3×C5 | semidirect |
| 97. #131 | C5×A4 | semidirect |
| 104. C22×C8 | C5×A4 | semidirect |
| 164. C5 | #85666 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5950 | 2 |
| C5×#3573 | 3 |
| C5×#131⋊C3 | 4 |
| C5×C8×A4 | 4 |
| #85666 | 5 |