Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
188 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 6. C5×#870 | C4 | semidirect |
| 11. C5×#803 | C4 | semidirect |
| 12. #67539 | C5 | direct (N × H) |
| 48. #870 | C4×C5 | semidirect |
| 53. #803 | C4×C5 | semidirect |
| 137. C3×C5 | #1412 | semidirect |
| 167. C5 | #67539 | direct (N × H) |
| 178. C3 | C5×#1412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5071 | 2 |
| C3×C5×#353 | 2 |
| C5×#4545 | 2 |
| C5×#1412 | 3 |
| #67539 | 5 |