Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
196 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 196 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 |
|---|---|---|
| 8. C5×#869 | C4 | semidirect |
| 11. C5×#803 | C4 | semidirect |
| 12. #67545 | C5 | direct (N × H) |
| 53. #869 | C4×C5 | semidirect |
| 56. #803 | C4×C5 | semidirect |
| 143. C3×C5 | #1407 | semidirect |
| 170. C5 | #67545 | direct (N × H) |
| 179. C3 | C5×#1407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5060 | 2 |
| C3×C5×#354 | 2 |
| C5×#4542 | 2 |
| C5×#1407 | 3 |
| #67545 | 5 |