Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
400 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 186 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×#815 | C4 | semidirect |
| 9. C5×C8×Dic3 | C4 | semidirect |
| 10. #68717 | C5 | direct (N × H) |
| 41. #815 | C4×C5 | semidirect |
| 42. C8×Dic3 | C4×C5 | semidirect |
| 101. C3×C5 | #1747 | semidirect |
| 118. C5 | #68717 | direct (N × H) |
| 124. C3 | C5×#1747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5122 | 2 |
| C3×C5×#338 | 2 |
| C5×#4557 | 2 |
| C5×#1747 | 3 |
| #68717 | 5 |