Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
412 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 18. #68505 | C5 | direct (N × H) |
| 66. C5×Dic6 | Q16 | semidirect |
| 159. Dic6 | C5×Q16 | semidirect |
| 185. C3×C5 | #1633 | semidirect |
| 211. C5 | #68505 | direct (N × H) |
| 220. C3 | C5×#1633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5722 | 2 |
| C5×#5092 | 2 |
| C5×#4850 | 2 |
| C3×C5×#333 | 2 |
| C5×#4484 | 2 |
| C5×#1633 | 3 |
| #68505 | 5 |