Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
304 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 110 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. #68552 | C5 | direct (N × H) |
| 65. C3×C5×C8 | Q16 | semidirect |
| 129. C5×C8 | Dic12 | semidirect |
| 155. C3×C8 | C5×Q16 | semidirect |
| 178. C3×C5 | #1694 | semidirect |
| 202. C8 | C5×Dic12 | semidirect |
| 206. C5 | #68552 | direct (N × H) |
| 215. C3 | C5×#1694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4849 | 2 |
| C5×#4682 | 2 |
| C5×#4679 | 2 |
| C3×C5×#334 | 2 |
| C5×#4482 | 2 |
| C5×#1694 | 3 |
| #68552 | 5 |