Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
296 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 14. #70539 | C5 | direct (N × H) |
| 155. C3×C5 | #2103 | semidirect |
| 179. C5 | #70539 | direct (N × H) |
| 187. C3 | C5×#2103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#424 | 2 |
| C5×#5125 | 2 |
| C5×C3⋊#338 | 2 |
| C5×#4552 | 2 |
| C5×#4533 | 2 |
| C5×#2103 | 3 |
| #70539 | 5 |