Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
360 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 17. #85416 | C5 | direct (N × H) |
| 34. C5×#226 | Q8 | semidirect |
| 163. #226 | C5×Q8 | semidirect |
| 325. C5 | #85416 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#557⋊C3 | 2 |
| C5×#5391 | 2 |
| C5×#5389 | 2 |
| C5×#5388 | 2 |
| C4×C5×#226 | 2 |
| C5×#3390 | 3 |
| C5×#889 | 4 |
| #85416 | 5 |