Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
160 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 12. #67563 | C5 | direct (N × H) |
| 124. C3×C5 | #1363 | semidirect |
| 147. C5 | #67563 | direct (N × H) |
| 155. C3 | C5×#1363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4683 | 2 |
| C3×C5×C4⋊C16 | 2 |
| C5×#4457 | 2 |
| C5×#1363 | 3 |
| #67563 | 5 |