Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
148 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 7. Dic120 | C4 | semidirect |
| 8. C5×Dic24 | C4 | semidirect |
| 48. Dic24 | AGL(1,𝔽5) | semidirect |
| 115. C3×C5 | #1416 | semidirect |
| 136. C5 | #67597 | semidirect |
| 143. C3 | #10598682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×Dic24 | 2 |
| #11746720 | 2 |
| C3×D5⋊C32 | 2 |
| #10598682 | 3 |
| #67597 | 5 |