Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
148 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 2. #11746713 | C2 | semidirect |
| 3. C3×#64850 | C2 | semidirect |
| 7. Dic120 | C4 | semidirect |
| 8. C5×D48 | C4 | semidirect |
| 14. #64850 | D3 | semidirect |
| 48. D48 | AGL(1,𝔽5) | semidirect |
| 115. C3×C5 | #1418 | semidirect |
| 136. C5 | #67580 | semidirect |
| 143. C3 | #10598679 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11746832 | 2 |
| #11746713 | 2 |
| C3×#64850 | 2 |
| #10598679 | 3 |
| #67580 | 5 |