Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
244 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 37 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. #11746796 | C2 | semidirect |
| 3. #11746793 | C2 | semidirect |
| 5. C3×C5×H(5,𝔽2) | C4 | semidirect |
| 11. C3×#3965 | C4 | semidirect |
| 32. C5×H(5,𝔽2) | Dic3 | semidirect |
| 38. #3965 | Dic3 | semidirect |
| 58. C3×H(5,𝔽2) | AGL(1,𝔽5) | semidirect |
| 124. H(5,𝔽2) | ΓL(1,𝔽16) | semidirect |
| 179. C3×C5 | #1402 | semidirect |
| 220. C5 | #67770 | semidirect |
| 233. C3 | #10598833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65530 | 2 |
| #11746796 | 2 |
| #11746793 | 2 |
| #10598833 | 3 |
| #67770 | 5 |