Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
524 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. C3×C5×H(3,𝔽4) | C2 | semidirect |
| 2. #11751159 | C2 | semidirect |
| 3. #11746361 | C2 | semidirect |
| 10. #91763 | C22 | semidirect |
| 11. #91087 | C22 | semidirect |
| 13. C5×H(3,𝔽4) | D3 | semidirect |
| 28. C3×H(3,𝔽4) | D5 | semidirect |
| 69. H(3,𝔽4) | D15 | semidirect |
| 142. C3×C5 | #1655 | semidirect |
| 167. C5 | #71948 | semidirect |
| 175. C3 | #10602741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×H(3,𝔽4) | 2 |
| #11751159 | 2 |
| #11746361 | 2 |
| #10602741 | 3 |
| #71948 | 5 |