Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
444 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 94 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. C2×#91221 | C2 | semidirect |
| 2. #11751825 | C2 | semidirect |
| 6. C3×#64896 | C2 | semidirect |
| 7. #11746524 | C2 | semidirect |
| 22. #91105 | C4 | semidirect |
| 23. C5×#816 | C4 | semidirect |
| 24. #90973 | C4 | semidirect |
| 25. #90969 | C4 | semidirect |
| 32. #64896 | D3 | semidirect |
| 130. #816 | AGL(1,𝔽5) | semidirect |
| 342. C3×C5 | #1938 | semidirect |
| 399. C5 | #68919 | semidirect |
| 416. C3 | #10603988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91221 | 2 |
| #11751825 | 2 |
| #11751814 | 2 |
| C2×#91157 | 2 |
| #11747642 | 2 |
| C3×#64896 | 2 |
| #11746524 | 2 |
| #10603988 | 3 |
| #68919 | 5 |