Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 77 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. #11752399 | C2 | semidirect |
| 3. #11746780 | C2 | semidirect |
| 4. #11746723 | C2 | semidirect |
| 5. #11746715 | C2 | semidirect |
| 13. C3×C5×Q32 | C4 | semidirect |
| 14. C3×#3960 | C4 | semidirect |
| 15. C3×D80 | C4 | semidirect |
| 47. C5×Q32 | Dic3 | semidirect |
| 48. #3960 | Dic3 | semidirect |
| 49. D80 | Dic3 | semidirect |
| 64. C3×Q32 | AGL(1,𝔽5) | semidirect |
| 121. Q32 | ΓL(1,𝔽16) | semidirect |
| 161. C3×C5 | #2179 | semidirect |
| 184. C5 | #71512 | semidirect |
| 191. C3 | #10604137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752399 | 2 |
| C3×#65208 | 2 |
| #11746780 | 2 |
| #11746723 | 2 |
| #11746715 | 2 |
| #10604137 | 3 |
| #71512 | 5 |