Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
568 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 10. #91758 | C4 | semidirect |
| 11. C5×#869 | C4 | semidirect |
| 13. #91388 | C4 | semidirect |
| 35. C4×ΓL(1,𝔽16) | Q8 | semidirect |
| 99. #869 | AGL(1,𝔽5) | semidirect |
| 265. C3×C5 | #1994 | semidirect |
| 307. C5 | #70514 | semidirect |
| 322. C3 | #10604665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752506 | 2 |
| C42×ΓL(1,𝔽16) | 2 |
| C3×#65681 | 2 |
| #11746524 | 2 |
| #10604665 | 3 |
| #70514 | 5 |