Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
416 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 16. C3×C5×#106 | C4 | semidirect |
| 17. C3×#3949 | C4 | semidirect |
| 18. C3×#3939 | C4 | semidirect |
| 57. C5×#106 | Dic3 | semidirect |
| 58. #3949 | Dic3 | semidirect |
| 59. #3939 | Dic3 | semidirect |
| 83. C3×#106 | AGL(1,𝔽5) | semidirect |
| 163. #106 | ΓL(1,𝔽16) | semidirect |
| 215. C3×C5 | #1945 | semidirect |
| 250. C5 | #70662 | semidirect |
| 262. C3 | #10604057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91224 | 2 |
| C2×C8×ΓL(1,𝔽16) | 2 |
| #11752367 | 2 |
| C3×#65149 | 2 |
| #11746746 | 2 |
| #10604057 | 3 |
| #70662 | 5 |