Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
264 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 8. #91227 | C4 | semidirect |
| 13. C2×C3⋊#672 | C4 | semidirect |
| 14. C2×C5×C3⋊C16 | C4 | semidirect |
| 77. C2×C3⋊C16 | AGL(1,𝔽5) | semidirect |
| 189. C3×C5 | #1378 | semidirect |
| 220. C5 | #67672 | semidirect |
| 230. C3 | #10598661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5⋊#812 | 2 |
| C3×#65718 | 2 |
| C2×#90934 | 2 |
| #10598661 | 3 |
| #67672 | 5 |