Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
304 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 4. #11746477 | C2 | semidirect |
| 5. #11746476 | C2 | semidirect |
| 14. C2×C3⋊#672 | C4 | semidirect |
| 15. C2×C5×C3⋊C16 | C4 | semidirect |
| 16. D5×C3⋊C16 | C4 | semidirect |
| 17. D5×C3⋊C16 | C4 | semidirect |
| 87. C2×C3⋊C16 | AGL(1,𝔽5) | semidirect |
| 207. C3×C5 | #2158 | semidirect |
| 239. C5 | #70648 | semidirect |
| 250. C3 | #10604107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752380 | 2 |
| C3×#65721 | 2 |
| C2×D5×C3⋊C16 | 2 |
| #11746477 | 2 |
| #11746476 | 2 |
| #10604107 | 3 |
| #70648 | 5 |