Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
330 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 2. C5×#568⋊C3 | C2 | semidirect |
| 3. C5×#5423 | C2 | semidirect |
| 8. C2×C5×GL(2,𝔽3) | C4 | semidirect |
| 12. #73131 | C5 | direct (N × H) |
| 14. C5×#568 | D3 | semidirect |
| 28. #568⋊C3 | C2×C5 | semidirect |
| 29. #5423 | C2×C5 | semidirect |
| 61. C2×GL(2,𝔽3) | C4×C5 | semidirect |
| 99. #568 | C5×D3 | semidirect |
| 257. C5 | #73131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#986 | 2 |
| C5×#568⋊C3 | 2 |
| C5×#5423 | 2 |
| C5×#1903 | 3 |
| C5×#823 | 4 |
| #73131 | 5 |