Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
420 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 60 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×#5426 | C2 | semidirect |
| 3. C2×C5×GU(2,𝔽3) | C2 | semidirect |
| 6. C5×#994 | C4 | semidirect |
| 12. #73153 | C5 | direct (N × H) |
| 28. #5426 | C2×C5 | semidirect |
| 29. C2×GU(2,𝔽3) | C2×C5 | semidirect |
| 33. C5×H(5,𝔽2) | Dic3 | semidirect |
| 58. C5×SL(2,𝔽3) | C22⋊C4 | semidirect |
| 61. #994 | C4×C5 | semidirect |
| 163. H(5,𝔽2) | C5×Dic3 | semidirect |
| 190. SL(2,𝔽3) | C5×C22⋊C4 | semidirect |
| 298. C5 | #73153 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#994 | 2 |
| C5×#5426 | 2 |
| C2×C5×GU(2,𝔽3) | 2 |
| C5×#1792 | 3 |
| C5×#835 | 4 |
| #73153 | 5 |