Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
608 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 120 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×#5423 | C2 | semidirect |
| 3. C2×C5×GU(2,𝔽3) | C2 | semidirect |
| 5. C5×2−1+4⋊C3 | C4 | semidirect |
| 6. C5×#994 | C4 | semidirect |
| 9. C5×GU(2,𝔽3) | C22 | semidirect |
| 10. C5×GU(2,𝔽3) | C22 | semidirect |
| 11. #85541 | C5 | direct (N × H) |
| 20. C5×#41⋊C3 | C2×C4 | semidirect |
| 22. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 26. #5423 | C2×C5 | semidirect |
| 27. C2×GU(2,𝔽3) | C2×C5 | semidirect |
| 55. 2−1+4⋊C3 | C4×C5 | semidirect |
| 56. #994 | C4×C5 | semidirect |
| 59. GU(2,𝔽3) | C22×C5 | semidirect |
| 60. GU(2,𝔽3) | C22×C5 | semidirect |
| 103. #41⋊C3 | C2×C4×C5 | semidirect |
| 105. C2×SL(2,𝔽3) | C2×C4×C5 | semidirect |
| 236. C5 | #85541 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5945 | 2 |
| C5×#5423 | 2 |
| C2×C5×GU(2,𝔽3) | 2 |
| C5×#2901 | 3 |
| C5×#948 | 4 |
| #85541 | 5 |