Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 88 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. C2×C5×GU(2,𝔽3) | C2 | semidirect |
| 4. C5×#5405 | C2 | semidirect |
| 5. C5×#5404 | C2 | semidirect |
| 8. C5×#986 | C4 | semidirect |
| 10. C5×#984 | C4 | semidirect |
| 11. C5×#983 | C4 | semidirect |
| 13. C5×#131⋊C3 | C22 | semidirect |
| 14. C5×GU(2,𝔽3) | C22 | semidirect |
| 15. C5×GU(2,𝔽3) | C22 | semidirect |
| 16. #85453 | C5 | direct (N × H) |
| 19. C5×#568 | D3 | semidirect |
| 32. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 33. C5×#226 | C2×C4 | semidirect |
| 39. #568⋊C3 | C2×C5 | semidirect |
| 40. C2×GU(2,𝔽3) | C2×C5 | semidirect |
| 41. #5405 | C2×C5 | semidirect |
| 42. #5404 | C2×C5 | semidirect |
| 86. #986 | C4×C5 | semidirect |
| 88. #984 | C4×C5 | semidirect |
| 89. #983 | C4×C5 | semidirect |
| 91. #131⋊C3 | C22×C5 | semidirect |
| 92. GU(2,𝔽3) | C22×C5 | semidirect |
| 93. GU(2,𝔽3) | C22×C5 | semidirect |
| 141. #568 | C5×D3 | semidirect |
| 159. GL(2,𝔽3) | C2×C4×C5 | semidirect |
| 160. #226 | C2×C4×C5 | semidirect |
| 343. C5 | #85453 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5923 | 2 |
| C5×#568⋊C3 | 2 |
| C2×C5×GU(2,𝔽3) | 2 |
| C5×#5405 | 2 |
| C5×#5404 | 2 |
| C5×#2956 | 3 |
| C5×#907 | 4 |
| #85453 | 5 |