Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
594 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 1. C5×#5945 | C2 | semidirect |
| 2. C5×#5923 | C2 | semidirect |
| 3. C5×#5431 | C2 | semidirect |
| 4. C5×#5430 | C2 | semidirect |
| 5. C5×#5429 | C2 | semidirect |
| 6. C5×#5428 | C2 | semidirect |
| 7. C2×C5×GU(2,𝔽3) | C2 | semidirect |
| 14. C5×#986 | C22 | semidirect |
| 16. C5×#984 | C22 | semidirect |
| 19. C5×GU(2,𝔽3) | C22 | semidirect |
| 20. C5×GU(2,𝔽3) | C22 | semidirect |
| 21. #85544 | C5 | direct (N × H) |
| 22. C5×#585 | D3 | semidirect |
| 40. C5×#41⋊C3 | D4 | semidirect |
| 43. C2×C5×SL(2,𝔽3) | D4 | semidirect |
| 51. #5945 | C2×C5 | semidirect |
| 52. #5923 | C2×C5 | semidirect |
| 53. #5431 | C2×C5 | semidirect |
| 54. #5430 | C2×C5 | semidirect |
| 55. #5429 | C2×C5 | semidirect |
| 56. #5428 | C2×C5 | semidirect |
| 57. C2×GU(2,𝔽3) | C2×C5 | semidirect |
| 125. #986 | C22×C5 | semidirect |
| 127. #984 | C22×C5 | semidirect |
| 130. GU(2,𝔽3) | C22×C5 | semidirect |
| 131. GU(2,𝔽3) | C22×C5 | semidirect |
| 206. #585 | C5×D3 | semidirect |
| 231. #41⋊C3 | C5×D4 | semidirect |
| 234. C2×SL(2,𝔽3) | C5×D4 | semidirect |
| 523. C5 | #85544 | 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×#5923 | 2 |
| C5×#5431 | 2 |
| C5×#5430 | 2 |
| C5×#5429 | 2 |
| C5×#5428 | 2 |
| C2×C5×GU(2,𝔽3) | 2 |
| C5×#3018 | 3 |
| C5×#950 | 4 |
| #85544 | 5 |