Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
612 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 612 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. C2×C5×#986 | C2 | semidirect |
| 3. C5×#5431 | C2 | semidirect |
| 4. C5×#5429 | C2 | semidirect |
| 5. C5×#5423 | C2 | semidirect |
| 8. C5×2−1+4⋊C3 | C22 | semidirect |
| 9. C5×#994 | C22 | semidirect |
| 13. C5×#986 | C22 | semidirect |
| 16. C5×GU(2,𝔽3) | C22 | semidirect |
| 17. #85543 | C5 | direct (N × H) |
| 18. C5×#585 | D3 | semidirect |
| 32. C5×#41⋊C3 | D4 | semidirect |
| 35. C2×C5×SL(2,𝔽3) | D4 | semidirect |
| 40. #5945 | C2×C5 | semidirect |
| 41. C2×#986 | C2×C5 | semidirect |
| 42. #5431 | C2×C5 | semidirect |
| 43. #5429 | C2×C5 | semidirect |
| 44. #5423 | C2×C5 | semidirect |
| 47. C5×2−1+4 | C2×D3 | semidirect |
| 50. C5×H(5,𝔽2) | C2×D3 | semidirect |
| 94. 2−1+4⋊C3 | C22×C5 | semidirect |
| 95. #994 | C22×C5 | semidirect |
| 99. #986 | C22×C5 | semidirect |
| 102. GU(2,𝔽3) | C22×C5 | semidirect |
| 163. #585 | C5×D3 | semidirect |
| 184. #41⋊C3 | C5×D4 | semidirect |
| 187. C2×SL(2,𝔽3) | C5×D4 | semidirect |
| 240. 2−1+4 | C2×C5×D3 | semidirect |
| 243. H(5,𝔽2) | C2×C5×D3 | semidirect |
| 433. C5 | #85543 | 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 |
| C2×C5×#986 | 2 |
| C5×#5431 | 2 |
| C5×#5429 | 2 |
| C5×#5423 | 2 |
| C5×#3021 | 3 |
| C5×#949 | 4 |
| #85543 | 5 |