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. C5×#5423 | C2 | semidirect |
| 4. C5×#5405 | C2 | semidirect |
| 5. C5×#5404 | C2 | semidirect |
| 8. C5×#985 | C4 | semidirect |
| 9. C5×#985 | C4 | semidirect |
| 12. C2×C5×GL(2,𝔽3) | C4 | semidirect |
| 13. C2×C5×#226 | C4 | semidirect |
| 15. C5×#131⋊C3 | C22 | semidirect |
| 16. C5×GU(2,𝔽3) | C22 | semidirect |
| 17. #85452 | C5 | direct (N × H) |
| 20. C5×#568 | D3 | semidirect |
| 42. #568⋊C3 | C2×C5 | semidirect |
| 43. #5423 | C2×C5 | semidirect |
| 44. #5405 | C2×C5 | semidirect |
| 45. #5404 | C2×C5 | semidirect |
| 64. C5×#131 | C2×D3 | semidirect |
| 92. #985 | C4×C5 | semidirect |
| 93. #985 | C4×C5 | semidirect |
| 96. C2×GL(2,𝔽3) | C4×C5 | semidirect |
| 97. C2×#226 | C4×C5 | semidirect |
| 99. #131⋊C3 | C22×C5 | semidirect |
| 100. GU(2,𝔽3) | C22×C5 | semidirect |
| 158. #568 | C5×D3 | semidirect |
| 241. #131 | C2×C5×D3 | semidirect |
| 395. C5 | #85452 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#985 | 2 |
| C5×#568⋊C3 | 2 |
| C5×#5423 | 2 |
| C5×#5405 | 2 |
| C5×#5404 | 2 |
| C5×#2957 | 3 |
| C5×D3×M16 | 4 |
| #85452 | 5 |