Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
540 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 110 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×#4740 | C2 | semidirect |
| 3. C3×C5×#353 | C2 | semidirect |
| 4. C5×#4545 | C2 | semidirect |
| 5. C5×#4474 | C2 | semidirect |
| 8. C2×C5×D3×D4 | C4 | semidirect |
| 13. C5×#936 | C4 | semidirect |
| 15. C5×#875 | C4 | semidirect |
| 16. C5×#872 | C4 | semidirect |
| 17. C3×C5×#99 | C22 | semidirect |
| 18. C5×#834 | C22 | semidirect |
| 20. #69152 | C5 | direct (N × H) |
| 25. C5×#353 | D3 | semidirect |
| 50. #4740 | C2×C5 | semidirect |
| 51. C3×#353 | C2×C5 | semidirect |
| 52. #4545 | C2×C5 | semidirect |
| 53. #4474 | C2×C5 | semidirect |
| 66. C5×#99 | C2×D3 | semidirect |
| 93. C2×D3×D4 | C4×C5 | semidirect |
| 98. #936 | C4×C5 | semidirect |
| 100. #875 | C4×C5 | semidirect |
| 101. #872 | C4×C5 | semidirect |
| 102. C3×#99 | C22×C5 | semidirect |
| 103. #834 | C22×C5 | semidirect |
| 132. #353 | C5×D3 | semidirect |
| 209. #99 | C2×C5×D3 | semidirect |
| 280. C3×C5 | #2128 | semidirect |
| 334. C5 | #69152 | direct (N × H) |
| 352. C3 | C5×#2128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5715 | 2 |
| C5×#4740 | 2 |
| C3×C5×#353 | 2 |
| C5×#4545 | 2 |
| C5×#4474 | 2 |
| C5×#2128 | 3 |
| #69152 | 5 |