Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
616 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 106 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×#4947 | C2 | semidirect |
| 3. C5×#4738 | C2 | semidirect |
| 4. C3×C5×#323 | C2 | semidirect |
| 5. C5×#4470 | C2 | semidirect |
| 8. C22×C5×Dic6 | C22 | semidirect |
| 16. C3×C5×C22⋊C8 | C22 | semidirect |
| 18. C5×C3⋊#95 | C22 | semidirect |
| 20. #68108 | C5 | direct (N × H) |
| 25. C5×#323 | D3 | semidirect |
| 50. #4947 | C2×C5 | semidirect |
| 51. #4738 | C2×C5 | semidirect |
| 52. C3×#323 | C2×C5 | semidirect |
| 53. #4470 | C2×C5 | semidirect |
| 64. C5×C22⋊C8 | C2×D3 | semidirect |
| 72. C23×C3×C5 | SD16 | semidirect |
| 99. C22×Dic6 | C22×C5 | semidirect |
| 107. C3×C22⋊C8 | C22×C5 | semidirect |
| 109. C3⋊#95 | C22×C5 | semidirect |
| 138. #323 | C5×D3 | semidirect |
| 189. C23×C5 | #204 | semidirect |
| 221. C22⋊C8 | C2×C5×D3 | semidirect |
| 235. C23×C3 | C5×SD16 | semidirect |
| 303. C3×C5 | #1601 | semidirect |
| 338. C23 | C5×#204 | semidirect |
| 367. C5 | #68108 | direct (N × H) |
| 387. C3 | C5×#1601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5493 | 2 |
| C5×#4947 | 2 |
| C5×#4738 | 2 |
| C3×C5×#323 | 2 |
| C5×#4470 | 2 |
| C5×#1601 | 3 |
| #68108 | 5 |