Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
664 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 134 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×#4835 | C2 | semidirect |
| 3. C3×C5×#331 | C2 | semidirect |
| 4. C5×#4544 | C2 | semidirect |
| 5. C5×#4485 | C2 | semidirect |
| 14. C3×C5×C4⋊C8 | C22 | semidirect |
| 17. C5×C4⋊(C3⋊C8) | C22 | semidirect |
| 18. #68387 | C5 | direct (N × H) |
| 23. C5×#331 | D3 | semidirect |
| 42. #4835 | C2×C5 | semidirect |
| 43. C3×#331 | C2×C5 | semidirect |
| 44. #4544 | C2×C5 | semidirect |
| 45. #4485 | C2×C5 | semidirect |
| 54. C5×C4⋊C8 | C2×D3 | semidirect |
| 87. C3×C4⋊C8 | C22×C5 | semidirect |
| 90. C4⋊(C3⋊C8) | C22×C5 | semidirect |
| 112. #331 | C5×D3 | semidirect |
| 173. C4⋊C8 | C2×C5×D3 | semidirect |
| 233. C3×C5 | #1555 | semidirect |
| 279. C5 | #68387 | direct (N × H) |
| 293. C3 | C5×#1555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×#127 | 2 |
| C5×#4835 | 2 |
| C3×C5×#331 | 2 |
| C5×#4544 | 2 |
| C5×#4485 | 2 |
| C5×#1555 | 3 |
| #68387 | 5 |