Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
436 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 436 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×#5092 | C2 | semidirect |
| 3. C5×#4842 | C2 | semidirect |
| 4. C3×C5×#333 | C2 | semidirect |
| 5. C5×#4483 | C2 | semidirect |
| 18. #68493 | C5 | direct (N × H) |
| 22. C5×#333 | D3 | semidirect |
| 40. #5092 | C2×C5 | semidirect |
| 41. #4842 | C2×C5 | semidirect |
| 42. C3×#333 | C2×C5 | semidirect |
| 43. #4483 | C2×C5 | semidirect |
| 100. #333 | C5×D3 | semidirect |
| 196. C3×C5 | #1634 | semidirect |
| 228. C5 | #68493 | direct (N × H) |
| 239. C3 | C5×#1634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5734 | 2 |
| C5×#5092 | 2 |
| C5×#4842 | 2 |
| C3×C5×#333 | 2 |
| C5×#4483 | 2 |
| C5×#1634 | 3 |
| #68493 | 5 |