Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 332 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×#4699 | C2 | semidirect |
| 4. C3×C5×#334 | C2 | semidirect |
| 5. C5×#4486 | C2 | semidirect |
| 18. #68541 | C5 | direct (N × H) |
| 22. C5×#334 | D3 | semidirect |
| 40. #4699 | C2×C5 | semidirect |
| 42. C3×#334 | C2×C5 | semidirect |
| 43. #4486 | C2×C5 | semidirect |
| 100. #334 | C5×D3 | semidirect |
| 197. C3×C5 | #1689 | semidirect |
| 231. C5 | #68541 | direct (N × H) |
| 242. C3 | C5×#1689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4846 | 2 |
| C5×#4699 | 2 |
| C5×#4688 | 2 |
| C3×C5×#334 | 2 |
| C5×#4486 | 2 |
| C5×#1689 | 3 |
| #68541 | 5 |