Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
480 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 1. C5×#5734 | C2 | semidirect |
| 2. C5×#5085 | C2 | semidirect |
| 3. C5×#4843 | C2 | semidirect |
| 4. C3×C5×#333 | C2 | semidirect |
| 5. C5×#4483 | C2 | semidirect |
| 18. #68491 | C5 | direct (N × H) |
| 22. C5×#333 | D3 | semidirect |
| 40. #5734 | C2×C5 | semidirect |
| 41. #5085 | C2×C5 | semidirect |
| 42. #4843 | C2×C5 | semidirect |
| 43. C3×#333 | C2×C5 | semidirect |
| 44. #4483 | C2×C5 | semidirect |
| 104. #333 | C5×D3 | semidirect |
| 209. C3×C5 | #1624 | semidirect |
| 246. C5 | #68491 | direct (N × H) |
| 258. C3 | C5×#1624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5734 | 2 |
| C5×#5085 | 2 |
| C5×#4843 | 2 |
| C3×C5×#333 | 2 |
| C5×#4483 | 2 |
| C5×#1624 | 3 |
| #68491 | 5 |