Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
492 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 72 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×#5923 | C2 | semidirect |
| 2. C2×C5×#131⋊C3 | C2 | semidirect |
| 3. C5×#5407 | C2 | semidirect |
| 4. C5×#5406 | C2 | semidirect |
| 5. C5×#5403 | C2 | semidirect |
| 15. #85451 | C5 | direct (N × H) |
| 18. C2×C5×#131 | D3 | semidirect |
| 37. #5923 | C2×C5 | semidirect |
| 38. C2×#131⋊C3 | C2×C5 | semidirect |
| 39. #5407 | C2×C5 | semidirect |
| 40. #5406 | C2×C5 | semidirect |
| 41. #5403 | C2×C5 | semidirect |
| 134. C2×#131 | C5×D3 | semidirect |
| 323. C5 | #85451 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5923 | 2 |
| C2×C5×#131⋊C3 | 2 |
| C5×#5407 | 2 |
| C5×#5406 | 2 |
| C5×#5403 | 2 |
| C5×#3067 | 3 |
| C5×#904 | 4 |
| #85451 | 5 |