Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 98 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×#5070 | C2 | semidirect |
| 3. C5×#4842 | C2 | semidirect |
| 4. C5×#4838 | C2 | semidirect |
| 5. C3×C5×#331 | C2 | semidirect |
| 6. C5×#4481 | C2 | semidirect |
| 7. C5×#4479 | C2 | semidirect |
| 24. #68400 | C5 | direct (N × H) |
| 31. C5×#331 | D3 | semidirect |
| 51. #5070 | C2×C5 | semidirect |
| 52. #4842 | C2×C5 | semidirect |
| 53. #4838 | C2×C5 | semidirect |
| 54. C3×#331 | C2×C5 | semidirect |
| 55. #4481 | C2×C5 | semidirect |
| 56. #4479 | C2×C5 | semidirect |
| 134. #331 | C5×D3 | semidirect |
| 263. C3×C5 | #1697 | semidirect |
| 310. C5 | #68400 | direct (N × H) |
| 325. C3 | C5×#1697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5072 | 2 |
| C5×#5070 | 2 |
| C5×#4842 | 2 |
| C5×#4838 | 2 |
| C3×C5×#331 | 2 |
| C5×#4481 | 2 |
| C5×#4479 | 2 |
| C5×#1697 | 3 |
| #68400 | 5 |