Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
422 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 68 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×#5425 | C2 | semidirect |
| 3. C5×#5424 | C2 | semidirect |
| 4. C5×#5419 | C2 | semidirect |
| 5. C2×C5×#859 | C2 | semidirect |
| 6. C5×#5389 | C2 | semidirect |
| 7. C4×C5×#226 | C2 | semidirect |
| 17. #85375 | C5 | direct (N × H) |
| 45. #5425 | C2×C5 | semidirect |
| 46. #5424 | C2×C5 | semidirect |
| 47. #5419 | C2×C5 | semidirect |
| 48. C2×#859 | C2×C5 | semidirect |
| 49. #5389 | C2×C5 | semidirect |
| 50. C4×#226 | C2×C5 | semidirect |
| 375. C5 | #85375 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#548⋊C3 | 2 |
| C5×#5425 | 2 |
| C5×#5424 | 2 |
| C5×#5419 | 2 |
| C2×C5×#859 | 2 |
| C5×#5389 | 2 |
| C4×C5×#226 | 2 |
| C5×#3300 | 3 |
| C5×#877 | 4 |
| #85375 | 5 |