Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
412 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 412 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 |
|---|---|---|
| 3. C5×C4⋊#226 | C2 | semidirect |
| 4. C4×C5×#226 | C2 | semidirect |
| 5. C5×#5386 | C2 | semidirect |
| 13. #85335 | C5 | direct (N × H) |
| 35. C4⋊#226 | C2×C5 | semidirect |
| 36. C4×#226 | C2×C5 | semidirect |
| 37. #5386 | C2×C5 | semidirect |
| 270. C5 | #85335 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#41⋊C3 | 2 |
| C5×#5425 | 2 |
| C5×C4⋊#226 | 2 |
| C4×C5×#226 | 2 |
| C5×#5386 | 2 |
| C5×#3107 | 3 |
| C4×C5×Dic6 | 4 |
| #85335 | 5 |