Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
514 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
| 10. #85336 | C5 | direct (N × H) |
| 26. C4⋊#226 | C2×C5 | semidirect |
| 145. C4×C5 | #984 | semidirect |
| 197. C5 | #85336 | direct (N × H) |
| 206. C4 | C5×#984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#984 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C5×C4⋊#226 | 2 |
| C5×#3039 | 3 |
| C5×#869 | 4 |
| #85336 | 5 |