Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
390 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 76 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×#5389 | C2 | semidirect |
| 9. #85339 | C5 | direct (N × H) |
| 24. #5389 | C2×C5 | semidirect |
| 173. C5 | #85339 | 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×#5426 | 2 |
| C5×#5389 | 2 |
| C5×#3080 | 3 |
| C5×#870 | 4 |
| #85339 | 5 |