Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
486 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 1. C5×#557⋊C3 | C2 | semidirect |
| 4. C5×#3504 | C3 | semidirect |
| 9. #3504⋊C3 | C5 | direct (N × H) |
| 17. C5×#41⋊C3 | Q8 | semidirect |
| 22. #557⋊C3 | C2×C5 | semidirect |
| 45. #3504 | C3×C5 | semidirect |
| 87. #41⋊C3 | C5×Q8 | semidirect |
| 192. C5 | #3504⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#557⋊C3 | 2 |
| C5×#520⋊C3 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C5×#3504 | 3 |
| C3×C5×#125 | 4 |
| #3504⋊C3 | 5 |