Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
208 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 50 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×#4548 | C2 | semidirect |
| 9. #67789 | C5 | direct (N × H) |
| 21. #4548 | C2×C5 | semidirect |
| 106. C3×C5 | #1410 | semidirect |
| 128. C5 | #67789 | direct (N × H) |
| 135. C3 | C5×#1410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#492 | 2 |
| C5×#4548 | 2 |
| C5×#1410 | 3 |
| #67789 | 5 |