Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
250 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 5. C5×#131⋊C3 | C4 | semidirect |
| 8. #73125 | C5 | direct (N × H) |
| 23. C5×#131 | Dic3 | semidirect |
| 39. #131⋊C3 | C4×C5 | semidirect |
| 94. #131 | C5×Dic3 | semidirect |
| 166. C5 | #73125 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#131⋊C3 | 2 |
| C5×#5426 | 2 |
| C5×#1815 | 3 |
| C5×#817 | 4 |
| #73125 | 5 |