Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
192 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 56 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×#4628 | C2 | semidirect |
| 8. #73119 | C5 | direct (N × H) |
| 20. #4628 | C2×C5 | semidirect |
| 161. C5 | #73119 | 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×#4628 | 2 |
| C5×#2117 | 3 |
| C5×#812 | 4 |
| #73119 | 5 |