Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
168 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 72 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×#812 | C2 | semidirect |
| 3. C2×C3×#672 | C2 | semidirect |
| 4. #90936 | C2 | semidirect |
| 5. #90933 | C2 | semidirect |
| 18. C2×#672 | D3 | semidirect |
| 31. #812 | D5 | semidirect |
| 93. C3×C5 | #504 | semidirect |
| 113. C5 | #4901 | semidirect |
| 119. C3 | #65196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91790 | 2 |
| C5×#812 | 2 |
| C2×C3×#672 | 2 |
| #90936 | 2 |
| #90933 | 2 |
| #65196 | 3 |
| #4901 | 5 |