Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 64 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. C2×C3×Dic20 | C2 | semidirect |
| 3. C2×C3⋊#672 | C2 | semidirect |
| 4. #90941 | C2 | direct (N × H) |
| 12. C3×Dic20 | C22 | semidirect |
| 13. C3⋊#672 | C22 | semidirect |
| 16. C2×Dic20 | D3 | semidirect |
| 38. Dic20 | C2×D3 | semidirect |
| 68. C2×C3×C5 | SD32 | semidirect |
| 94. C3×C5 | C2×SD32 | semidirect |
| 102. C2×C5 | #828 | semidirect |
| 113. C2×C3 | #3959 | semidirect |
| 116. C5 | C2×#828 | semidirect |
| 123. C3 | C2×#3959 | semidirect |
| 125. C2 | #90941 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D24 | 2 |
| C2×C3×Dic20 | 2 |
| C2×C3⋊#672 | 2 |
| #90941 | 2 |
| C2×#3959 | 3 |
| C2×#828 | 5 |