Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
168 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 102 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. C3×C5×M32 | C2 | semidirect |
| 3. C2×C5×C3⋊C16 | C2 | semidirect |
| 4. C5×#798 | C2 | semidirect |
| 5. C5×D3×C16 | C2 | semidirect |
| 15. #4907 | C5 | direct (N × H) |
| 18. C5×M32 | D3 | semidirect |
| 30. C3×M32 | C2×C5 | semidirect |
| 31. C2×C3⋊C16 | C2×C5 | semidirect |
| 32. #798 | C2×C5 | semidirect |
| 33. D3×C16 | C2×C5 | semidirect |
| 66. M32 | C5×D3 | semidirect |
| 93. C3×C5 | #504 | semidirect |
| 113. C5 | #4907 | direct (N × H) |
| 119. C3 | C5×#504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#901 | 2 |
| C3×C5×M32 | 2 |
| C2×C5×C3⋊C16 | 2 |
| C5×#798 | 2 |
| C5×D3×C16 | 2 |
| C5×#504 | 3 |
| #4907 | 5 |