Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
380 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 134 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×C5×M16 | C2 | semidirect |
| 3. C2×C5×#208 | C2 | semidirect |
| 4. C5×(C2×D3)⋊C8 | C2 | semidirect |
| 14. C2×C3×C5×C8 | C22 | semidirect |
| 16. C2×C5×C3⋊C8 | C22 | semidirect |
| 17. #5126 | C5 | direct (N × H) |
| 20. C2×C5×M16 | D3 | semidirect |
| 38. C2×C3×M16 | C2×C5 | semidirect |
| 39. C2×#208 | C2×C5 | semidirect |
| 40. (C2×D3)⋊C8 | C2×C5 | semidirect |
| 51. C2×C5×C8 | C2×D3 | semidirect |
| 59. C2×C5×D3 | M16 | semidirect |
| 72. C2×C3×C8 | C22×C5 | semidirect |
| 74. C2×C3⋊C8 | C22×C5 | semidirect |
| 92. C2×M16 | C5×D3 | semidirect |
| 134. C2×C8 | C2×C5×D3 | semidirect |
| 135. C3×C5 | #407 | semidirect |
| 142. C2×D3 | C5×M16 | semidirect |
| 170. C5 | #5126 | direct (N × H) |
| 182. C3 | C5×#407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D3 | 2 |
| C2×C3×C5×M16 | 2 |
| C2×C5×#208 | 2 |
| C5×(C2×D3)⋊C8 | 2 |
| C5×#407 | 3 |
| #5126 | 5 |