Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
244 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 90 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×#6650 | C2 | semidirect |
| 3. C4×C3⋊#168 | C2 | semidirect |
| 4. C3×C4⋊#168 | C2 | semidirect |
| 5. (C2×D3)⋊#168 | C2 | semidirect |
| 20. C4⋊#168 | D3 | semidirect |
| 31. C3⋊#168 | D4 | semidirect |
| 53. C3×C4×C5 | M16 | semidirect |
| 103. C4×C5 | ΓL(1,𝔽25) | semidirect |
| 115. C3×C5 | #436 | semidirect |
| 121. C3×C4 | #681 | semidirect |
| 144. C5 | #4838 | semidirect |
| 151. C4 | #6650 | semidirect |
| 154. C3 | #65301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×D12 | 2 |
| C2×#6650 | 2 |
| C4×C3⋊#168 | 2 |
| C3×C4⋊#168 | 2 |
| (C2×D3)⋊#168 | 2 |
| #65301 | 3 |
| #4838 | 5 |