Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 1. C3×C5×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #91838 | C2 | semidirect |
| 3. #91837 | C2 | semidirect |
| 4. C2×#6715 | C2 | semidirect |
| 5. #91117 | C2 | semidirect |
| 6. #91107 | C2 | semidirect |
| 7. #91106 | C2 | semidirect |
| 25. C5×AGL(1,ℤ/8) | D3 | semidirect |
| 48. C3×AGL(1,ℤ/8) | D5 | semidirect |
| 112. AGL(1,ℤ/8) | D15 | semidirect |
| 163. C3×C5 | #472 | semidirect |
| 199. C5 | #5199 | semidirect |
| 209. C3 | #65488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×AGL(1,ℤ/8) | 2 |
| #91838 | 2 |
| #91837 | 2 |
| C2×#6715 | 2 |
| #91117 | 2 |
| #91107 | 2 |
| #91106 | 2 |
| #65488 | 3 |
| #5199 | 5 |