Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
220 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 74 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. C4⋊(C3⋊#170) | C2 | semidirect |
| 3. C3×C4⋊#170 | C2 | semidirect |
| 5. #91169 | C2 | semidirect |
| 21. C4⋊#170 | D3 | semidirect |
| 125. C3×C5 | #432 | semidirect |
| 158. C5 | #4835 | semidirect |
| 170. C3 | #65759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D3×Dic5 | 2 |
| C4⋊(C3⋊#170) | 2 |
| C3×C4⋊#170 | 2 |
| (C2×D3)⋊#170 | 2 |
| #91169 | 2 |
| #65759 | 3 |
| #4835 | 5 |