Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
252 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 3. C4⋊(C3⋊#170) | C2 | semidirect |
| 4. C3×C4⋊#170 | C2 | semidirect |
| 5. Dic3⋊#170 | C2 | semidirect |
| 22. C4⋊#170 | D3 | semidirect |
| 56. C3×C4×C5 | M16 | semidirect |
| 62. C5×Dic3 | M16 | semidirect |
| 114. C4×C5 | ΓL(1,𝔽25) | semidirect |
| 129. C3×C5 | #423 | semidirect |
| 137. C3×C4 | #700 | semidirect |
| 139. Dic3 | #700 | semidirect |
| 162. C5 | #4837 | semidirect |
| 173. C4 | #6740 | semidirect |
| 174. C3 | #65681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6740 | 2 |
| C4×#1200 | 2 |
| C4⋊(C3⋊#170) | 2 |
| C3×C4⋊#170 | 2 |
| Dic3⋊#170 | 2 |
| #65681 | 3 |
| #4837 | 5 |