Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
284 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 104 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. #91169 | C2 | semidirect |
| 12. #6740 | C4 | direct (N × H) |
| 22. C4×#170 | D3 | semidirect |
| 33. C3⋊#170 | C2×C4 | semidirect |
| 34. C3×#170 | C2×C4 | semidirect |
| 55. C3×C4×C5 | M16 | semidirect |
| 57. C3×Dic5 | M16 | semidirect |
| 82. #170 | C4×D3 | semidirect |
| 110. C4×C5 | ΓL(1,𝔽25) | semidirect |
| 112. Dic5 | ΓL(1,𝔽25) | semidirect |
| 124. C3×C5 | C4×M16 | semidirect |
| 131. C3×C4 | #700 | semidirect |
| 155. C5 | C4×ΓL(1,𝔽25) | semidirect |
| 165. C4 | #6740 | direct (N × H) |
| 166. C3 | C4×#700 | 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 |
| #91169 | 2 |
| C4×#700 | 3 |
| C4×ΓL(1,𝔽25) | 5 |