Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
252 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 116 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. C3×#4004 | C2 | semidirect |
| 4. C3×C4⋊#170 | C2 | semidirect |
| 5. #65758 | C3 | direct (N × H) |
| 18. #4004 | C2×C3 | semidirect |
| 19. C4⋊#170 | C2×C3 | semidirect |
| 51. C3×C4×C5 | M16 | semidirect |
| 54. C3×Dic5 | M16 | semidirect |
| 103. C4×C5 | C3×M16 | semidirect |
| 106. Dic5 | C3×M16 | semidirect |
| 118. C3×C5 | #423 | semidirect |
| 129. C3×C4 | #704 | semidirect |
| 150. C5 | C3×#423 | semidirect |
| 161. C4 | C3×#704 | semidirect |
| 162. C3 | #65758 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#704 | 2 |
| C2×C3×C4×Dic5 | 2 |
| C3×#4004 | 2 |
| C3×C4⋊#170 | 2 |
| #65758 | 3 |
| C3×#423 | 5 |