Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
252 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 122 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×C5×C4⋊C8 | C2 | semidirect |
| 4. C3×#3946 | C2 | semidirect |
| 5. C3×C4⋊#168 | C2 | semidirect |
| 6. #65126 | C3 | direct (N × H) |
| 20. C5×C4⋊C8 | C2×C3 | semidirect |
| 21. #3946 | C2×C3 | semidirect |
| 22. C4⋊#168 | C2×C3 | semidirect |
| 40. C3×C4⋊C8 | D5 | semidirect |
| 57. C3×C4×C5 | M16 | semidirect |
| 62. C3×Dic5 | M16 | semidirect |
| 90. C4⋊C8 | C3×D5 | semidirect |
| 113. C4×C5 | C3×M16 | semidirect |
| 118. Dic5 | C3×M16 | semidirect |
| 129. C3×C5 | #423 | semidirect |
| 138. C3×C4 | #676 | semidirect |
| 162. C5 | C3×#423 | semidirect |
| 171. C4 | C3×#676 | semidirect |
| 174. C3 | #65126 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#676 | 2 |
| C3×C42×D5 | 2 |
| C3×C5×C4⋊C8 | 2 |
| C3×#3946 | 2 |
| C3×C4⋊#168 | 2 |
| #65126 | 3 |
| C3×#423 | 5 |