Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
444 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 214 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 |
|---|---|---|
| 1. C3×C5×#125 | C2 | semidirect |
| 4. C3×#4034 | C2 | semidirect |
| 5. C3×#4033 | C2 | semidirect |
| 7. C3×#4016 | C2 | semidirect |
| 8. #66022 | C3 | direct (N × H) |
| 23. C5×#125 | C2×C3 | semidirect |
| 26. #4034 | C2×C3 | semidirect |
| 27. #4033 | C2×C3 | semidirect |
| 29. #4016 | C2×C3 | semidirect |
| 38. C3×C4×D5 | Q8 | semidirect |
| 42. C3×#125 | D5 | semidirect |
| 91. C4×D5 | C3×Q8 | semidirect |
| 95. #125 | C3×D5 | semidirect |
| 135. C3×C5 | #533 | semidirect |
| 161. C5 | C3×#533 | semidirect |
| 171. C3 | #66022 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#125 | 2 |
| C3×#4042 | 2 |
| C3×#4038 | 2 |
| C3×#4034 | 2 |
| C3×#4033 | 2 |
| C3×C42×D5 | 2 |
| C3×#4016 | 2 |
| #66022 | 3 |
| C3×#533 | 5 |