Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
384 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 190 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×#4036 | C2 | semidirect |
| 5. C3×#4033 | C2 | semidirect |
| 7. C3×#4015 | C2 | semidirect |
| 8. #66031 | C3 | direct (N × H) |
| 23. C5×#125 | C2×C3 | semidirect |
| 26. #4036 | C2×C3 | semidirect |
| 27. #4033 | C2×C3 | semidirect |
| 29. #4015 | C2×C3 | semidirect |
| 42. C3×#125 | D5 | semidirect |
| 94. #125 | C3×D5 | semidirect |
| 132. C3×C5 | #541 | semidirect |
| 157. C5 | C3×#541 | semidirect |
| 167. C3 | #66031 | 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×#4044 | 2 |
| C3×#4043 | 2 |
| C3×#4036 | 2 |
| C3×#4033 | 2 |
| C3×#4018 | 2 |
| C3×#4015 | 2 |
| #66031 | 3 |
| C3×#541 | 5 |