Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
204 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
| 5. C3×#3940 | C2 | semidirect |
| 6. C3×#3939 | C2 | semidirect |
| 7. C3×C4⋊#168 | C2 | semidirect |
| 8. #65355 | C3 | direct (N × H) |
| 21. C5×#125 | C2×C3 | semidirect |
| 25. #3940 | C2×C3 | semidirect |
| 26. #3939 | C2×C3 | semidirect |
| 27. C4⋊#168 | C2×C3 | semidirect |
| 40. C3×#125 | D5 | semidirect |
| 93. #125 | C3×D5 | semidirect |
| 138. C3×C5 | #478 | semidirect |
| 170. C5 | C3×#478 | semidirect |
| 182. C3 | #65355 | 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×C4×D20 | 2 |
| C3×#3941 | 2 |
| C3×#3940 | 2 |
| C3×#3939 | 2 |
| C3×C4⋊#168 | 2 |
| #65355 | 3 |
| C3×#478 | 5 |