Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
220 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. C3×#4016 | C2 | semidirect |
| 3. C3×C5×#97 | C2 | semidirect |
| 4. C3×#3953 | C2 | semidirect |
| 5. #65002 | C3 | direct (N × H) |
| 14. #4016 | C2×C3 | semidirect |
| 15. C5×#97 | C2×C3 | semidirect |
| 16. #3953 | C2×C3 | semidirect |
| 27. C3×#97 | D5 | semidirect |
| 57. #97 | C3×D5 | semidirect |
| 80. C3×C5 | #490 | semidirect |
| 100. C5 | C3×#490 | semidirect |
| 107. C3 | #65002 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4020 | 2 |
| C3×#4016 | 2 |
| C3×C5×#97 | 2 |
| C3×#3953 | 2 |
| #65002 | 3 |
| C3×#490 | 5 |