Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
200 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×C3×Dic20 | C2 | semidirect |
| 4. C3×C5×#108 | C2 | semidirect |
| 5. C3×#3956 | C2 | semidirect |
| 6. #65185 | C3 | direct (N × H) |
| 20. C2×Dic20 | C2×C3 | semidirect |
| 22. C5×#108 | C2×C3 | semidirect |
| 23. #3956 | C2×C3 | semidirect |
| 39. C3×#108 | D5 | semidirect |
| 85. #108 | C3×D5 | semidirect |
| 119. C3×C5 | #473 | semidirect |
| 144. C5 | C3×#473 | semidirect |
| 151. C3 | #65185 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4055 | 2 |
| C2×C3×Dic20 | 2 |
| C3×#4047 | 2 |
| C3×C5×#108 | 2 |
| C3×#3956 | 2 |
| #65185 | 3 |
| C3×#473 | 5 |