Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 2. C5×#888 | C2 | semidirect |
| 3. C3×C5×#107 | C2 | semidirect |
| 5. C5×Dic3⋊C8 | C2 | semidirect |
| 7. C5×#807 | C2 | semidirect |
| 20. #4890 | C5 | direct (N × H) |
| 24. C5×#107 | D3 | semidirect |
| 36. C5×D12 | Q8 | semidirect |
| 42. #888 | C2×C5 | semidirect |
| 43. C3×#107 | C2×C5 | semidirect |
| 45. Dic3⋊C8 | C2×C5 | semidirect |
| 47. #807 | C2×C5 | semidirect |
| 98. #107 | C5×D3 | semidirect |
| 114. D12 | C5×Q8 | semidirect |
| 141. C3×C5 | #474 | semidirect |
| 174. C5 | #4890 | direct (N × H) |
| 186. C3 | C5×#474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#893 | 2 |
| C5×#888 | 2 |
| C3×C5×#107 | 2 |
| C5×#821 | 2 |
| C5×Dic3⋊C8 | 2 |
| C5×#809 | 2 |
| C5×#807 | 2 |
| C5×#474 | 3 |
| #4890 | 5 |