Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
284 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 284 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. C5×#944 | C2 | semidirect |
| 3. C5×#909 | C2 | semidirect |
| 4. C3×C5×#101 | C2 | semidirect |
| 5. C5×#825 | C2 | semidirect |
| 18. #4752 | C5 | direct (N × H) |
| 23. C5×#101 | D3 | semidirect |
| 39. #944 | C2×C5 | semidirect |
| 40. #909 | C2×C5 | semidirect |
| 41. C3×#101 | C2×C5 | semidirect |
| 42. #825 | C2×C5 | semidirect |
| 91. #101 | C5×D3 | semidirect |
| 127. C3×C5 | #456 | semidirect |
| 155. C5 | #4752 | direct (N × H) |
| 163. C3 | C5×#456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1007 | 2 |
| C5×#944 | 2 |
| C5×#909 | 2 |
| C3×C5×#101 | 2 |
| C5×#825 | 2 |
| C5×#456 | 3 |
| #4752 | 5 |