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. C3×C5×C4⋊Q8 | C2 | semidirect |
| 3. C5×#942 | C2 | semidirect |
| 4. C5×#836 | C2 | semidirect |
| 5. C5×#805 | C2 | semidirect |
| 18. #5095 | C5 | direct (N × H) |
| 21. C5×C4⋊Q8 | D3 | semidirect |
| 39. C3×C4⋊Q8 | C2×C5 | semidirect |
| 40. #942 | C2×C5 | semidirect |
| 41. #836 | C2×C5 | semidirect |
| 42. #805 | C2×C5 | semidirect |
| 89. C4⋊Q8 | C5×D3 | semidirect |
| 127. C3×C5 | #456 | semidirect |
| 155. C5 | #5095 | 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 |
| C3×C5×C4⋊Q8 | 2 |
| C5×#942 | 2 |
| C5×#836 | 2 |
| C5×#805 | 2 |
| C5×#456 | 3 |
| #5095 | 5 |