Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 1. C3×C5×C4⋊Q8 | C2 | semidirect |
| 4. C5×#835 | C2 | semidirect |
| 5. C5×C4⋊(C3⋊C8) | C2 | semidirect |
| 17. #5083 | C5 | direct (N × H) |
| 19. C5×C4⋊Q8 | D3 | semidirect |
| 35. C3×C4⋊Q8 | C2×C5 | semidirect |
| 38. #835 | C2×C5 | semidirect |
| 39. C4⋊(C3⋊C8) | C2×C5 | semidirect |
| 57. C3×C4×C5 | SD16 | semidirect |
| 84. C4⋊Q8 | C5×D3 | semidirect |
| 111. C4×C5 | #215 | semidirect |
| 124. C3×C5 | #461 | semidirect |
| 131. C3×C4 | C5×SD16 | semidirect |
| 155. C5 | #5083 | direct (N × H) |
| 163. C4 | C5×#215 | semidirect |
| 166. C3 | C5×#461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C4⋊Q8 | 2 |
| C2×C5×#215 | 2 |
| C4×C5×D12 | 2 |
| C5×#835 | 2 |
| C5×C4⋊(C3⋊C8) | 2 |
| C5×#461 | 3 |
| #5083 | 5 |