Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
| 2. C2×C5×#216 | C2 | semidirect |
| 5. C5×#803 | C2 | semidirect |
| 16. #5086 | C5 | direct (N × H) |
| 19. C5×C4⋊Q8 | D3 | semidirect |
| 32. C3×C4⋊Q8 | C2×C5 | semidirect |
| 33. C2×#216 | C2×C5 | semidirect |
| 36. #803 | C2×C5 | semidirect |
| 75. C4⋊Q8 | C5×D3 | semidirect |
| 107. C3×C5 | #497 | semidirect |
| 131. C5 | #5086 | direct (N × H) |
| 139. C3 | C5×#497 | 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×#216 | 2 |
| C2×C5×#215 | 2 |
| C5×#875 | 2 |
| C5×#803 | 2 |
| C5×#497 | 3 |
| #5086 | 5 |