Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
624 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 226 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. C2×C3×C5×#41 | C2 | semidirect |
| 2. C2×C5×#239 | C2 | semidirect |
| 3. C5×Q8×Dic3 | C2 | semidirect |
| 4. C5×#940 | C2 | semidirect |
| 5. C5×#938 | C2 | semidirect |
| 6. C5×#930 | C2 | semidirect |
| 7. C4×C5×#67 | C2 | semidirect |
| 23. #5834 | C5 | direct (N × H) |
| 25. C2×C5×#41 | D3 | semidirect |
| 33. C3×C5×Q8 | D4 | semidirect |
| 45. C2×C3×#41 | C2×C5 | semidirect |
| 46. C2×#239 | C2×C5 | semidirect |
| 47. Q8×Dic3 | C2×C5 | semidirect |
| 48. #940 | C2×C5 | semidirect |
| 49. #938 | C2×C5 | semidirect |
| 50. #930 | C2×C5 | semidirect |
| 51. C4×#67 | C2×C5 | semidirect |
| 78. C5×Dic3 | #41 | semidirect |
| 95. C5×Q8 | #67 | semidirect |
| 108. C2×#41 | C5×D3 | semidirect |
| 121. C3×Q8 | C5×D4 | semidirect |
| 159. C3×C5 | #550 | semidirect |
| 171. Dic3 | C5×#41 | semidirect |
| 179. Q8 | C5×#67 | semidirect |
| 196. C5 | #5834 | direct (N × H) |
| 209. C3 | C5×#550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×#41 | 2 |
| C2×C5×#239 | 2 |
| C5×Q8×Dic3 | 2 |
| C5×#940 | 2 |
| C5×#938 | 2 |
| C5×#930 | 2 |
| C4×C5×#67 | 2 |
| C5×#550 | 3 |
| #5834 | 5 |