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×C3×#713 | C2 | semidirect |
| 3. C3×Q8×Dic5 | C2 | semidirect |
| 4. C3×#4086 | C2 | semidirect |
| 5. C3×#4084 | C2 | semidirect |
| 6. C3×#4076 | C2 | semidirect |
| 7. C3×C4×C22⋊D5 | C2 | semidirect |
| 8. #66168 | C3 | direct (N × H) |
| 24. C2×C5×#41 | C2×C3 | semidirect |
| 25. C2×#713 | C2×C3 | semidirect |
| 26. Q8×Dic5 | C2×C3 | semidirect |
| 27. #4086 | C2×C3 | semidirect |
| 28. #4084 | C2×C3 | semidirect |
| 29. #4076 | C2×C3 | semidirect |
| 30. C4×C22⋊D5 | C2×C3 | semidirect |
| 33. C3×C5×Q8 | D4 | semidirect |
| 46. C2×C3×#41 | D5 | semidirect |
| 78. C3×Dic5 | #41 | semidirect |
| 95. C5×Q8 | C3×D4 | semidirect |
| 108. C2×#41 | C3×D5 | semidirect |
| 121. C3×Q8 | C22⋊D5 | semidirect |
| 144. Dic5 | C3×#41 | semidirect |
| 159. C3×C5 | #550 | semidirect |
| 179. Q8 | C3×C22⋊D5 | semidirect |
| 196. C5 | C3×#550 | semidirect |
| 209. C3 | #66168 | direct (N × H) |
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×C3×#713 | 2 |
| C3×Q8×Dic5 | 2 |
| C3×#4086 | 2 |
| C3×#4084 | 2 |
| C3×#4076 | 2 |
| C3×C4×C22⋊D5 | 2 |
| #66168 | 3 |
| C3×#550 | 5 |