Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
472 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 198 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. C3×#4093 | C2 | semidirect |
| 3. C3×#4041 | C2 | semidirect |
| 4. C3×#4038 | C2 | semidirect |
| 5. C3×C4×D20 | C2 | semidirect |
| 6. #66068 | C3 | direct (N × H) |
| 18. C5×C4⋊Q8 | C2×C3 | semidirect |
| 19. #4093 | C2×C3 | semidirect |
| 20. #4041 | C2×C3 | semidirect |
| 21. #4038 | C2×C3 | semidirect |
| 22. C4×D20 | C2×C3 | semidirect |
| 32. C3×C4⋊Q8 | D5 | semidirect |
| 75. C4⋊Q8 | C3×D5 | semidirect |
| 110. C3×C5 | #555 | semidirect |
| 134. C5 | C3×#555 | semidirect |
| 143. C3 | #66068 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C4⋊Q8 | 2 |
| C3×#4093 | 2 |
| C3×#4041 | 2 |
| C3×#4038 | 2 |
| C3×C4×D20 | 2 |
| #66068 | 3 |
| C3×#555 | 5 |