Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
256 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 94 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×C4×C5×Q8 | C2 | semidirect |
| 2. C2×C3×#688 | C2 | semidirect |
| 4. C3×#3941 | C2 | semidirect |
| 5. C3×C4⋊#168 | C2 | semidirect |
| 6. #65316 | C3 | direct (N × H) |
| 18. C4×C5×Q8 | C2×C3 | semidirect |
| 19. C2×#688 | C2×C3 | semidirect |
| 21. #3941 | C2×C3 | semidirect |
| 22. C4⋊#168 | C2×C3 | semidirect |
| 25. C3×C5×Q8 | D4 | semidirect |
| 38. C3×C4×Q8 | D5 | semidirect |
| 59. C3×C4×C5 | SD16 | semidirect |
| 74. C5×Q8 | C3×D4 | semidirect |
| 87. C4×Q8 | C3×D5 | semidirect |
| 96. C3×Q8 | D20 | semidirect |
| 114. C4×C5 | C3×SD16 | semidirect |
| 127. C3×C5 | #460 | semidirect |
| 135. C3×C4 | #688 | semidirect |
| 144. Q8 | C3×D20 | semidirect |
| 159. C5 | C3×#460 | semidirect |
| 167. C4 | C3×#688 | semidirect |
| 170. C3 | #65316 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×Q8 | 2 |
| C2×C3×#688 | 2 |
| C3×#4020 | 2 |
| C3×#3941 | 2 |
| C3×C4⋊#168 | 2 |
| #65316 | 3 |
| C3×#460 | 5 |