Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
560 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 246 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×Q8×D5 | C2 | semidirect |
| 2. C3×C4×C5×Q8 | C2 | semidirect |
| 3. C3×#4043 | C2 | semidirect |
| 5. C3×#4015 | C2 | semidirect |
| 6. Q8×D20 | C3 | direct (N × H) |
| 18. C2×Q8×D5 | C2×C3 | semidirect |
| 19. C4×C5×Q8 | C2×C3 | semidirect |
| 20. #4043 | C2×C3 | semidirect |
| 22. #4015 | C2×C3 | semidirect |
| 24. C3×C5×Q8 | D4 | semidirect |
| 29. C3×D20 | Q8 | direct (N × H) |
| 35. C3×C4×Q8 | D5 | semidirect |
| 51. C2×C3×D5 | C2×Q8 | semidirect |
| 54. C3×C4×C5 | C2×Q8 | semidirect |
| 67. C5×Q8 | C3×D4 | semidirect |
| 72. D20 | C3×Q8 | direct (N × H) |
| 78. C4×Q8 | C3×D5 | semidirect |
| 86. C3×Q8 | D20 | direct (N × H) |
| 96. C2×D5 | C2×C3×Q8 | semidirect |
| 99. C4×C5 | C2×C3×Q8 | semidirect |
| 111. C3×C5 | D4×Q8 | semidirect |
| 119. C3×C4 | Q8×D5 | semidirect |
| 126. Q8 | C3×D20 | direct (N × H) |
| 137. C5 | C3×D4×Q8 | semidirect |
| 145. C4 | C3×Q8×D5 | semidirect |
| 146. C3 | Q8×D20 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×D5 | 2 |
| C3×C4×C5×Q8 | 2 |
| C3×#4043 | 2 |
| C3×C4×D20 | 2 |
| C3×#4015 | 2 |
| Q8×D20 | 3 |
| C3×D4×Q8 | 5 |