Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
620 conjugacy classes of subgroups; only the 335 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 335 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 |
|---|---|---|
| 2. Q8×Dic15 | C2 | semidirect |
| 3. D4×Dic15 | C2 | semidirect |
| 4. #91815 | C2 | semidirect |
| 5. C2×C4×Dic15 | C2 | semidirect |
| 7. C3×C5×#41 | C4 | semidirect |
| 24. C3×C5×Q8 | C2×C4 | semidirect |
| 25. C3×C5×D4 | C2×C4 | semidirect |
| 26. C2×C3×C4×C5 | C2×C4 | semidirect |
| 37. C5×#41 | Dic3 | semidirect |
| 54. Dic15 | #41 | direct (N × H) |
| 55. C3×#41 | Dic5 | semidirect |
| 66. C5×Q8 | C2×Dic3 | semidirect |
| 67. C5×D4 | C2×Dic3 | semidirect |
| 68. C2×C4×C5 | C2×Dic3 | semidirect |
| 83. C3×Q8 | C2×Dic5 | semidirect |
| 84. C3×D4 | C2×Dic5 | semidirect |
| 85. C2×C3×C4 | C2×Dic5 | semidirect |
| 98. #41 | Dic15 | direct (N × H) |
| 108. C3×C5 | C4×#41 | semidirect |
| 120. Q8 | C2×Dic15 | semidirect |
| 121. D4 | C2×Dic15 | semidirect |
| 125. C2×C4 | C2×Dic15 | semidirect |
| 131. C5 | Dic3×#41 | semidirect |
| 139. C3 | #41×Dic5 | 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 |
| Q8×Dic15 | 2 |
| D4×Dic15 | 2 |
| #91815 | 2 |
| C2×C4×Dic15 | 2 |
| #41×Dic5 | 3 |
| Dic3×#41 | 5 |