Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
532 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 205 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. C3×C5×#131 | C2 | semidirect |
| 3. #91837 | C2 | semidirect |
| 4. #91796 | C2 | semidirect |
| 5. M16×D15 | C2 | semidirect |
| 6. #91790 | C2 | semidirect |
| 7. C2×C8×D15 | C2 | semidirect |
| 16. C3×C5×M16 | C22 | semidirect |
| 17. C2×C3×C5×C8 | C22 | semidirect |
| 18. #6710 | C22 | semidirect |
| 19. C2×C3⋊#168 | C22 | semidirect |
| 20. #6705 | C22 | semidirect |
| 23. C8×D15 | C22 | semidirect |
| 24. C8×D15 | C22 | semidirect |
| 27. C5×#131 | D3 | semidirect |
| 50. C3×#131 | D5 | semidirect |
| 63. C5×M16 | C2×D3 | semidirect |
| 64. C2×C5×C8 | C2×D3 | semidirect |
| 88. C3×M16 | C2×D5 | semidirect |
| 89. C2×C3×C8 | C2×D5 | semidirect |
| 117. #131 | D15 | direct (N × H) |
| 123. D15 | #131 | direct (N × H) |
| 157. M16 | C2×D15 | semidirect |
| 163. C2×C8 | C2×D15 | semidirect |
| 164. C3×C5 | C2×#131 | semidirect |
| 197. C5 | D3×#131 | semidirect |
| 206. C3 | D5×#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D15 | 2 |
| C3×C5×#131 | 2 |
| #91837 | 2 |
| #91796 | 2 |
| M16×D15 | 2 |
| #91790 | 2 |
| C2×C8×D15 | 2 |
| D5×#131 | 3 |
| D3×#131 | 5 |