Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
172 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 34 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. AGL(1,𝔽5)×SL(2,𝔽3) | C2 | semidirect |
| 3. #66262 | C3 | semidirect |
| 4. C2×C5×SL(2,𝔽3) | C4 | semidirect |
| 6. D5×SL(2,𝔽3) | C4 | semidirect |
| 11. Q8×AGL(1,𝔽5) | C2×C3 | semidirect |
| 19. C2×C5×Q8 | C3×C4 | semidirect |
| 22. Q8×D5 | C3×C4 | semidirect |
| 40. C2×SL(2,𝔽3) | AGL(1,𝔽5) | semidirect |
| 83. C2×Q8 | C3×AGL(1,𝔽5) | semidirect |
| 119. C5 | #519⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×SL(2,𝔽3) | 2 |
| AGL(1,𝔽5)×SL(2,𝔽3) | 2 |
| #66262 | 3 |
| C3×C22⋊AGL(1,𝔽5) | 4 |
| #519⋊C3 | 5 |