Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
168 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 168 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. #66266 | C3 | semidirect |
| 4. C5×#41⋊C3 | C4 | semidirect |
| 7. C5⋊(#41⋊C3) | C4 | semidirect |
| 16. C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 20. C5×#41 | C3×C4 | semidirect |
| 21. #713 | C3×C4 | semidirect |
| 38. #41⋊C3 | AGL(1,𝔽5) | semidirect |
| 66. SL(2,𝔽3) | C2×AGL(1,𝔽5) | semidirect |
| 81. #41 | C3×AGL(1,𝔽5) | semidirect |
| 119. C5 | #520⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#41⋊C3 | 2 |
| AGL(1,𝔽5)×SL(2,𝔽3) | 2 |
| #66266 | 3 |
| C3×C4⋊AGL(1,𝔽5) | 4 |
| #520⋊C3 | 5 |