Finite Group DatabasebetaFinite Group Databasebeta← C3×(C2×AGL(1,𝔽5))⋊C8 #11746669
Order 960.
236 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 4. (C2×AGL(1,𝔽5))⋊C8 | C3 | direct (N × H) |
| 7. C2×C3×#170 | C4 | semidirect |
| 12. C2×C3×C5×C8 | C4 | semidirect |
| 13. C2×C3×#168 | C4 | semidirect |
| 23. C2×C3×AGL(1,𝔽5) | C8 | semidirect |
| 38. C2×#170 | C3×C4 | semidirect |
| 43. C2×C5×C8 | C3×C4 | semidirect |
| 44. C2×#168 | C3×C4 | semidirect |
| 66. C2×C3×C8 | AGL(1,𝔽5) | semidirect |
| 72. C2×AGL(1,𝔽5) | C3×C8 | semidirect |
| 121. C2×C8 | C3×AGL(1,𝔽5) | semidirect |
| 124. C3×C5 | #336 | semidirect |
| 158. C5 | C3×#336 | semidirect |
| 169. C3 | (C2×AGL(1,𝔽5))⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×AGL(1,𝔽5) | 2 |
| C2×C3×D5⋊C8 | 2 |
| C2×C3×C8×D5 | 2 |
| (C2×AGL(1,𝔽5))⋊C8 | 3 |
| C3×#336 | 5 |