Finite Group DatabasebetaFinite Group Databasebeta← C2×(C2×AGL(1,𝔽5))⋊D11 #13183310
Order 1760.
264 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 70 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. C22×C11⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C22×C11×AGL(1,𝔽5) | C2 | semidirect |
| 4. (C2×AGL(1,𝔽5))⋊D11 | C2 | direct (N × H) |
| 5. C22×D55 | C4 | semidirect |
| 7. C22×C5×D11 | C4 | semidirect |
| 10. C2×D5×D11 | C4 | semidirect |
| 13. C2×C11⋊AGL(1,𝔽5) | C22 | semidirect |
| 15. C2×C11×AGL(1,𝔽5) | C22 | semidirect |
| 19. C2×D55 | C2×C4 | semidirect |
| 25. C2×C5×D11 | C2×C4 | semidirect |
| 36. C2×C5×C11 | C22⋊C4 | semidirect |
| 40. D5×C11 | C22⋊C4 | semidirect |
| 49. C22×D11 | AGL(1,𝔽5) | semidirect |
| 56. C22×AGL(1,𝔽5) | D11 | semidirect |
| 58. C5×C11 | C2×C22⋊C4 | semidirect |
| 70. C2×D11 | C2×AGL(1,𝔽5) | semidirect |
| 83. C2×AGL(1,𝔽5) | C2×D11 | semidirect |
| 88. C2×C11 | C22⋊AGL(1,𝔽5) | semidirect |
| 110. C11 | C2×C22⋊AGL(1,𝔽5) | semidirect |
| 112. C2×C5 | (C2×D11)⋊C4 | semidirect |
| 115. D5 | (C2×D11)⋊C4 | semidirect |
| 129. C5 | C2×(C2×D11)⋊C4 | semidirect |
| 149. C2 | (C2×AGL(1,𝔽5))⋊D11 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×D11 | 2 |
| C22×C11⋊AGL(1,𝔽5) | 2 |
| C22×C11×AGL(1,𝔽5) | 2 |
| (C2×AGL(1,𝔽5))⋊D11 | 2 |
| C2×(C2×D11)⋊C4 | 5 |
| C2×C22⋊AGL(1,𝔽5) | 11 |