Finite Group DatabasebetaFinite Group Databasebeta← C2×C11×C22⋊AGL(1,𝔽5) #13183343
Order 1760.
264 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 92 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. C11×C22⋊AGL(1,𝔽5) | C2 | direct (N × H) |
| 4. C23×C5×C11 | C4 | semidirect |
| 6. C22×D5×C11 | C4 | semidirect |
| 7. C22×D5×C11 | C4 | semidirect |
| 11. C2×C11×AGL(1,𝔽5) | C22 | semidirect |
| 15. C22×C5×C11 | C2×C4 | semidirect |
| 20. C2×D5×C11 | C2×C4 | semidirect |
| 27. C2×C22⋊AGL(1,𝔽5) | C11 | direct (N × H) |
| 29. C2×C5×C11 | C22⋊C4 | semidirect |
| 32. D5×C11 | C22⋊C4 | semidirect |
| 39. C23×C11 | AGL(1,𝔽5) | semidirect |
| 43. C22×AGL(1,𝔽5) | C2×C11 | semidirect |
| 44. C22⋊AGL(1,𝔽5) | C2×C11 | direct (N × H) |
| 45. C5×C11 | C2×C22⋊C4 | semidirect |
| 55. C22×C11 | C2×AGL(1,𝔽5) | semidirect |
| 57. C23×C5 | C4×C11 | semidirect |
| 59. C22×D5 | C4×C11 | semidirect |
| 60. C22×D5 | C4×C11 | semidirect |
| 64. C2×AGL(1,𝔽5) | C22×C11 | semidirect |
| 70. C2×C11 | C22⋊AGL(1,𝔽5) | direct (N × H) |
| 74. C22×C5 | C2×C4×C11 | semidirect |
| 79. C2×D5 | C2×C4×C11 | semidirect |
| 86. C11 | C2×C22⋊AGL(1,𝔽5) | direct (N × H) |
| 88. C2×C5 | C11×C22⋊C4 | semidirect |
| 91. D5 | C11×C22⋊C4 | semidirect |
| 98. C23 | C11×AGL(1,𝔽5) | semidirect |
| 101. C5 | C2×C11×C22⋊C4 | semidirect |
| 111. C22 | C2×C11×AGL(1,𝔽5) | semidirect |
| 117. C2 | C11×C22⋊AGL(1,𝔽5) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D5×C11 | 2 |
| C22×C11×AGL(1,𝔽5) | 2 |
| C11×C22⋊AGL(1,𝔽5) | 2 |
| C2×C11×C22⋊C4 | 5 |
| C2×C22⋊AGL(1,𝔽5) | 11 |