Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
100 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 36 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. C11×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C11×D5⋊C8 | C2 | semidirect |
| 6. C5×D4×C11 | C4 | semidirect |
| 8. C11×D20 | C4 | semidirect |
| 23. #4007 | C11 | direct (N × H) |
| 32. D4×C11 | AGL(1,𝔽5) | semidirect |
| 37. C4⋊AGL(1,𝔽5) | C2×C11 | semidirect |
| 38. D5⋊C8 | C2×C11 | semidirect |
| 39. C5×C11 | #102 | semidirect |
| 50. C5×D4 | C4×C11 | semidirect |
| 52. D20 | C4×C11 | semidirect |
| 72. C11 | #4007 | direct (N × H) |
| 81. D4 | C11×AGL(1,𝔽5) | semidirect |
| 85. C5 | C11×#102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D5×C11 | 2 |
| C11×C4⋊AGL(1,𝔽5) | 2 |
| C11×D5⋊C8 | 2 |
| C11×#102 | 5 |
| #4007 | 11 |