Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
264 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×C4×D35 | C2 | semidirect |
| 3. C5×C7×C22⋊C4 | C2 | semidirect |
| 4. C22⋊Dic35 | C2 | semidirect |
| 5. #10587902 | C2 | semidirect |
| 8. C22×D35 | C4 | semidirect |
| 11. C2×C4×C5×C7 | C22 | semidirect |
| 12. C2×Dic35 | C22 | semidirect |
| 17. C22×C5×C7 | C2×C4 | semidirect |
| 22. C2×D35 | C2×C4 | semidirect |
| 28. C7×C22⋊C4 | D5 | semidirect |
| 33. C5×C22⋊C4 | D7 | semidirect |
| 40. D35 | C22⋊C4 | direct (N × H) |
| 46. C2×C4×C7 | C2×D5 | semidirect |
| 54. C2×C4×C5 | C2×D7 | semidirect |
| 57. C5×C7 | C2×C22⋊C4 | semidirect |
| 60. C22×C7 | C4×D5 | semidirect |
| 70. C22×C5 | C4×D7 | semidirect |
| 83. C22⋊C4 | D35 | direct (N × H) |
| 101. C2×C4 | C2×D35 | semidirect |
| 102. C7 | D5×C22⋊C4 | semidirect |
| 103. C5 | D7×C22⋊C4 | semidirect |
| 110. C22 | C4×D35 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D35 | 2 |
| C2×C4×D35 | 2 |
| C5×C7×C22⋊C4 | 2 |
| C22⋊Dic35 | 2 |
| #10587902 | 2 |
| D7×C22⋊C4 | 5 |
| D5×C22⋊C4 | 7 |