Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 40 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 |
|---|---|---|
| 1. C5×#1161 | C2 | semidirect |
| 2. #10587945 | C2 | semidirect |
| 3. #10587906 | C2 | semidirect |
| 4. C7×#688 | C2 | semidirect |
| 5. #10587846 | C2 | semidirect |
| 6. #10587841 | C2 | semidirect |
| 7. D7×#168 | C2 | semidirect |
| 28. #1161 | D5 | semidirect |
| 38. #688 | D7 | semidirect |
| 68. C5×C7 | #135 | semidirect |
| 110. C7 | #4096 | semidirect |
| 111. C5 | #6479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1161 | 2 |
| #10587945 | 2 |
| #10587906 | 2 |
| C7×#688 | 2 |
| #10587846 | 2 |
| #10587841 | 2 |
| D7×#168 | 2 |
| #6479 | 5 |
| #4096 | 7 |