Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
156 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 66 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×C5×Dic7 | C2 | semidirect |
| 3. C5×C22⋊Dic7 | C2 | semidirect |
| 4. C5×C22⋊Dic7 | C2 | semidirect |
| 5. C5×Dic7⋊C4 | C2 | semidirect |
| 13. #6498 | C5 | direct (N × H) |
| 24. C22×Dic7 | C2×C5 | semidirect |
| 25. C22⋊Dic7 | C2×C5 | semidirect |
| 26. C22⋊Dic7 | C2×C5 | semidirect |
| 27. Dic7⋊C4 | C2×C5 | semidirect |
| 51. C5×C7 | #123 | semidirect |
| 89. C7 | C5×#123 | semidirect |
| 90. C5 | #6498 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C7×D4 | 2 |
| C22×C5×Dic7 | 2 |
| C5×C22⋊Dic7 | 2 |
| C5×Dic7⋊C4 | 2 |
| #6498 | 5 |
| C5×#123 | 7 |