Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 4. C5×C4⋊Dic7 | C2 | semidirect |
| 5. C5×Dic7⋊C4 | C2 | semidirect |
| 6. C5×Dic7⋊C4 | C2 | semidirect |
| 7. C4×C5×Dic7 | C2 | semidirect |
| 15. #6442 | C5 | direct (N × H) |
| 30. C4⋊Dic7 | C2×C5 | semidirect |
| 31. Dic7⋊C4 | C2×C5 | semidirect |
| 32. Dic7⋊C4 | C2×C5 | semidirect |
| 33. C4×Dic7 | C2×C5 | semidirect |
| 59. C5×C7 | #126 | semidirect |
| 103. C7 | C5×#126 | semidirect |
| 104. C5 | #6442 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C7×C22⋊C4 | 2 |
| C5×C22⋊Dic7 | 2 |
| C5×C4⋊Dic7 | 2 |
| C5×Dic7⋊C4 | 2 |
| C4×C5×Dic7 | 2 |
| #6442 | 5 |
| C5×#126 | 7 |