Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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. #10587900 | C2 | semidirect |
| 2. C4×C7×Dic5 | C2 | semidirect |
| 4. #10587858 | C2 | semidirect |
| 5. Dic7⋊Dic5 | C2 | semidirect |
| 40. C4×Dic5 | D7 | semidirect |
| 59. C5×C7 | #126 | semidirect |
| 103. C7 | #4025 | semidirect |
| 104. C5 | #6439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10587900 | 2 |
| C4×C7×Dic5 | 2 |
| C5×(C2×D7)⋊C4 | 2 |
| #10587858 | 2 |
| Dic7⋊Dic5 | 2 |
| (C2×D7)⋊Dic5 | 2 |
| #6439 | 5 |
| #4025 | 7 |