Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
188 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 60 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. C2×C4×D35 | C2 | semidirect |
| 3. C2×D7×Dic5 | C2 | semidirect |
| 4. C7×#683 | C2 | semidirect |
| 5. C5×(C2×D7)⋊C4 | C2 | semidirect |
| 6. #10587856 | C2 | semidirect |
| 7. Dic5×Dic7 | C2 | semidirect |
| 16. #63306 | C4 | semidirect |
| 23. C2×D35 | C2×C4 | semidirect |
| 26. C2×C5×D7 | C2×C4 | semidirect |
| 28. Dic35 | D4 | semidirect |
| 31. C7×Dic5 | C2×C4 | semidirect |
| 37. (C2×D7)⋊C4 | D5 | semidirect |
| 44. #683 | D7 | semidirect |
| 71. C5×C7 | C4×D4 | semidirect |
| 79. C2×D7 | C4×D5 | semidirect |
| 96. Dic5 | C4×D7 | semidirect |
| 124. C7 | #4027 | semidirect |
| 125. C5 | #6456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D35 | 2 |
| C2×#63306 | 2 |
| C2×D7×Dic5 | 2 |
| C7×#683 | 2 |
| C5×(C2×D7)⋊C4 | 2 |
| #10587856 | 2 |
| Dic5×Dic7 | 2 |
| #6456 | 5 |
| #4027 | 7 |