Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×C4×C7×D5 | C2 | semidirect |
| 3. C2×D5×Dic7 | C2 | semidirect |
| 4. #10587902 | C2 | semidirect |
| 5. C5×(C2×D7)⋊C4 | C2 | semidirect |
| 6. #10587856 | C2 | semidirect |
| 7. (C2×D7)⋊Dic5 | C2 | semidirect |
| 13. C2×D5×D7 | C4 | semidirect |
| 14. C2×C4×C5×C7 | C22 | semidirect |
| 15. C2×Dic35 | C22 | semidirect |
| 16. C2×C7×Dic5 | C22 | semidirect |
| 18. C2×C5×Dic7 | C22 | semidirect |
| 25. C2×D35 | C2×C4 | semidirect |
| 31. C2×C5×D7 | C2×C4 | semidirect |
| 43. (C2×D7)⋊C4 | D5 | direct (N × H) |
| 46. C2×C4×D5 | D7 | semidirect |
| 56. C7×D5 | C22⋊C4 | semidirect |
| 65. C2×C4×C7 | C2×D5 | semidirect |
| 68. C2×Dic7 | C2×D5 | semidirect |
| 76. C2×C4×C5 | C2×D7 | semidirect |
| 78. C2×Dic5 | C2×D7 | semidirect |
| 81. C5×C7 | C2×C22⋊C4 | semidirect |
| 93. C2×D7 | C4×D5 | semidirect |
| 131. D5 | (C2×D7)⋊C4 | direct (N × H) |
| 143. C2×C4 | D5×D7 | semidirect |
| 144. C7 | D5×C22⋊C4 | semidirect |
| 145. C5 | C2×(C2×D7)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×D7 | 2 |
| C2×C4×C7×D5 | 2 |
| C2×D5×Dic7 | 2 |
| #10587902 | 2 |
| C5×(C2×D7)⋊C4 | 2 |
| #10587856 | 2 |
| (C2×D7)⋊Dic5 | 2 |
| C2×(C2×D7)⋊C4 | 5 |
| D5×C22⋊C4 | 7 |