Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
188 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 62 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×C7×D5 | C2 | semidirect |
| 3. C2×#63304 | C2 | semidirect |
| 4. #10587902 | C2 | semidirect |
| 5. C5×Dic7⋊C4 | C2 | semidirect |
| 6. #10587855 | C2 | semidirect |
| 7. Dic5×Dic7 | C2 | semidirect |
| 16. #63307 | C4 | semidirect |
| 23. C2×D35 | C2×C4 | semidirect |
| 26. C2×C7×D5 | C2×C4 | semidirect |
| 30. C5×Dic7 | C2×C4 | semidirect |
| 31. C7×Dic5 | D4 | semidirect |
| 37. Dic7⋊C4 | D5 | semidirect |
| 41. C2×C4×D5 | D7 | semidirect |
| 71. C5×C7 | C4×D4 | semidirect |
| 84. Dic7 | C4×D5 | semidirect |
| 91. C2×D5 | C4×D7 | semidirect |
| 96. Dic5 | C22⋊D7 | semidirect |
| 124. C7 | #4039 | semidirect |
| 125. C5 | C4×C22⋊D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D5 | 2 |
| C2×#63307 | 2 |
| C2×#63304 | 2 |
| #10587902 | 2 |
| C5×Dic7⋊C4 | 2 |
| #10587855 | 2 |
| Dic5×Dic7 | 2 |
| C4×C22⋊D7 | 5 |
| #4039 | 7 |