Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 70 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×C5×C7×D4 | C2 | semidirect |
| 2. C2×C5×C22⋊D7 | C2 | semidirect |
| 3. C2×C4×C5×D7 | C2 | semidirect |
| 4. C5×C22⋊Dic7 | C2 | semidirect |
| 5. C5×C4⋊Dic7 | C2 | semidirect |
| 14. #6501 | C5 | direct (N × H) |
| 22. C2×C5×D7 | D4 | semidirect |
| 23. C4×C5×C7 | D4 | semidirect |
| 26. C2×C7×D4 | C2×C5 | semidirect |
| 27. C2×C22⋊D7 | C2×C5 | semidirect |
| 28. C2×C4×D7 | C2×C5 | semidirect |
| 29. C22⋊Dic7 | C2×C5 | semidirect |
| 30. C4⋊Dic7 | C2×C5 | semidirect |
| 32. C2×C5×D4 | D7 | semidirect |
| 57. C5×C7 | #121 | semidirect |
| 65. C2×D7 | C5×D4 | semidirect |
| 66. C4×C7 | C5×D4 | semidirect |
| 78. C4×C5 | C22⋊D7 | semidirect |
| 80. C2×D4 | C5×D7 | semidirect |
| 102. C7 | C5×#121 | semidirect |
| 103. C5 | #6501 | direct (N × H) |
| 113. C4 | C5×C22⋊D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C7×D4 | 2 |
| C2×C5×C22⋊D7 | 2 |
| C2×C4×C5×D7 | 2 |
| C5×C22⋊Dic7 | 2 |
| C5×C4⋊Dic7 | 2 |
| #6501 | 5 |
| C5×#121 | 7 |