Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 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 |
|---|---|---|
| 1. C23×C7×D5 | C2 | semidirect |
| 2. C2×C7×C22⋊D5 | C2 | semidirect |
| 3. C2×C7×D20 | C2 | semidirect |
| 4. C5×C7×C22⋊C4 | C2 | semidirect |
| 5. C7×#685 | C2 | semidirect |
| 10. C22×C7×D5 | C22 | semidirect |
| 11. C2×C4×C5×C7 | C22 | semidirect |
| 13. C2×C7×Dic5 | C22 | semidirect |
| 16. #4028 | C7 | direct (N × H) |
| 18. C22×C5×C7 | D4 | semidirect |
| 25. C2×C7×D5 | D4 | semidirect |
| 32. C7×C22⋊C4 | D5 | semidirect |
| 33. C23×D5 | C2×C7 | semidirect |
| 34. C2×C22⋊D5 | C2×C7 | semidirect |
| 35. C2×D20 | C2×C7 | semidirect |
| 36. C5×C22⋊C4 | C2×C7 | semidirect |
| 37. #685 | C2×C7 | semidirect |
| 51. C2×C4×C7 | C2×D5 | semidirect |
| 56. C22×D5 | C22×C7 | semidirect |
| 57. C2×C4×C5 | C22×C7 | semidirect |
| 59. C2×Dic5 | C22×C7 | semidirect |
| 61. C5×C7 | #120 | semidirect |
| 70. C22×C7 | D20 | semidirect |
| 75. C22×C5 | C7×D4 | semidirect |
| 82. C2×D5 | C7×D4 | semidirect |
| 89. C22⋊C4 | C7×D5 | semidirect |
| 108. C2×C4 | C2×C7×D5 | semidirect |
| 109. C7 | #4028 | direct (N × H) |
| 110. C5 | C7×#120 | semidirect |
| 118. C22 | C7×D20 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C7×D5 | 2 |
| C2×C7×C22⋊D5 | 2 |
| C2×C7×D20 | 2 |
| C5×C7×C22⋊C4 | 2 |
| C7×#685 | 2 |
| C7×#120 | 5 |
| #4028 | 7 |