Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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. C5×#1161 | C2 | semidirect |
| 2. C5×D4×D7 | C2 | semidirect |
| 3. C5×C7×SD16 | C2 | semidirect |
| 4. C5×#1143 | C2 | semidirect |
| 5. C5×#1141 | C2 | semidirect |
| 6. C5×D56 | C2 | semidirect |
| 7. C5×#1131 | C2 | semidirect |
| 9. C5×C7×Q8 | C22 | semidirect |
| 14. C5×D28 | C22 | semidirect |
| 17. C5×C7×C8 | C22 | semidirect |
| 18. C5×C7⋊C8 | C22 | semidirect |
| 19. #6477 | C5 | direct (N × H) |
| 29. #1161 | C2×C5 | semidirect |
| 30. D4×D7 | C2×C5 | semidirect |
| 31. C7×SD16 | C2×C5 | semidirect |
| 32. #1143 | C2×C5 | semidirect |
| 33. #1141 | C2×C5 | semidirect |
| 34. D56 | C2×C5 | semidirect |
| 35. #1131 | C2×C5 | semidirect |
| 39. C5×SD16 | D7 | semidirect |
| 49. C7×Q8 | C22×C5 | semidirect |
| 54. D28 | C22×C5 | semidirect |
| 57. C7×C8 | C22×C5 | semidirect |
| 58. C7⋊C8 | C22×C5 | semidirect |
| 60. C5×Q8 | C2×D7 | semidirect |
| 69. C5×C8 | C2×D7 | semidirect |
| 70. C5×C7 | AGL(1,ℤ/8) | semidirect |
| 91. SD16 | C5×D7 | semidirect |
| 106. Q8 | C2×C5×D7 | semidirect |
| 115. C8 | C2×C5×D7 | semidirect |
| 116. C7 | C5×AGL(1,ℤ/8) | semidirect |
| 117. C5 | #6477 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1161 | 2 |
| C5×D4×D7 | 2 |
| C5×C7×SD16 | 2 |
| C5×#1143 | 2 |
| C5×#1141 | 2 |
| C5×D56 | 2 |
| C5×#1131 | 2 |
| #6477 | 5 |
| C5×AGL(1,ℤ/8) | 7 |