Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 47 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×C7×#41 | C2 | semidirect |
| 2. C2×D140 | C2 | semidirect |
| 3. #10587905 | C2 | semidirect |
| 4. #10587903 | C2 | semidirect |
| 5. #10587898 | C2 | semidirect |
| 7. C5×C7×Q8 | C22 | semidirect |
| 9. C5×C7×D4 | C22 | semidirect |
| 14. C7⋊#168 | C22 | semidirect |
| 24. C7×#41 | D5 | semidirect |
| 29. C5×#41 | D7 | semidirect |
| 39. C7×Q8 | C2×D5 | semidirect |
| 41. C7×D4 | C2×D5 | semidirect |
| 48. C5×Q8 | C2×D7 | semidirect |
| 50. C5×D4 | C2×D7 | semidirect |
| 56. C5×C7 | AGL(1,ℤ/8) | semidirect |
| 72. #41 | D35 | semidirect |
| 86. Q8 | C2×D35 | semidirect |
| 90. D4 | C2×D35 | semidirect |
| 94. C7 | #4095 | semidirect |
| 95. C5 | #6512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C7×#41 | 2 |
| C2×D140 | 2 |
| #10587905 | 2 |
| #10587903 | 2 |
| #10587898 | 2 |
| #6512 | 5 |
| #4095 | 7 |