Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 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 |
|---|---|---|
| 2. C5×Q8×D7 | C2 | semidirect |
| 3. C5×C7×Q16 | C2 | semidirect |
| 4. C5×#1144 | C2 | semidirect |
| 5. C5×#1143 | C2 | semidirect |
| 6. C5×#1132 | C2 | semidirect |
| 7. C5×#1131 | C2 | semidirect |
| 19. #6481 | C5 | direct (N × H) |
| 29. Q8×D7 | C2×C5 | semidirect |
| 30. C7×Q16 | C2×C5 | semidirect |
| 31. #1144 | C2×C5 | semidirect |
| 32. #1143 | C2×C5 | semidirect |
| 33. #1132 | C2×C5 | semidirect |
| 34. #1131 | C2×C5 | semidirect |
| 38. C5×Q16 | D7 | semidirect |
| 67. C5×C7 | #137 | semidirect |
| 86. Q16 | C5×D7 | semidirect |
| 107. C7 | C5×#137 | semidirect |
| 108. C5 | #6481 | 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×Q8×D7 | 2 |
| C5×C7×Q16 | 2 |
| C5×#1144 | 2 |
| C5×#1143 | 2 |
| C5×#1132 | 2 |
| C5×#1131 | 2 |
| #6481 | 5 |
| C5×#137 | 7 |