Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
124 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 124 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×#1159 | C2 | semidirect |
| 3. C5×C7×SD16 | C2 | semidirect |
| 4. C5×#1144 | C2 | semidirect |
| 5. C5×#1141 | C2 | semidirect |
| 6. C5×#1132 | C2 | semidirect |
| 7. C5×C8×D7 | C2 | semidirect |
| 19. #6479 | C5 | direct (N × H) |
| 28. #1161 | C2×C5 | semidirect |
| 29. #1159 | C2×C5 | semidirect |
| 30. C7×SD16 | C2×C5 | semidirect |
| 31. #1144 | C2×C5 | semidirect |
| 32. #1141 | C2×C5 | semidirect |
| 33. #1132 | C2×C5 | semidirect |
| 34. C8×D7 | C2×C5 | semidirect |
| 39. C5×SD16 | D7 | semidirect |
| 68. C5×C7 | #135 | semidirect |
| 88. SD16 | C5×D7 | semidirect |
| 110. C7 | C5×#135 | semidirect |
| 111. C5 | #6479 | 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×#1159 | 2 |
| C5×C7×SD16 | 2 |
| C5×#1144 | 2 |
| C5×#1141 | 2 |
| C5×#1132 | 2 |
| C5×C8×D7 | 2 |
| #6479 | 5 |
| C5×#135 | 7 |