Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
152 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 3. C4⋊(C7⋊AGL(1,𝔽5)) | C2 | semidirect |
| 4. C4×C7⋊AGL(1,𝔽5) | C2 | semidirect |
| 7. C2×C4×C5×C7 | C4 | semidirect |
| 8. C2×C7×Dic5 | C4 | semidirect |
| 9. C4×C7×D5 | C4 | semidirect |
| 10. C4×C7×D5 | C4 | semidirect |
| 42. C2×C4×C7 | AGL(1,𝔽5) | semidirect |
| 46. C2×C4×C5 | Dic7 | semidirect |
| 47. C2×Dic5 | Dic7 | semidirect |
| 48. C4×D5 | Dic7 | semidirect |
| 49. C4×D5 | Dic7 | semidirect |
| 52. C5×C7 | #117 | semidirect |
| 91. C2×C4 | C7⋊AGL(1,𝔽5) | semidirect |
| 92. C7 | #4130 | semidirect |
| 93. C5 | #6489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D5 | 2 |
| C22⋊(C7⋊AGL(1,𝔽5)) | 2 |
| C4⋊(C7⋊AGL(1,𝔽5)) | 2 |
| C4×C7⋊AGL(1,𝔽5) | 2 |
| #6489 | 5 |
| #4130 | 7 |