Finite Group DatabasebetaFinite Group Databasebeta← C2×C4⋊(C7⋊AGL(1,𝔽5)) #11765359
Order 1120.
184 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 81 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 | direct (N × H) |
| 7. C2×C4×C5×C7 | C4 | semidirect |
| 8. C2×C7×Dic5 | C4 | semidirect |
| 9. C4×C7×D5 | C4 | semidirect |
| 19. C4×C5×C7 | C2×C4 | semidirect |
| 20. C7×Dic5 | C2×C4 | semidirect |
| 27. C2×C5×C7 | C4⋊C4 | semidirect |
| 29. C7×D5 | C4⋊C4 | semidirect |
| 36. C2×C4×C7 | AGL(1,𝔽5) | semidirect |
| 42. C2×C4×C5 | Dic7 | semidirect |
| 43. C2×Dic5 | Dic7 | semidirect |
| 44. C4×D5 | Dic7 | semidirect |
| 46. C5×C7 | C2×C4⋊C4 | semidirect |
| 54. C4×C7 | C2×AGL(1,𝔽5) | semidirect |
| 62. C4×C5 | C2×Dic7 | semidirect |
| 63. Dic5 | C2×Dic7 | semidirect |
| 70. C2×C7 | C4⋊AGL(1,𝔽5) | semidirect |
| 72. C2×C5 | C4⋊Dic7 | semidirect |
| 74. D5 | C4⋊Dic7 | semidirect |
| 83. C2×C4 | C7⋊AGL(1,𝔽5) | semidirect |
| 84. C7 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 85. C5 | C2×C4⋊Dic7 | semidirect |
| 93. C4 | C2×C7⋊AGL(1,𝔽5) | semidirect |
| 97. C2 | C4⋊(C7⋊AGL(1,𝔽5)) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7⋊AGL(1,𝔽5) | 2 |
| C2×C4×C7×D5 | 2 |
| C4⋊(C7⋊AGL(1,𝔽5)) | 2 |
| C2×C4⋊Dic7 | 5 |
| C2×C4⋊AGL(1,𝔽5) | 7 |