Finite Group DatabasebetaFinite Group Databasebeta← C7×C13⋊C3×C7⋊AGL(1,𝔽5) #50303887
Order 38220.
144 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 42 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. C7×C13×C7⋊AGL(1,𝔽5) | C3 | semidirect |
| 3. C5×C72×C13⋊C3 | C4 | semidirect |
| 6. C13⋊C3×C7⋊AGL(1,𝔽5) | C7 | direct (N × H) |
| 9. C5×C72×C13 | C3×C4 | semidirect |
| 15. C72×C13⋊C3 | AGL(1,𝔽5) | semidirect |
| 16. C13×C7⋊AGL(1,𝔽5) | C3×C7 | semidirect |
| 20. C5×C7×C13⋊C3 | Dic7 | semidirect |
| 21. C5×C7×C13⋊C3 | C4×C7 | semidirect |
| 25. C7×C7⋊AGL(1,𝔽5) | C13⋊C3 | direct (N × H) |
| 31. C72×C13 | C3×AGL(1,𝔽5) | semidirect |
| 38. C5×C7×C13 | C3×Dic7 | semidirect |
| 39. C5×C7×C13 | C3×C4×C7 | semidirect |
| 47. C7×C13⋊C3 | C7×AGL(1,𝔽5) | semidirect |
| 48. C7×C13⋊C3 | C7⋊AGL(1,𝔽5) | direct (N × H) |
| 50. C5×C72 | C4×C13⋊C3 | semidirect |
| 55. C5×C13⋊C3 | C7×Dic7 | semidirect |
| 61. C7⋊AGL(1,𝔽5) | C7×C13⋊C3 | direct (N × H) |
| 69. C7×C13 | C3×C7×AGL(1,𝔽5) | semidirect |
| 70. C7×C13 | C3×C7⋊AGL(1,𝔽5) | semidirect |
| 77. C5×C13 | C3×C7×Dic7 | semidirect |
| 80. C72 | AGL(1,𝔽5)×C13⋊C3 | semidirect |
| 84. C13⋊C3 | C7×C7⋊AGL(1,𝔽5) | direct (N × H) |
| 86. C5×C7 | Dic7×C13⋊C3 | semidirect |
| 87. C5×C7 | C4×C7×C13⋊C3 | semidirect |
| 100. C13 | C3×C7×C7⋊AGL(1,𝔽5) | semidirect |
| 104. C7 | C7×AGL(1,𝔽5)×C13⋊C3 | semidirect |
| 105. C7 | C13⋊C3×C7⋊AGL(1,𝔽5) | direct (N × H) |
| 107. C5 | C7×Dic7×C13⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C72×D5×C13⋊C3 | 2 |
| C7×C13×C7⋊AGL(1,𝔽5) | 3 |
| C7×Dic7×C13⋊C3 | 5 |
| C13⋊C3×C7⋊AGL(1,𝔽5) | 7 |
| C7×AGL(1,𝔽5)×C13⋊C3 | 7 |
| C3×C7×C7⋊AGL(1,𝔽5) | 13 |