Finite Group DatabasebetaFinite Group Databasebeta← C7×AGL(1,𝔽5)×#63270 #50303845
Order 38220.
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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. C72×C13×AGL(1,𝔽5) | C3 | semidirect |
| 3. C5×C7×#63270 | C4 | semidirect |
| 6. AGL(1,𝔽5)×#63270 | C7 | direct (N × H) |
| 9. C5×C72×C13 | C3×C4 | semidirect |
| 14. C7×#63270 | AGL(1,𝔽5) | direct (N × H) |
| 16. C7×C13×AGL(1,𝔽5) | ΓL(1,𝔽8) | semidirect |
| 17. C7×C13×AGL(1,𝔽5) | C3×C7 | semidirect |
| 19. C5×#63270 | C4×C7 | semidirect |
| 24. C72×AGL(1,𝔽5) | C13⋊C3 | semidirect |
| 30. C72×C13 | C3×AGL(1,𝔽5) | semidirect |
| 36. C5×C7×C13 | C4×ΓL(1,𝔽8) | semidirect |
| 37. C5×C7×C13 | C3×C4×C7 | semidirect |
| 45. #63270 | C7×AGL(1,𝔽5) | direct (N × H) |
| 47. C13×AGL(1,𝔽5) | C7×ΓL(1,𝔽8) | semidirect |
| 48. C5×C72 | C4×C13⋊C3 | semidirect |
| 59. C7×AGL(1,𝔽5) | C7×C13⋊C3 | semidirect |
| 60. C7×AGL(1,𝔽5) | #63270 | direct (N × H) |
| 66. C7×C13 | AGL(1,𝔽5)×ΓL(1,𝔽8) | semidirect |
| 67. C7×C13 | C3×C7×AGL(1,𝔽5) | semidirect |
| 74. C5×C13 | C4×C7×ΓL(1,𝔽8) | semidirect |
| 77. C72 | AGL(1,𝔽5)×C13⋊C3 | semidirect |
| 82. C5×C7 | C4×C7×C13⋊C3 | semidirect |
| 83. C5×C7 | C4×#63270 | semidirect |
| 91. AGL(1,𝔽5) | C7×#63270 | direct (N × H) |
| 96. C13 | C7×AGL(1,𝔽5)×ΓL(1,𝔽8) | semidirect |
| 100. C7 | C7×AGL(1,𝔽5)×C13⋊C3 | semidirect |
| 101. C7 | AGL(1,𝔽5)×#63270 | direct (N × H) |
| 103. C5 | C4×C7×#63270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D5×#63270 | 2 |
| C72×C13×AGL(1,𝔽5) | 3 |
| C4×C7×#63270 | 5 |
| AGL(1,𝔽5)×#63270 | 7 |
| C7×AGL(1,𝔽5)×C13⋊C3 | 7 |
| C7×AGL(1,𝔽5)×ΓL(1,𝔽8) | 13 |