Finite Group DatabasebetaFinite Group Databasebeta← AGL(1,𝔽5)×AGL(1,𝔽13) #72218859
Order 3120.
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.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13 | C3×C42 |
| prime radical | D5×D13⋊C3 | C22 |
| cosocle | D5×D13 | C22×C3 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. AGL(1,𝔽5)×#261 | C3 | semidirect |
| 6. #63118⋊C3 | C4 | semidirect |
| 7. #63120⋊C3 | C4 | semidirect |
| 8. #63121⋊C3 | C4 | semidirect |
| 9. #63122⋊C3 | C4 | semidirect |
| 10. AGL(1,𝔽5)×C13⋊C3 | C4 | semidirect |
| 11. C5×AGL(1,𝔽13) | C4 | semidirect |
| 23. #63122 | C3×C4 | semidirect |
| 24. #63121 | C3×C4 | semidirect |
| 25. #63120 | C3×C4 | semidirect |
| 26. C13×AGL(1,𝔽5) | C3×C4 | semidirect |
| 27. #63118 | C3×C4 | semidirect |
| 28. C5×#261 | C3×C4 | semidirect |
| 31. C5×C13⋊C3 | C42 | semidirect |
| 36. AGL(1,𝔽13) | AGL(1,𝔽5) | direct (N × H) |
| 52. C5×C13 | C3×C42 | semidirect |
| 64. #261 | C3×AGL(1,𝔽5) | semidirect |
| 71. C13⋊C3 | C4×AGL(1,𝔽5) | semidirect |
| 85. AGL(1,𝔽5) | AGL(1,𝔽13) | direct (N × H) |
| 90. C13 | C3×C4×AGL(1,𝔽5) | semidirect |
| 107. C5 | C4×AGL(1,𝔽13) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×AGL(1,𝔽13) | 2 |
| AGL(1,𝔽5)×D13⋊C3 | 2 |
| D5⋊AGL(1,𝔽13) | 2 |
| AGL(1,𝔽5)×#261 | 3 |
| C4×AGL(1,𝔽13) | 5 |
| C3×C4×AGL(1,𝔽5) | 13 |