Finite Group DatabasebetaFinite Group Databasebeta← C2×C5×C4⋊AGL(1,𝔽5) #11717411
Order 800.
192 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 92 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. C5×C4⋊AGL(1,𝔽5) | C2 | direct (N × H) |
| 7. C2×C4×C52 | C4 | semidirect |
| 8. C2×C5×Dic5 | C4 | semidirect |
| 9. C4×C5×D5 | C4 | semidirect |
| 11. C2×C4⋊AGL(1,𝔽5) | C5 | direct (N × H) |
| 19. C4×C52 | C2×C4 | semidirect |
| 20. C5×Dic5 | C2×C4 | semidirect |
| 25. C4⋊AGL(1,𝔽5) | C2×C5 | direct (N × H) |
| 27. C2×C52 | C4⋊C4 | semidirect |
| 29. C5×D5 | C4⋊C4 | semidirect |
| 42. C2×C4×C5 | C4×C5 | semidirect |
| 43. C2×C4×C5 | AGL(1,𝔽5) | semidirect |
| 44. C2×Dic5 | C4×C5 | semidirect |
| 45. C4×D5 | C4×C5 | semidirect |
| 48. C52 | C2×C4⋊C4 | semidirect |
| 64. C4×C5 | C2×C4×C5 | semidirect |
| 65. C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 66. Dic5 | C2×C4×C5 | semidirect |
| 75. C2×C5 | C5×C4⋊C4 | semidirect |
| 76. C2×C5 | C4⋊AGL(1,𝔽5) | direct (N × H) |
| 79. D5 | C5×C4⋊C4 | semidirect |
| 88. C2×C4 | C5×AGL(1,𝔽5) | semidirect |
| 90. C5 | C2×C5×C4⋊C4 | semidirect |
| 91. C5 | C2×C4⋊AGL(1,𝔽5) | direct (N × H) |
| 99. C4 | C2×C5×AGL(1,𝔽5) | semidirect |
| 103. C2 | C5×C4⋊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×C5×AGL(1,𝔽5) | 2 |
| C2×C4×C5×D5 | 2 |
| C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×C4⋊AGL(1,𝔽5) | 5 |
| C2×C5×C4⋊C4 | 5 |