Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
275 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 1. C5×D4×AGL(1,𝔽5) | C2 | semidirect |
| 3. C5×#4007 | C2 | semidirect |
| 4. C5×#3993 | C2 | semidirect |
| 5. C5×#3992 | C2 | semidirect |
| 12. C52×D8 | C4 | semidirect |
| 13. C5×#686 | C4 | semidirect |
| 14. C5×D40 | C4 | semidirect |
| 16. #65731 | C5 | direct (N × H) |
| 22. C52×D4 | C2×C4 | semidirect |
| 24. C5×D20 | C2×C4 | semidirect |
| 27. C52×C8 | C2×C4 | semidirect |
| 28. C5×#168 | C2×C4 | semidirect |
| 29. D4×AGL(1,𝔽5) | C2×C5 | semidirect |
| 33. #4007 | C2×C5 | semidirect |
| 34. #3993 | C2×C5 | semidirect |
| 35. #3992 | C2×C5 | semidirect |
| 59. C5×D8 | C4×C5 | semidirect |
| 60. C5×D8 | AGL(1,𝔽5) | semidirect |
| 66. #686 | C4×C5 | semidirect |
| 67. D40 | C4×C5 | semidirect |
| 82. C5×D4 | C2×C4×C5 | semidirect |
| 83. C5×D4 | C2×AGL(1,𝔽5) | semidirect |
| 89. D20 | C2×C4×C5 | semidirect |
| 95. C5×C8 | C2×C4×C5 | semidirect |
| 96. C5×C8 | C2×AGL(1,𝔽5) | semidirect |
| 97. #168 | C2×C4×C5 | semidirect |
| 103. C52 | #442 | semidirect |
| 128. D8 | C5×AGL(1,𝔽5) | semidirect |
| 147. D4 | C2×C5×AGL(1,𝔽5) | semidirect |
| 154. C8 | C2×C5×AGL(1,𝔽5) | semidirect |
| 156. C5 | C5×#442 | semidirect |
| 157. C5 | #65731 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×AGL(1,𝔽5) | 2 |
| C5×D5×D8 | 2 |
| C5×#4007 | 2 |
| C5×#3993 | 2 |
| C5×#3992 | 2 |
| #65731 | 5 |
| C5×#442 | 5 |