Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
702 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 214 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. C52×H(5,𝔽2) | C2 | semidirect |
| 2. C5×#4149 | C2 | semidirect |
| 3. C5×#4096 | C2 | semidirect |
| 4. C5×#4095 | C2 | semidirect |
| 5. C5×#4094 | C2 | semidirect |
| 6. C5×#4078 | C2 | semidirect |
| 7. C2×C5×#686 | C2 | semidirect |
| 10. C52×#41 | C22 | semidirect |
| 12. C2×C52×D4 | C22 | semidirect |
| 15. C5×#709 | C22 | semidirect |
| 16. C2×C5×D20 | C22 | semidirect |
| 17. C5×#689 | C22 | semidirect |
| 18. C5×#688 | C22 | semidirect |
| 19. C5×#687 | C22 | semidirect |
| 20. C5×#686 | C22 | semidirect |
| 21. C5×#686 | C22 | semidirect |
| 22. C5×#681 | C22 | semidirect |
| 23. C2×C5×#168 | C22 | semidirect |
| 25. #66169 | C5 | direct (N × H) |
| 45. C5×H(5,𝔽2) | D5 | semidirect |
| 46. C5×H(5,𝔽2) | C2×C5 | semidirect |
| 47. #4149 | C2×C5 | semidirect |
| 53. #4096 | C2×C5 | semidirect |
| 54. #4095 | C2×C5 | semidirect |
| 55. #4094 | C2×C5 | semidirect |
| 56. #4078 | C2×C5 | semidirect |
| 57. C2×#686 | C2×C5 | semidirect |
| 75. C5×#41 | C2×D5 | semidirect |
| 77. C5×#41 | C22×C5 | semidirect |
| 84. C2×C5×D4 | C2×D5 | semidirect |
| 85. C2×C5×D4 | C22×C5 | semidirect |
| 88. #709 | C22×C5 | semidirect |
| 89. C2×D20 | C22×C5 | semidirect |
| 97. #689 | C22×C5 | semidirect |
| 98. #688 | C22×C5 | semidirect |
| 99. #687 | C22×C5 | semidirect |
| 100. #686 | C22×C5 | semidirect |
| 101. #686 | C22×C5 | semidirect |
| 102. #681 | C22×C5 | semidirect |
| 103. C2×#168 | C22×C5 | semidirect |
| 153. H(5,𝔽2) | C5×D5 | semidirect |
| 159. C52 | #576 | semidirect |
| 188. #41 | C2×C5×D5 | semidirect |
| 192. C2×D4 | C2×C5×D5 | semidirect |
| 229. C5 | #66169 | direct (N × H) |
| 230. C5 | C5×#576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×H(5,𝔽2) | 2 |
| C5×#4149 | 2 |
| C5×#4096 | 2 |
| C5×#4095 | 2 |
| C5×#4094 | 2 |
| C5×#4078 | 2 |
| C2×C5×#686 | 2 |
| C5×#576 | 5 |
| #66169 | 5 |