Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1962 conjugacy classes of subgroups; only the 890 normal subgroups are shown.
This group has 1962 conjugacy classes of subgroups — too many to draw. Only its 890 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×D5×#41 | C2 | semidirect |
| 4. C5×#4144 | C2 | semidirect |
| 5. C2×C5×D4×D5 | C2 | semidirect |
| 6. C23×C5×D5 | C22 | semidirect |
| 7. C52×#41 | C22 | semidirect |
| 8. C2×C52×D4 | C22 | semidirect |
| 9. C2×C5×C22⋊D5 | C22 | semidirect |
| 10. C5×#713 | C22 | semidirect |
| 11. C5×Q8×D5 | C22 | semidirect |
| 12. C5×#711 | C22 | semidirect |
| 13. C5×D4×D5 | C22 | semidirect |
| 14. C5×D4×D5 | C22 | semidirect |
| 15. C5×#709 | C22 | semidirect |
| 16. C2×C5×D20 | C22 | semidirect |
| 17. C2×C4×C5×D5 | C22 | semidirect |
| 19. D5×H(5,𝔽2) | C5 | direct (N × H) |
| 20. C23×C52 | C23 | semidirect |
| 23. C22×C5×D5 | C23 | semidirect |
| 24. C52×Q8 | C23 | semidirect |
| 25. C52×D4 | C23 | semidirect |
| 26. C2×C4×C52 | C23 | semidirect |
| 27. C5×C22⋊D5 | C23 | semidirect |
| 28. C2×C5×Dic5 | C23 | semidirect |
| 29. C5×D20 | C23 | semidirect |
| 31. C4×C5×D5 | C23 | semidirect |
| 32. C5×Dic10 | C23 | semidirect |
| 36. C5×H(5,𝔽2) | D5 | direct (N × H) |
| 37. C5×H(5,𝔽2) | C2×C5 | semidirect |
| 40. #4149 | C2×C5 | semidirect |
| 41. D5×#41 | C2×C5 | semidirect |
| 42. #4144 | C2×C5 | semidirect |
| 43. C2×D4×D5 | C2×C5 | semidirect |
| 53. C23×D5 | C22×C5 | semidirect |
| 58. C5×#41 | C2×D5 | semidirect |
| 59. C5×#41 | C22×C5 | semidirect |
| 66. C2×C5×D4 | C2×D5 | semidirect |
| 67. C2×C5×D4 | C22×C5 | semidirect |
| 69. C2×C22⋊D5 | C22×C5 | semidirect |
| 70. #713 | C22×C5 | semidirect |
| 71. Q8×D5 | C22×C5 | semidirect |
| 72. #711 | C22×C5 | semidirect |
| 73. D4×D5 | C22×C5 | semidirect |
| 74. D4×D5 | C22×C5 | semidirect |
| 75. #709 | C22×C5 | semidirect |
| 76. C2×D20 | C22×C5 | semidirect |
| 77. C2×C4×D5 | C22×C5 | semidirect |
| 82. C5×D5 | H(5,𝔽2) | direct (N × H) |
| 87. C23×C5 | C22×D5 | semidirect |
| 88. C23×C5 | C23×C5 | semidirect |
| 91. C22×D5 | C23×C5 | semidirect |
| 94. C5×Q8 | C22×D5 | semidirect |
| 95. C5×Q8 | C23×C5 | semidirect |
| 99. C5×D4 | C22×D5 | semidirect |
| 100. C5×D4 | C23×C5 | semidirect |
| 105. C2×C4×C5 | C22×D5 | semidirect |
| 106. C2×C4×C5 | C23×C5 | semidirect |
| 107. C22⋊D5 | C23×C5 | semidirect |
| 108. C2×Dic5 | C23×C5 | semidirect |
| 109. D20 | C23×C5 | semidirect |
| 111. C4×D5 | C23×C5 | semidirect |
| 112. Dic10 | C23×C5 | semidirect |
| 115. H(5,𝔽2) | C5×D5 | direct (N × H) |
| 118. C52 | C2×H(5,𝔽2) | semidirect |
| 142. #41 | C2×C5×D5 | semidirect |
| 148. C2×D4 | C2×C5×D5 | semidirect |
| 159. D5 | C5×H(5,𝔽2) | direct (N × H) |
| 163. C23 | C22×C5×D5 | semidirect |
| 165. Q8 | C22×C5×D5 | semidirect |
| 168. D4 | C22×C5×D5 | semidirect |
| 172. C2×C4 | C22×C5×D5 | semidirect |
| 174. C5 | D5×H(5,𝔽2) | direct (N × H) |
| 175. C5 | C2×C5×H(5,𝔽2) | 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×D5×#41 | 2 |
| C5×#4144 | 2 |
| C2×C5×D4×D5 | 2 |
| C2×C5×H(5,𝔽2) | 5 |
| D5×H(5,𝔽2) | 5 |