Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
879 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 879 conjugacy classes of subgroups — too many to draw. Only its 210 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. C22×D5×AGL(1,𝔽5) | C2 | semidirect |
| 3. C2×C4⋊#1042 | C2 | semidirect |
| 4. C2×C4×C5×AGL(1,𝔽5) | C2 | semidirect |
| 5. C2×(C2×AGL(1,𝔽5))⋊D5 | C2 | semidirect |
| 6. AGL(1,𝔽5)×D20 | C2 | direct (N × H) |
| 12. C2×D5×AGL(1,𝔽5) | C22 | semidirect |
| 13. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 14. C2×C5×D20 | C4 | semidirect |
| 16. C2×#6038 | C4 | semidirect |
| 17. D5×D20 | C4 | semidirect |
| 19. C4⋊#1042 | C22 | semidirect |
| 20. C4×C5×AGL(1,𝔽5) | C22 | semidirect |
| 21. (C2×AGL(1,𝔽5))⋊D5 | C22 | semidirect |
| 24. C22×C5⋊D5 | C2×C4 | semidirect |
| 25. C22×C5×D5 | C2×C4 | semidirect |
| 29. C2×D52 | C2×C4 | semidirect |
| 34. C2×C5×AGL(1,𝔽5) | D4 | semidirect |
| 38. C2×C4×C52 | C2×C4 | semidirect |
| 39. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 40. C2×C5×Dic5 | C2×C4 | semidirect |
| 41. C5×D20 | C2×C4 | semidirect |
| 42. C4×C5×D5 | C2×C4 | semidirect |
| 44. #6038 | C2×C4 | semidirect |
| 52. C2×C4×AGL(1,𝔽5) | D5 | semidirect |
| 59. C2×C5⋊D5 | C22×C4 | semidirect |
| 62. C2×C5×D5 | C22×C4 | semidirect |
| 71. C5×AGL(1,𝔽5) | C2×D4 | semidirect |
| 72. C4×C52 | C22×C4 | semidirect |
| 73. C5×Dic5 | C22×C4 | semidirect |
| 95. C2×D20 | AGL(1,𝔽5) | direct (N × H) |
| 101. C4×AGL(1,𝔽5) | C2×D5 | semidirect |
| 106. C2×C52 | C4×D4 | semidirect |
| 110. C5×D5 | C4×D4 | semidirect |
| 126. C22×D5 | C2×AGL(1,𝔽5) | semidirect |
| 132. C2×AGL(1,𝔽5) | D20 | direct (N × H) |
| 144. C2×C4×C5 | C4×D5 | semidirect |
| 145. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 149. C2×Dic5 | C4×D5 | semidirect |
| 154. D20 | C2×AGL(1,𝔽5) | direct (N × H) |
| 156. C4×D5 | C4×D5 | semidirect |
| 164. C52 | C2×C4×D4 | semidirect |
| 190. C2×D5 | C22×AGL(1,𝔽5) | semidirect |
| 194. AGL(1,𝔽5) | C2×D20 | direct (N × H) |
| 199. C4×C5 | C2×C4×D5 | semidirect |
| 200. C4×C5 | C22×AGL(1,𝔽5) | semidirect |
| 202. Dic5 | C2×C4×D5 | semidirect |
| 224. C2×C5 | C4×D20 | semidirect |
| 225. C2×C5 | D4×AGL(1,𝔽5) | semidirect |
| 232. D5 | C4×D20 | semidirect |
| 255. C2×C4 | D5×AGL(1,𝔽5) | semidirect |
| 257. C5 | C2×C4×D20 | semidirect |
| 258. C5 | C2×D4×AGL(1,𝔽5) | semidirect |
| 275. C4 | C2×D5×AGL(1,𝔽5) | semidirect |
| 281. C2 | AGL(1,𝔽5)×D20 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×AGL(1,𝔽5) | 2 |
| C2×D5×D20 | 2 |
| C2×C4⋊#1042 | 2 |
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C2×(C2×AGL(1,𝔽5))⋊D5 | 2 |
| AGL(1,𝔽5)×D20 | 2 |
| C2×D4×AGL(1,𝔽5) | 5 |
| C2×C4×D20 | 5 |