Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
863 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 863 conjugacy classes of subgroups — too many to draw. Only its 341 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. C2×C4⋊#1042 | C2 | direct (N × H) |
| 7. C22×C4×C52 | C4 | semidirect |
| 8. C22×C5×Dic5 | C4 | semidirect |
| 9. C2×C4×C5×D5 | C4 | semidirect |
| 11. C4⋊#1042 | C22 | direct (N × H) |
| 21. C2×C4×C52 | C2×C4 | semidirect |
| 22. C2×C5×Dic5 | C2×C4 | semidirect |
| 23. C4×C5×D5 | C2×C4 | semidirect |
| 31. C22×C52 | C4⋊C4 | semidirect |
| 33. C2×C5×D5 | C4⋊C4 | semidirect |
| 39. C4×C52 | C22×C4 | semidirect |
| 40. C5×Dic5 | C22×C4 | semidirect |
| 49. C22×C4×C5 | Dic5 | semidirect |
| 50. C22×C4×C5 | AGL(1,𝔽5) | semidirect |
| 53. C22×Dic5 | Dic5 | semidirect |
| 54. C2×C4×D5 | Dic5 | semidirect |
| 59. C2×C52 | C2×C4⋊C4 | semidirect |
| 61. C5×D5 | C2×C4⋊C4 | semidirect |
| 81. C2×C4×C5 | C2×Dic5 | semidirect |
| 82. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 85. C2×Dic5 | C2×Dic5 | semidirect |
| 86. C4×D5 | C2×Dic5 | semidirect |
| 91. C52 | C22×C4⋊C4 | semidirect |
| 99. C22×C5 | C4⋊Dic5 | semidirect |
| 100. C22×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 103. C2×D5 | C4⋊Dic5 | semidirect |
| 111. C4×C5 | C22×Dic5 | semidirect |
| 112. C4×C5 | C22×AGL(1,𝔽5) | semidirect |
| 114. Dic5 | C22×Dic5 | semidirect |
| 121. C22×C4 | #1042 | semidirect |
| 128. C2×C5 | C2×C4⋊Dic5 | semidirect |
| 129. C2×C5 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 132. D5 | C2×C4⋊Dic5 | semidirect |
| 145. C2×C4 | C2×#1042 | semidirect |
| 147. C5 | C22×C4⋊Dic5 | semidirect |
| 148. C5 | C22×C4⋊AGL(1,𝔽5) | semidirect |
| 154. C22 | C4⋊#1042 | direct (N × H) |
| 158. C4 | C22×#1042 | semidirect |
| 162. C2 | C2×C4⋊#1042 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1042 | 2 |
| C22×C4×C5×D5 | 2 |
| C2×C4⋊#1042 | 2 |
| C22×C4⋊AGL(1,𝔽5) | 5 |
| C22×C4⋊Dic5 | 5 |