Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1072 conjugacy classes of subgroups; only the 574 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 574 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×C5×C4⋊Dic5 | C2 | direct (N × H) |
| 5. C22×C4×C52 | C4 | semidirect |
| 9. C5×C4⋊Dic5 | C22 | direct (N × H) |
| 11. C22×C4⋊Dic5 | C5 | direct (N × H) |
| 16. C2×C4×C52 | C2×C4 | semidirect |
| 26. C2×C4⋊Dic5 | C2×C5 | direct (N × H) |
| 27. C22×C52 | C4⋊C4 | semidirect |
| 32. C4×C52 | C22×C4 | semidirect |
| 41. C22×C4×C5 | Dic5 | semidirect |
| 42. C22×C4×C5 | C4×C5 | semidirect |
| 48. C4⋊Dic5 | C22×C5 | direct (N × H) |
| 50. C2×C52 | C2×C4⋊C4 | semidirect |
| 70. C2×C4×C5 | C2×Dic5 | semidirect |
| 71. C2×C4×C5 | C2×C4×C5 | semidirect |
| 79. C52 | C22×C4⋊C4 | semidirect |
| 85. C22×C5 | C4⋊Dic5 | direct (N × H) |
| 86. C22×C5 | C5×C4⋊C4 | semidirect |
| 97. C4×C5 | C22×Dic5 | semidirect |
| 98. C4×C5 | C22×C4×C5 | semidirect |
| 103. C22×C4 | C5×Dic5 | semidirect |
| 110. C2×C5 | C2×C4⋊Dic5 | direct (N × H) |
| 111. C2×C5 | C2×C5×C4⋊C4 | semidirect |
| 124. C2×C4 | C2×C5×Dic5 | semidirect |
| 127. C5 | C22×C4⋊Dic5 | direct (N × H) |
| 128. C5 | C22×C5×C4⋊C4 | semidirect |
| 129. C22 | C5×C4⋊Dic5 | direct (N × H) |
| 135. C4 | C22×C5×Dic5 | semidirect |
| 136. C2 | C2×C5×C4⋊Dic5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C52 | 2 |
| C23×C5×Dic5 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C22×C5×C4⋊C4 | 5 |
| C22×C4⋊Dic5 | 5 |