Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1011 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 1011 conjugacy classes of subgroups — too many to draw. Only its 223 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 |
|---|---|---|
| 2. C23×#1035 | C2 | semidirect |
| 3. C2×C22⋊#1035 | C2 | direct (N × H) |
| 4. C24×C25 | C4 | semidirect |
| 6. C23×D25 | C4 | semidirect |
| 7. C23×D25 | C4 | semidirect |
| 11. C22×#1035 | C22 | semidirect |
| 12. C22⋊#1035 | C22 | direct (N × H) |
| 16. C23×C25 | C2×C4 | semidirect |
| 21. C22×D25 | C2×C4 | semidirect |
| 22. C22×D25 | C2×C4 | semidirect |
| 27. C2×#1035 | C23 | semidirect |
| 32. C22×C25 | C22⋊C4 | semidirect |
| 34. C22×C25 | C22×C4 | semidirect |
| 38. C2×D25 | C22⋊C4 | semidirect |
| 40. C2×D25 | C22×C4 | semidirect |
| 55. C2×C25 | C2×C22⋊C4 | semidirect |
| 58. D25 | C2×C22⋊C4 | semidirect |
| 77. C25 | C22×C22⋊C4 | semidirect |
| 96. C24 | #1035 | semidirect |
| 117. C23 | C2×#1035 | semidirect |
| 130. C22 | C22⋊#1035 | direct (N × H) |
| 132. C22 | C22×#1035 | semidirect |
| 138. C2 | C2×C22⋊#1035 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D25 | 2 |
| C23×#1035 | 2 |
| C2×C22⋊#1035 | 2 |
| C22×C22⋊AGL(1,𝔽5) | 5 |