Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1368 conjugacy classes of subgroups; only the 299 normal subgroups are shown.
This group has 1368 conjugacy classes of subgroups — too many to draw. Only its 299 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. C22×C4×C5⋊D5 | C2 | semidirect |
| 3. C2×C52×C22⋊C4 | C2 | semidirect |
| 4. C2×C22⋊#1039 | C2 | semidirect |
| 5. C2×#87808 | C2 | semidirect |
| 6. C2×C4⋊#1039 | C2 | semidirect |
| 7. C2×#87806 | C2 | semidirect |
| 8. #11717203 | C2 | direct (N × H) |
| 19. C2×C4×C5⋊D5 | C22 | semidirect |
| 20. C52×C22⋊C4 | C22 | semidirect |
| 21. C22⋊#1039 | C22 | semidirect |
| 22. #87808 | C22 | semidirect |
| 23. C4⋊#1039 | C22 | semidirect |
| 24. #87806 | C22 | semidirect |
| 49. C2×C5×C22⋊C4 | D5 | semidirect |
| 83. C5×C22⋊C4 | C2×D5 | semidirect |
| 90. C2×C52 | #123 | semidirect |
| 123. C2×C22⋊C4 | C5⋊D5 | semidirect |
| 124. C52 | C2×#123 | semidirect |
| 157. C22⋊C4 | C2×C5⋊D5 | semidirect |
| 159. C2×C5 | #4029 | semidirect |
| 185. C5 | C2×#4029 | semidirect |
| 205. C2 | #11717203 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊(C5⋊D5) | 2 |
| C22×C4×C5⋊D5 | 2 |
| C2×C52×C22⋊C4 | 2 |
| C2×C22⋊#1039 | 2 |
| C2×#87808 | 2 |
| C2×C4⋊#1039 | 2 |
| C2×#87806 | 2 |
| #11717203 | 2 |
| C2×#4029 | 5 |