Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1176 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1176 conjugacy classes of subgroups — too many to draw. Only its 331 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. C52×#117 | C2 | semidirect |
| 3. C2×C4⋊#1039 | C2 | semidirect |
| 4. #11717212 | C2 | semidirect |
| 5. C4⋊C4×C5⋊D5 | C2 | semidirect |
| 6. #11717201 | C2 | semidirect |
| 7. C4×C4⋊(C5⋊D5) | C2 | semidirect |
| 8. C4×#6045 | C2 | semidirect |
| 12. #87900 | C4 | semidirect |
| 29. C2×C4×C52 | C2×C4 | semidirect |
| 34. C22⋊(C5⋊D5) | C2×C4 | semidirect |
| 38. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 40. C4×C5⋊D5 | C2×C4 | semidirect |
| 41. #6045 | C2×C4 | semidirect |
| 43. C5×#117 | D5 | semidirect |
| 88. C2×C4×C5 | C4×D5 | semidirect |
| 106. #117 | C5⋊D5 | semidirect |
| 109. C52 | #520 | semidirect |
| 155. C2×C4 | C4×C5⋊D5 | semidirect |
| 160. C5 | #65857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C52×#117 | 2 |
| C2×C4⋊#1039 | 2 |
| #11717212 | 2 |
| C4⋊C4×C5⋊D5 | 2 |
| #11717201 | 2 |
| C4×C4⋊(C5⋊D5) | 2 |
| C4×#6045 | 2 |
| #65857 | 5 |