Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
792 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 1. C22×C4⋊(C5⋊D5) | C2 | semidirect |
| 2. C52×#121 | C2 | semidirect |
| 3. C2×#87809 | C2 | semidirect |
| 4. C22⋊#6029 | C2 | semidirect |
| 5. #11716676 | C2 | semidirect |
| 8. C2×C52×D4 | C22 | semidirect |
| 13. C52×C4⋊C4 | C22 | semidirect |
| 16. C2×#6029 | C22 | semidirect |
| 32. C4⋊(C5⋊D5) | D4 | semidirect |
| 35. C5×#121 | D5 | semidirect |
| 44. C22×C52 | D8 | semidirect |
| 55. C2×C5×D4 | C2×D5 | semidirect |
| 60. C5×C4⋊C4 | C2×D5 | semidirect |
| 89. #121 | C5⋊D5 | semidirect |
| 92. C52 | #447 | semidirect |
| 98. C22×C5 | #686 | semidirect |
| 112. C2×D4 | C2×C5⋊D5 | semidirect |
| 116. C4⋊C4 | C2×C5⋊D5 | semidirect |
| 140. C5 | #65325 | semidirect |
| 150. C22 | #87809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C5⋊D5) | 2 |
| C52×#121 | 2 |
| C2×#87809 | 2 |
| C22⋊#6029 | 2 |
| #11716676 | 2 |
| #65325 | 5 |