Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
760 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 195 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×#87804 | C2 | semidirect |
| 4. #11716676 | C2 | semidirect |
| 9. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 11. C52×C4⋊C4 | C22 | semidirect |
| 15. C2×#6029 | C22 | semidirect |
| 31. C5×#117 | D5 | semidirect |
| 50. C5×C4⋊C4 | C2×D5 | semidirect |
| 75. #117 | C5⋊D5 | semidirect |
| 77. C52 | #418 | semidirect |
| 96. C4⋊C4 | C2×C5⋊D5 | semidirect |
| 116. C5 | #65290 | 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×#117 | 2 |
| C2×#87804 | 2 |
| #11716676 | 2 |
| #65290 | 5 |