Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
632 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11717197 | C2 | semidirect |
| 3. C52×#99 | C2 | semidirect |
| 4. #11716701 | C2 | semidirect |
| 5. #11716673 | C2 | semidirect |
| 7. C2×C22⋊(C5⋊D5) | C4 | semidirect |
| 9. C22×#1039 | C4 | semidirect |
| 13. C2×C4×C5⋊D5 | C4 | semidirect |
| 14. C2×#6045 | C4 | semidirect |
| 41. C5×#99 | D5 | semidirect |
| 100. #99 | C5⋊D5 | semidirect |
| 101. C52 | #410 | semidirect |
| 153. C5 | #65029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87902 | 2 |
| #11717197 | 2 |
| C52×#99 | 2 |
| #11716701 | 2 |
| #11716673 | 2 |
| #65029 | 5 |