Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
640 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 111 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. #11717255 | C2 | semidirect |
| 3. #11717206 | C2 | semidirect |
| 4. C52×#99 | C2 | semidirect |
| 5. #11716673 | C2 | semidirect |
| 9. C22×#1039 | C22 | semidirect |
| 13. C52×C22⋊C4 | C22 | semidirect |
| 15. C22⋊#1039 | C22 | semidirect |
| 41. C5×#99 | D5 | semidirect |
| 63. C5×C22⋊C4 | C2×D5 | semidirect |
| 97. #99 | C5⋊D5 | semidirect |
| 98. C52 | #458 | semidirect |
| 124. C22⋊C4 | C2×C5⋊D5 | semidirect |
| 148. C5 | #65031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717517 | 2 |
| #11717255 | 2 |
| #11717206 | 2 |
| C52×#99 | 2 |
| #11716673 | 2 |
| #65031 | 5 |