Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
912 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 251 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. C52×C22⋊Q8 | C2 | semidirect |
| 2. #11717266 | C2 | semidirect |
| 3. Q8×#1039 | C2 | semidirect |
| 5. C2×C4⋊#1039 | C2 | semidirect |
| 6. #11717217 | C2 | semidirect |
| 7. C4⋊C4×C5⋊D5 | C2 | semidirect |
| 8. #11717209 | C2 | semidirect |
| 9. #11717208 | C2 | semidirect |
| 11. #11717198 | C2 | semidirect |
| 44. C22⋊(C5⋊D5) | Q8 | semidirect |
| 54. C5×C22⋊Q8 | D5 | semidirect |
| 133. C22⋊Q8 | C5⋊D5 | semidirect |
| 139. C52 | #554 | semidirect |
| 202. C5 | #65969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C22⋊Q8 | 2 |
| #11717266 | 2 |
| Q8×#1039 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| C2×C4⋊#1039 | 2 |
| #11717217 | 2 |
| C4⋊C4×C5⋊D5 | 2 |
| #11717209 | 2 |
| #11717208 | 2 |
| #11717201 | 2 |
| #11717198 | 2 |
| #65969 | 5 |