Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
760 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 199 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. C2×C52×M16 | C2 | semidirect |
| 3. C2×#87804 | C2 | semidirect |
| 4. #11716687 | C2 | semidirect |
| 13. C2×C52×C8 | C22 | semidirect |
| 15. C2×#6029 | C22 | semidirect |
| 33. C2×C5×M16 | D5 | semidirect |
| 42. C2×C5⋊D5 | M16 | semidirect |
| 55. C2×C5×C8 | C2×D5 | semidirect |
| 80. C2×M16 | C5⋊D5 | semidirect |
| 82. C52 | #407 | semidirect |
| 104. C2×C8 | C2×C5⋊D5 | semidirect |
| 124. C5 | #65415 | 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 |
| C2×C52×M16 | 2 |
| C2×#87804 | 2 |
| #11716687 | 2 |
| #65415 | 5 |