Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
616 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 108 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×C5×#681 | C2 | semidirect |
| 3. #11716598 | C2 | semidirect |
| 11. C2×C5×#168 | C22 | semidirect |
| 28. C2×#681 | D5 | semidirect |
| 36. C2×C5⋊D5 | M16 | semidirect |
| 56. C2×#168 | C2×D5 | semidirect |
| 91. C52 | #407 | semidirect |
| 142. 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×C5×#681 | 2 |
| #11716598 | 2 |
| #65415 | 5 |