Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
224 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 95 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×#87765 | C2 | semidirect |
| 3. C2×#87764 | C2 | semidirect |
| 4. D5⋊#674 | C2 | direct (N × H) |
| 10. #87765 | C22 | semidirect |
| 11. #87764 | C22 | semidirect |
| 32. C2×C5×D5 | C16 | semidirect |
| 54. C2×C52 | C2×C16 | semidirect |
| 56. C5×D5 | C2×C16 | semidirect |
| 80. C52 | C22×C16 | semidirect |
| 86. C2×D5 | #674 | semidirect |
| 106. C2×C5 | D5⋊C16 | semidirect |
| 107. C2×C5 | C2×#674 | semidirect |
| 110. D5 | C2×#674 | semidirect |
| 120. C5 | C2×D5⋊C16 | semidirect |
| 121. C5 | C22×#674 | semidirect |
| 129. C2 | D5⋊#674 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#168 | 2 |
| C2×#87765 | 2 |
| C2×#87764 | 2 |
| D5⋊#674 | 2 |
| C22×#674 | 5 |
| C2×D5⋊C16 | 5 |