Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
207 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 207 conjugacy classes of subgroups — too many to draw. Only its 98 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×#87763 | C2 | semidirect |
| 3. C2×C5×#674 | C2 | semidirect |
| 4. D5×#674 | C2 | direct (N × H) |
| 10. #87763 | C22 | semidirect |
| 11. C5×#674 | C22 | semidirect |
| 26. C2×#674 | D5 | direct (N × H) |
| 31. C2×C5×D5 | C16 | semidirect |
| 48. #674 | C2×D5 | direct (N × H) |
| 52. C2×C52 | C2×C16 | semidirect |
| 54. C5×D5 | C2×C16 | semidirect |
| 77. C52 | C22×C16 | semidirect |
| 83. C2×D5 | #674 | direct (N × H) |
| 103. C2×C5 | D5×C16 | semidirect |
| 104. C2×C5 | C2×#674 | semidirect |
| 107. D5 | C2×#674 | direct (N × H) |
| 117. C5 | C2×D5×C16 | semidirect |
| 118. C5 | C22×#674 | semidirect |
| 126. 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×#87763 | 2 |
| C2×C5×#674 | 2 |
| D5×#674 | 2 |
| C22×#674 | 5 |
| C2×D5×C16 | 5 |