Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
191 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11716748 | C2 | direct (N × H) |
| 10. #87763 | C22 | semidirect |
| 11. C5×#674 | C22 | semidirect |
| 26. C2×#674 | D5 | semidirect |
| 48. #674 | C2×D5 | semidirect |
| 52. C2×C52 | M32 | semidirect |
| 77. C52 | C2×M32 | semidirect |
| 103. C2×C5 | #3930 | semidirect |
| 104. C2×C5 | #3998 | semidirect |
| 117. C5 | C2×#3930 | semidirect |
| 118. C5 | C2×#3998 | semidirect |
| 126. C2 | #11716748 | 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 |
| #11716748 | 2 |
| C2×#3998 | 5 |
| C2×#3930 | 5 |