Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
208 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 96 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×#87756 | C2 | semidirect |
| 3. C2×C5×#672 | C2 | semidirect |
| 4. #11716584 | C2 | direct (N × H) |
| 10. #87756 | C22 | semidirect |
| 11. C5×#672 | C22 | semidirect |
| 29. C2×#672 | D5 | semidirect |
| 52. #672 | C2×D5 | semidirect |
| 54. C2×C52 | M32 | semidirect |
| 80. C52 | C2×M32 | semidirect |
| 106. C2×C5 | #3930 | semidirect |
| 107. C2×C5 | #3944 | semidirect |
| 120. C5 | C2×#3930 | semidirect |
| 121. C5 | C2×#3944 | semidirect |
| 129. C2 | #11716584 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C8×D5 | 2 |
| C2×#87756 | 2 |
| C2×C5×#672 | 2 |
| #11716584 | 2 |
| C2×#3944 | 5 |
| C2×#3930 | 5 |