Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
256 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 74 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. #11716883 | C2 | direct (N × H) |
| 9. #87765 | C22 | semidirect |
| 41. C2×C52 | M32 | semidirect |
| 63. C52 | C2×M32 | semidirect |
| 84. C2×C5 | #3990 | semidirect |
| 97. C5 | C2×#3990 | semidirect |
| 105. C2 | #11716883 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C5⋊D5 | 2 |
| C2×#87765 | 2 |
| #11716883 | 2 |
| C2×#3990 | 5 |