Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
744 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 118 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×#87860 | C2 | semidirect |
| 3. #11716881 | C2 | direct (N × H) |
| 12. #87860 | C22 | semidirect |
| 62. C2×C52 | #100 | semidirect |
| 84. C52 | C2×#100 | semidirect |
| 112. C2×C5 | #4013 | semidirect |
| 131. C5 | C2×#4013 | semidirect |
| 150. C2 | #11716881 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊(C5⋊D5) | 2 |
| C2×#87860 | 2 |
| #11716881 | 2 |
| C2×#4013 | 5 |