Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1672 conjugacy classes of subgroups; only the 715 normal subgroups are shown.
This group has 1672 conjugacy classes of subgroups — too many to draw. Only its 715 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 |
|---|---|---|
| 4. C2×#87806 | C2 | direct (N × H) |
| 9. C22×#1039 | C4 | semidirect |
| 12. #87806 | C22 | direct (N × H) |
| 21. C2×#1039 | C2×C4 | semidirect |
| 28. C22×C52 | C4⋊C4 | semidirect |
| 35. #1039 | C22×C4 | semidirect |
| 45. C2×C52 | C2×C4⋊C4 | semidirect |
| 63. C52 | C22×C4⋊C4 | semidirect |
| 64. C22×C5 | #683 | semidirect |
| 80. C2×C5 | C2×#683 | semidirect |
| 94. C5 | C22×#683 | semidirect |
| 95. C22 | #87806 | direct (N × H) |
| 103. C2 | C2×#87806 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C52 | 2 |
| C23×#1039 | 2 |
| C2×#87806 | 2 |
| C22×#683 | 5 |