Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
384 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 3. C4⋊#6034 | C2 | direct (N × H) |
| 13. C2×C4×C52 | C8 | semidirect |
| 30. C4×C52 | C2×C8 | semidirect |
| 48. C2×C52 | C4⋊C8 | semidirect |
| 56. C2×C4×C5 | #170 | semidirect |
| 74. C52 | C2×C4⋊C8 | semidirect |
| 84. C4×C5 | C2×#170 | semidirect |
| 104. C2×C5 | C4⋊#170 | semidirect |
| 115. C2×C4 | #6034 | semidirect |
| 119. C5 | C2×C4⋊#170 | semidirect |
| 128. C4 | C2×#6034 | semidirect |
| 129. C2 | C4⋊#6034 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6034 | 2 |
| C2×C4×#1039 | 2 |
| C4⋊#6034 | 2 |
| C2×C4⋊#170 | 5 |