Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
384 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 114 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. #11716897 | C2 | direct (N × H) |
| 15. C2×#1039 | C8 | semidirect |
| 32. #1039 | C2×C8 | semidirect |
| 48. C2×C52 | C4⋊C8 | semidirect |
| 74. C52 | C2×C4⋊C8 | semidirect |
| 104. C2×C5 | #4004 | semidirect |
| 119. C5 | C2×#4004 | semidirect |
| 129. C2 | #11716897 | 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 |
| #11716897 | 2 |
| C2×#4004 | 5 |