Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1032 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 263 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×C52×C4⋊C4 | C2 | semidirect |
| 3. C2×#87808 | C2 | semidirect |
| 4. C2×C4×#1039 | C2 | semidirect |
| 11. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 29. C2×#1039 | D4 | semidirect |
| 32. C2×C5×C4⋊C4 | D5 | semidirect |
| 46. C4×C52 | C22⋊C4 | semidirect |
| 81. C2×C4⋊C4 | C5⋊D5 | semidirect |
| 84. C52 | #390 | semidirect |
| 96. C4×C5 | #685 | semidirect |
| 129. C5 | #65277 | semidirect |
| 142. C4 | #87808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C5⋊D5) | 2 |
| C2×C52×C4⋊C4 | 2 |
| C2×#87808 | 2 |
| C2×C4×#1039 | 2 |
| #65277 | 5 |