Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
560 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C2×#87801 | C2 | semidirect |
| 2. #11717194 | C2 | semidirect |
| 3. C4×C4⋊(C5⋊D5) | C2 | semidirect |
| 4. C52×C4⋊C8 | C2 | semidirect |
| 5. #11716688 | C2 | semidirect |
| 28. C4⋊(C5⋊D5) | D4 | semidirect |
| 34. C5×C4⋊C8 | D5 | semidirect |
| 44. C4×C52 | D8 | semidirect |
| 81. C4⋊C8 | C5⋊D5 | semidirect |
| 83. C52 | #459 | semidirect |
| 92. C4×C5 | D40 | semidirect |
| 125. C5 | #65132 | semidirect |
| 135. C4 | #87801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87801 | 2 |
| #11717194 | 2 |
| C4×C4⋊(C5⋊D5) | 2 |
| C52×C4⋊C8 | 2 |
| #11716688 | 2 |
| #65132 | 5 |