Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
496 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 125 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. C52×#124 | C2 | semidirect |
| 2. C2×#87811 | C2 | semidirect |
| 4. C4×C4⋊(C5⋊D5) | C2 | semidirect |
| 5. #11716702 | C2 | semidirect |
| 6. #11716699 | C2 | semidirect |
| 7. C4⋊#6029 | C2 | semidirect |
| 38. C5×#124 | D5 | semidirect |
| 95. #124 | C5⋊D5 | semidirect |
| 100. C52 | #463 | semidirect |
| 148. C5 | #65346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#124 | 2 |
| C2×#87811 | 2 |
| C2×#87809 | 2 |
| C4×C4⋊(C5⋊D5) | 2 |
| #11716702 | 2 |
| #11716699 | 2 |
| C4⋊#6029 | 2 |
| #65346 | 5 |