Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
432 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 432 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 |
|---|---|---|
| 2. #11717189 | C2 | semidirect |
| 3. C52×C4⋊C8 | C2 | semidirect |
| 5. #11716684 | C2 | semidirect |
| 23. C4⋊(C5⋊D5) | Q8 | semidirect |
| 29. C5×C4⋊C8 | D5 | semidirect |
| 70. C4⋊C8 | C5⋊D5 | semidirect |
| 72. C52 | #476 | semidirect |
| 107. C5 | #65131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C5⋊D5) | 2 |
| #11717189 | 2 |
| C52×C4⋊C8 | 2 |
| #11716688 | 2 |
| #11716684 | 2 |
| #65131 | 5 |