Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
180 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 61 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. C25×C4⋊Q8 | C2 | semidirect |
| 4. #11716384 | C2 | semidirect |
| 5. C4⋊#6014 | C2 | semidirect |
| 40. C4×C25 | SD16 | semidirect |
| 72. C4⋊Q8 | D25 | semidirect |
| 76. C25 | #461 | semidirect |
| 121. C4 | #87724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C4⋊Q8 | 2 |
| C2×#87724 | 2 |
| C4×D100 | 2 |
| #11716384 | 2 |
| C4⋊#6014 | 2 |
| #65372 | 5 |