Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
243 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 243 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 |
|---|---|---|
| 4. #11716384 | C2 | direct (N × H) |
| 7. C2×Q8×C25 | C4 | semidirect |
| 20. Q8×C25 | C2×C4 | semidirect |
| 55. C2×C25 | #103 | semidirect |
| 76. C25 | C2×#103 | semidirect |
| 88. C2×Q8 | Dic25 | semidirect |
| 104. Q8 | C2×Dic25 | semidirect |
| 124. C2 | #11716384 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×C25 | 2 |
| C2×C4⋊Dic25 | 2 |
| C22×#6014 | 2 |
| #11716384 | 2 |
| C2×#3967 | 5 |