Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
195 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11716356 | C2 | direct (N × H) |
| 12. C2×#6014 | C4 | semidirect |
| 24. #6014 | C2×C4 | semidirect |
| 48. C2×C25 | #106 | semidirect |
| 66. C25 | C2×#106 | semidirect |
| 109. C2 | #11716356 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×C25 | 2 |
| C2×C4⋊Dic25 | 2 |
| C22×#6014 | 2 |
| #11716356 | 2 |
| C2×#3940 | 5 |