Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
195 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #11716411 | C2 | direct (N × H) |
| 8. C2×C8×C25 | C4 | semidirect |
| 9. C2×#6014 | C4 | semidirect |
| 10. C8×D25 | C4 | semidirect |
| 22. C8×C25 | C2×C4 | semidirect |
| 23. #6014 | C2×C4 | semidirect |
| 45. C2×C25 | #106 | semidirect |
| 47. D25 | #106 | semidirect |
| 63. C25 | C2×#106 | semidirect |
| 78. C2×C8 | #1035 | semidirect |
| 95. C8 | C2×#1035 | semidirect |
| 108. C2 | #11716411 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#1035 | 2 |
| C2×C8×D25 | 2 |
| #11716411 | 2 |
| C2×#3993 | 5 |