Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
243 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 243 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 |
|---|---|---|
| 4. #11716426 | C2 | direct (N × H) |
| 6. C2×Q8×C25 | C4 | semidirect |
| 9. Q8×D25 | C4 | semidirect |
| 14. C2×Dic50 | C4 | semidirect |
| 25. Q8×C25 | C2×C4 | semidirect |
| 39. Dic50 | C2×C4 | semidirect |
| 73. C2×C25 | #103 | semidirect |
| 75. D25 | #103 | semidirect |
| 102. C25 | C2×#103 | semidirect |
| 121. C2×Q8 | #1035 | semidirect |
| 141. Q8 | C2×#1035 | semidirect |
| 171. C2 | #11716426 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D25 | 2 |
| C2×C4⋊#1035 | 2 |
| C2×D25⋊C8 | 2 |
| #11716426 | 2 |
| C2×#4009 | 5 |