Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
255 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. C2×C4×#1035 | C2 | semidirect |
| 3. C2×#87735 | C2 | semidirect |
| 4. #11716425 | C2 | direct (N × H) |
| 6. C2×Q8×C25 | C4 | semidirect |
| 9. #87748 | C4 | semidirect |
| 12. C2×D100 | C4 | semidirect |
| 17. C4×#1035 | C22 | semidirect |
| 19. #87735 | C22 | semidirect |
| 26. Q8×C25 | C2×C4 | semidirect |
| 33. D100 | C2×C4 | semidirect |
| 73. C2×C25 | #104 | semidirect |
| 102. C25 | C2×#104 | semidirect |
| 119. C2×Q8 | #1035 | semidirect |
| 138. Q8 | C2×#1035 | semidirect |
| 171. C2 | #11716425 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87748 | 2 |
| C2×C4×#1035 | 2 |
| C2×#87735 | 2 |
| #11716425 | 2 |
| C2×#4010 | 5 |