Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
408 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 2. C2×C4×#1044 | C2 | semidirect |
| 3. C2×#87856 | C2 | semidirect |
| 4. #11716769 | C2 | direct (N × H) |
| 7. C2×C5×D20 | C4 | semidirect |
| 8. C2×C5×Dic10 | C4 | semidirect |
| 13. #87871 | C4 | semidirect |
| 16. C4×#1044 | C22 | semidirect |
| 19. #87856 | C22 | semidirect |
| 34. C5×D20 | C2×C4 | semidirect |
| 36. C5×Dic10 | C2×C4 | semidirect |
| 78. C2×D20 | AGL(1,𝔽5) | semidirect |
| 83. C2×Dic10 | AGL(1,𝔽5) | semidirect |
| 98. C2×C52 | #104 | semidirect |
| 131. D20 | C2×AGL(1,𝔽5) | semidirect |
| 147. Dic10 | C2×AGL(1,𝔽5) | semidirect |
| 155. C52 | C2×#104 | semidirect |
| 206. C2×C5 | #4008 | semidirect |
| 207. C2×C5 | #4010 | semidirect |
| 238. C5 | C2×#4008 | semidirect |
| 239. C5 | C2×#4010 | semidirect |
| 255. C2 | #11716769 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87871 | 2 |
| C2×C4×#1044 | 2 |
| C2×#87856 | 2 |
| #11716769 | 2 |
| C2×#4010 | 5 |
| C2×#4008 | 5 |