Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
367 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 367 conjugacy classes of subgroups — too many to draw. Only its 82 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×#1042 | C2 | semidirect |
| 3. C2×C5×#700 | C2 | semidirect |
| 4. #11716740 | C2 | direct (N × H) |
| 6. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 8. C2×C5×Dic10 | C4 | semidirect |
| 13. #87874 | C4 | semidirect |
| 16. C4×#1042 | C22 | semidirect |
| 19. C5×#700 | C22 | semidirect |
| 28. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 36. C5×Dic10 | C2×C4 | semidirect |
| 45. C2×#700 | D5 | semidirect |
| 82. C2×Dic10 | AGL(1,𝔽5) | semidirect |
| 87. #700 | C2×D5 | semidirect |
| 94. C2×C52 | #104 | semidirect |
| 140. Dic10 | C2×AGL(1,𝔽5) | semidirect |
| 147. C52 | C2×#104 | semidirect |
| 196. C2×C5 | #3957 | semidirect |
| 197. C2×C5 | #4010 | semidirect |
| 226. C5 | C2×#3957 | semidirect |
| 227. C5 | C2×#4010 | semidirect |
| 243. C2 | #11716740 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87874 | 2 |
| C2×C4×#1042 | 2 |
| C2×C5×#700 | 2 |
| #11716740 | 2 |
| C2×#4010 | 5 |
| C2×#3957 | 5 |