Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
487 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 487 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×C22⋊#1042 | C2 | semidirect |
| 3. C2×C5×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 4. #11716756 | C2 | direct (N × H) |
| 5. C23×C5⋊D5 | C4 | semidirect |
| 9. C22×C5×Dic5 | C4 | semidirect |
| 14. C2×#6038 | C4 | semidirect |
| 17. C22⋊#1042 | C22 | semidirect |
| 19. C5×C22⋊AGL(1,𝔽5) | C22 | semidirect |
| 26. C22×C5⋊D5 | C2×C4 | semidirect |
| 40. C2×C5×Dic5 | C2×C4 | semidirect |
| 48. C2×C22⋊AGL(1,𝔽5) | D5 | semidirect |
| 90. C22×Dic5 | AGL(1,𝔽5) | semidirect |
| 100. C22⋊AGL(1,𝔽5) | C2×D5 | semidirect |
| 108. C2×C52 | #99 | semidirect |
| 161. C2×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 170. C52 | C2×#99 | semidirect |
| 248. C2×C5 | #3938 | semidirect |
| 249. C2×C5 | #3999 | semidirect |
| 283. C5 | C2×#3938 | semidirect |
| 284. C5 | C2×#3999 | semidirect |
| 313. C2 | #11716756 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6038 | 2 |
| C2×C22⋊#1042 | 2 |
| C2×C5×C22⋊AGL(1,𝔽5) | 2 |
| #11716756 | 2 |
| C2×#3999 | 5 |
| C2×#3938 | 5 |