Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
447 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 68 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. D5×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. #11716842 | C2 | semidirect |
| 4. C5×#3999 | C2 | semidirect |
| 5. #11716756 | C2 | semidirect |
| 6. C22×D52 | C4 | semidirect |
| 9. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 11. C2×C4×C5×D5 | C4 | semidirect |
| 12. C2×#6038 | C4 | semidirect |
| 16. C22⋊#1042 | C22 | semidirect |
| 17. C5×C22⋊AGL(1,𝔽5) | C22 | semidirect |
| 22. C22×C5⋊D5 | C2×C4 | semidirect |
| 24. C22×C5×D5 | C2×C4 | semidirect |
| 35. C2×C4×C52 | C2×C4 | semidirect |
| 37. C2×C5×Dic5 | C2×C4 | semidirect |
| 49. #3999 | D5 | direct (N × H) |
| 93. C2×C4×D5 | AGL(1,𝔽5) | semidirect |
| 96. C22⋊AGL(1,𝔽5) | C2×D5 | semidirect |
| 108. C5×D5 | #99 | semidirect |
| 130. C22×D5 | C4×D5 | semidirect |
| 142. C2×C4×C5 | C4×D5 | semidirect |
| 143. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 147. C2×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 162. C52 | C2×#99 | semidirect |
| 241. D5 | #3999 | direct (N × H) |
| 263. C2×C4 | D5×AGL(1,𝔽5) | semidirect |
| 265. C5 | D5×#99 | semidirect |
| 266. C5 | C2×#3999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D20 | 2 |
| D5×C22⋊AGL(1,𝔽5) | 2 |
| #11716842 | 2 |
| C5×#3999 | 2 |
| #11716756 | 2 |
| C2×#3999 | 5 |
| D5×#99 | 5 |