Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
447 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 78 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 | semidirect |
| 5. #11716755 | C2 | semidirect |
| 7. C22×D52 | C4 | semidirect |
| 10. C2×C22⋊(C5⋊D5) | C4 | semidirect |
| 11. C2×C5×C22⋊D5 | C4 | semidirect |
| 18. C2×D5×Dic5 | C4 | semidirect |
| 20. C22⋊#1042 | C22 | semidirect |
| 22. C5×C22⋊AGL(1,𝔽5) | C22 | semidirect |
| 26. C22×C5⋊D5 | C2×C4 | semidirect |
| 29. C22×C5×D5 | C2×C4 | semidirect |
| 44. C2×#1039 | C2×C4 | semidirect |
| 47. C2×C5×Dic5 | C2×C4 | semidirect |
| 57. C2×C22⋊AGL(1,𝔽5) | D5 | semidirect |
| 106. C2×C22⋊D5 | AGL(1,𝔽5) | semidirect |
| 118. C22⋊AGL(1,𝔽5) | C2×D5 | semidirect |
| 133. C5×D5 | #99 | semidirect |
| 160. C22×D5 | C2×AGL(1,𝔽5) | semidirect |
| 192. C2×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 202. C52 | C2×#99 | semidirect |
| 299. D5 | #3938 | semidirect |
| 330. C5 | C2×#3938 | semidirect |
| 331. C5 | D5⋊#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×C22⋊D5 | 2 |
| C2×C22⋊#1042 | 2 |
| C2×C5×C22⋊AGL(1,𝔽5) | 2 |
| #11716756 | 2 |
| #11716755 | 2 |
| D5⋊#99 | 5 |
| C2×#3938 | 5 |