Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 161 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. #11717451 | C2 | semidirect |
| 3. #11717438 | C2 | semidirect |
| 4. D5⋊(C22⋊AGL(1,𝔽5)) | C2 | semidirect |
| 5. #11717365 | C2 | semidirect |
| 6. #11717363 | C2 | semidirect |
| 8. C2×D5⋊AGL(1,𝔽5) | C22 | semidirect |
| 10. C2×C5×D20 | C4 | semidirect |
| 11. C2×#6037 | C4 | semidirect |
| 12. #87877 | C4 | semidirect |
| 13. #87877 | C4 | semidirect |
| 17. C4⋊#1044 | C22 | semidirect |
| 18. C4×#1044 | C22 | semidirect |
| 20. C4⋊#1043 | C22 | semidirect |
| 21. C4×#1043 | C22 | semidirect |
| 22. #87831 | C22 | semidirect |
| 25. C22×C5×D5 | C2×C4 | semidirect |
| 27. C2×D52 | C2×C4 | semidirect |
| 32. C2×C4×C52 | C2×C4 | semidirect |
| 33. C2×#1039 | C2×C4 | semidirect |
| 34. C4×C5⋊D5 | C2×C4 | semidirect |
| 35. C4×C5⋊D5 | C2×C4 | semidirect |
| 38. C5×D20 | C2×C4 | semidirect |
| 39. C5×D20 | C2×C4 | semidirect |
| 40. #6037 | C2×C4 | semidirect |
| 41. #6037 | C2×C4 | semidirect |
| 71. C2×D20 | AGL(1,𝔽5) | semidirect |
| 96. C22×D5 | C2×AGL(1,𝔽5) | semidirect |
| 104. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 109. D20 | C2×AGL(1,𝔽5) | semidirect |
| 110. D20 | C2×AGL(1,𝔽5) | semidirect |
| 125. C52 | #518 | semidirect |
| 194. C2×C4 | D5⋊AGL(1,𝔽5) | semidirect |
| 196. C5 | #66258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87877 | 2 |
| #11717451 | 2 |
| #11717438 | 2 |
| D5⋊(C22⋊AGL(1,𝔽5)) | 2 |
| #11717365 | 2 |
| #11717363 | 2 |
| #66258 | 5 |