Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
360 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 360 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. D5⋊#681 | C2 | semidirect |
| 3. C2×C4×C5×AGL(1,𝔽5) | C2 | semidirect |
| 4. #11716741 | C2 | semidirect |
| 5. #11716739 | C2 | semidirect |
| 7. #87900 | C4 | semidirect |
| 8. C5×#709 | C4 | semidirect |
| 12. D5×D20 | C4 | semidirect |
| 17. D5×Dic10 | C4 | semidirect |
| 19. #87849 | C22 | semidirect |
| 22. C4×C5×AGL(1,𝔽5) | C22 | semidirect |
| 31. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 33. #6045 | C2×C4 | semidirect |
| 36. C5×D20 | C2×C4 | semidirect |
| 42. C5×Dic10 | C2×C4 | semidirect |
| 53. C2×C4×AGL(1,𝔽5) | D5 | semidirect |
| 94. #709 | AGL(1,𝔽5) | semidirect |
| 102. C4×AGL(1,𝔽5) | C2×D5 | semidirect |
| 116. C5×D5 | #104 | semidirect |
| 153. D20 | C2×AGL(1,𝔽5) | semidirect |
| 171. Dic10 | C2×AGL(1,𝔽5) | semidirect |
| 179. C52 | C2×#104 | semidirect |
| 244. D5 | #3937 | semidirect |
| 272. C5 | C2×#3937 | semidirect |
| 273. C5 | D5⋊#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#709 | 2 |
| D5⋊#681 | 2 |
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| #11716741 | 2 |
| #11716739 | 2 |
| D5⋊#104 | 5 |
| C2×#3937 | 5 |