Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
303 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | AGL(1,𝔽5)2 |
| commutator, socle | C2×C52 | C2×C42 |
| Frattini | C2 | C2×AGL(1,𝔽5)2 |
| Fitting | C4×C52 | C42 |
| prime radical | C2×D52 | C2×C4 |
| cosocle | D5×Dic5 | C23 |
| hypocenter | C52 | C2×#97 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11717301 | C2 | semidirect |
| 7. #87862 | C4 | semidirect |
| 8. #87855 | C4 | semidirect |
| 10. D5⋊#168 | C4 | semidirect |
| 12. C5×D5⋊C8 | C4 | semidirect |
| 13. D5⋊#170 | C4 | semidirect |
| 15. #87827 | C4 | semidirect |
| 30. #6034 | C2×C4 | semidirect |
| 31. #6033 | C2×C4 | semidirect |
| 32. #6032 | C2×C4 | semidirect |
| 33. C5×#170 | C2×C4 | semidirect |
| 71. D5⋊C8 | AGL(1,𝔽5) | semidirect |
| 81. C5⋊D5 | #97 | semidirect |
| 82. C5×D5 | #97 | semidirect |
| 111. #170 | C2×AGL(1,𝔽5) | semidirect |
| 118. C52 | C2×#97 | semidirect |
| 163. D5 | #3992 | semidirect |
| 180. C5 | #65676 | semidirect |
| 181. C5 | C2×#3992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5⋊(D5⋊C8) | 2 |
| C4×D5×AGL(1,𝔽5) | 2 |
| D5×D5⋊C8 | 2 |
| #11717301 | 2 |
| C2×#3992 | 5 |
| #65676 | 5 |