Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
403 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 403 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×AGL(1,𝔽5)2 |
| commutator, socle | C2×C52 | C2×C42 |
| Fitting | C4×C52 | C42 |
| prime radical, cosocle | C2×D52 | C23 |
| hypercenter | C4 | AGL(1,𝔽5)2 |
| hypocenter | C52 | C4×C4⋊C4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. C4×#1044 | C4 | semidirect |
| 11. C4×#1043 | C4 | semidirect |
| 12. C4⋊#1042 | C4 | semidirect |
| 13. C5×C4⋊AGL(1,𝔽5) | C4 | semidirect |
| 14. #87830 | C4 | semidirect |
| 15. #87830 | C4 | semidirect |
| 16. #87825 | C4 | semidirect |
| 45. #1044 | C4⋊C4 | semidirect |
| 47. #1043 | C4⋊C4 | semidirect |
| 50. C4×C52 | C42 | semidirect |
| 51. #1039 | C42 | semidirect |
| 52. C5×Dic5 | C42 | semidirect |
| 60. C4⋊AGL(1,𝔽5) | AGL(1,𝔽5) | semidirect |
| 106. C52 | C4×C4⋊C4 | semidirect |
| 126. C4×C5 | C4×AGL(1,𝔽5) | semidirect |
| 130. Dic5 | C4×AGL(1,𝔽5) | semidirect |
| 170. C5 | C4⋊C4×AGL(1,𝔽5) | semidirect |
| 184. C4 | AGL(1,𝔽5)2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×AGL(1,𝔽5)2 | 2 |
| C4×D5⋊AGL(1,𝔽5) | 2 |
| D5×C4⋊AGL(1,𝔽5) | 2 |
| (C2×AGL(1,𝔽5))⋊AGL(1,𝔽5) | 2 |
| C4⋊C4×AGL(1,𝔽5) | 5 |