Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
400 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C2×C4×C8 |
| Frattini | C22 | C2×D5⋊AGL(1,𝔽5) |
| Fitting, socle, prime radical | C23×C52 | C2×C4 |
| cosocle | C2×#1039 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11716777 | C2 | direct (N × H) |
| 7. C2×#6034 | C4 | semidirect |
| 9. C2×#6033 | C4 | semidirect |
| 19. C2×C5×Dic5 | C8 | semidirect |
| 21. #6034 | C2×C4 | semidirect |
| 22. #6033 | C2×C4 | semidirect |
| 34. C5×Dic5 | C2×C8 | semidirect |
| 48. C2×C52 | C4×C8 | semidirect |
| 63. C2×Dic5 | #170 | semidirect |
| 72. C52 | C2×C4×C8 | semidirect |
| 87. Dic5 | C2×#170 | semidirect |
| 99. C2×C5 | C4×#170 | semidirect |
| 113. C5 | C2×C4×#170 | semidirect |
| 121. C2 | #11716777 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6034 | 2 |
| C22×#6033 | 2 |
| C2×Dic52 | 2 |
| #11716777 | 2 |
| C2×C4×#170 | 5 |