Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1072 conjugacy classes of subgroups; only the 432 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 432 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D52 |
| commutator | C2×C52 | C23×C4 |
| Frattini | C22 | C22×D52 |
| Fitting, socle, prime radical | C24×C52 | C22 |
| cosocle | C22×C52 | C24 |
| hypocenter | C52 | C22×C4⋊C4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#87780 | C2 | direct (N × H) |
| 9. C22×C5×Dic5 | C4 | semidirect |
| 12. #87780 | C22 | direct (N × H) |
| 22. C2×C5×Dic5 | C2×C4 | semidirect |
| 34. C22×C52 | C4⋊C4 | semidirect |
| 41. C5×Dic5 | C22×C4 | semidirect |
| 56. C22×Dic5 | Dic5 | semidirect |
| 62. C2×C52 | C2×C4⋊C4 | semidirect |
| 89. C2×Dic5 | C2×Dic5 | semidirect |
| 96. C52 | C22×C4⋊C4 | semidirect |
| 102. C22×C5 | #683 | semidirect |
| 103. C22×C5 | C4⋊Dic5 | semidirect |
| 118. Dic5 | C22×Dic5 | semidirect |
| 131. C2×C5 | C2×#683 | semidirect |
| 132. C2×C5 | C2×C4⋊Dic5 | semidirect |
| 150. C5 | C22×#683 | semidirect |
| 151. C5 | C22×C4⋊Dic5 | semidirect |
| 152. C22 | #87780 | direct (N × H) |
| 160. C2 | C2×#87780 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1039 | 2 |
| C23×C5×Dic5 | 2 |
| C2×#87780 | 2 |
| C22×C4⋊Dic5 | 5 |
| C22×#683 | 5 |