Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
616 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 616 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, Frattini | C22 | C22×#1044 |
| commutator, socle | C22×C52 | C22×C4 |
| Fitting, prime radical | C24×C52 | C4 |
| cosocle | C2×#1039 | C23 |
| hypercenter | C24 | #1044 |
| hypocenter | C52 | #407 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#87867 | C2 | semidirect |
| 3. C22⋊#6034 | C2 | semidirect |
| 11. C2×#6034 | C22 | semidirect |
| 34. C22×C52 | M16 | semidirect |
| 84. C52 | #407 | semidirect |
| 96. C22×C5 | #704 | semidirect |
| 134. C5 | #65798 | semidirect |
| 139. C22 | #87867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1039 | 2 |
| C2×#87867 | 2 |
| C22⋊#6034 | 2 |
| #65798 | 5 |