Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
447 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 109 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×#1042 |
| commutator, socle | C22×C52 | C22×C4 |
| Fitting, prime radical | C24×C52 | C4 |
| cosocle | C2×C5×Dic5 | C23 |
| hypercenter | C24 | #1042 |
| 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×#87853 | C2 | semidirect |
| 3. C22⋊#6032 | C2 | semidirect |
| 11. C2×#6032 | C22 | semidirect |
| 37. C22×C52 | M16 | semidirect |
| 95. C52 | #407 | semidirect |
| 111. C22×C5 | #681 | semidirect |
| 113. C22×C5 | #704 | semidirect |
| 156. C5 | #65496 | semidirect |
| 157. C5 | #65798 | semidirect |
| 162. C22 | #87853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×Dic5 | 2 |
| C2×#87853 | 2 |
| C22⋊#6032 | 2 |
| #65798 | 5 |
| #65496 | 5 |