Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
376 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 149 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×C4 | C22×C5⋊D5 |
| commutator, socle, prime radical | C22×C52 | C22×C4 |
| Fitting | C52×#97 | C2 |
| cosocle | C2×C4×C52 | C23 |
| hypercenter | #97 | C5⋊D5 |
| hypocenter | C52 | #446 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 29. C52×C8 | Q8 | semidirect |
| 72. C5×C8 | Dic10 | semidirect |
| 82. C52 | #446 | semidirect |
| 117. C8 | #6045 | semidirect |
| 118. C5 | #64990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6045 | 2 |
| C52×#97 | 2 |
| #11716682 | 2 |
| #11716681 | 2 |
| C8×#1039 | 2 |
| C4⋊#6029 | 2 |
| #64990 | 5 |