Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
736 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 168 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×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C2×C52×Q8 | C22 |
| prime radical | C22×C5⋊D5 | C23 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | C2×C4⋊Q8 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C5×#4090 | C2 | semidirect |
| 6. #11716983 | C2 | semidirect |
| 7. #11716958 | C2 | semidirect |
| 39. #6036 | Q8 | semidirect |
| 45. #4090 | D5 | semidirect |
| 58. C5×Dic5 | C2×Q8 | semidirect |
| 87. C5⋊D5 | C4⋊Q8 | semidirect |
| 124. C52 | C2×C4⋊Q8 | semidirect |
| 142. Dic5 | Q8×D5 | semidirect |
| 181. C5 | D5×C4⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C5⋊D5 | 2 |
| C2×#87872 | 2 |
| C5×#4090 | 2 |
| #11717001 | 2 |
| C4×#6036 | 2 |
| #11716983 | 2 |
| #11716958 | 2 |
| D5×C4⋊Q8 | 5 |