Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
488 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 160 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 | C22×C4×C52 | C22 |
| prime radical | C23×C52 | C23 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #544 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #11717037 | C2 | semidirect |
| 6. #11717036 | C2 | semidirect |
| 7. #11716991 | C2 | semidirect |
| 8. #11716988 | C2 | semidirect |
| 28. C2×C4×C52 | Q8 | semidirect |
| 118. C2×C4×C5 | Dic10 | semidirect |
| 119. C2×C4×C5 | Dic10 | semidirect |
| 144. C52 | #544 | semidirect |
| 211. C2×C4 | #6039 | semidirect |
| 215. C5 | #65834 | semidirect |
| 216. C5 | #65853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717246 | 2 |
| C5×#4072 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| #11717082 | 2 |
| #11717037 | 2 |
| #11717036 | 2 |
| #11716991 | 2 |
| #11716988 | 2 |
| #65853 | 5 |
| #65834 | 5 |