Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
552 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Frattini | C22 | C22×D52 |
| Fitting | C42×C52 | C22 |
| prime radical | C22×C5⋊D5 | C23 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | #533 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C5×Dic10 | C2 | semidirect |
| 3. #11717037 | C2 | semidirect |
| 4. C4×#6039 | C2 | semidirect |
| 7. #11716989 | C2 | semidirect |
| 8. #11716985 | C2 | semidirect |
| 37. C4×C5⋊D5 | Q8 | semidirect |
| 53. C4×Dic10 | D5 | semidirect |
| 137. C52 | #533 | semidirect |
| 202. C5 | #65912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C5⋊D5 | 2 |
| C4×C5×Dic10 | 2 |
| #11717037 | 2 |
| C4×#6039 | 2 |
| #11716992 | 2 |
| #11716990 | 2 |
| #11716989 | 2 |
| #11716985 | 2 |
| #11716984 | 2 |
| #65912 | 5 |