Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
552 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D52 |
| commutator, socle, cosocle | C23×C52 | C23 |
| Fitting | C22×C4×C52 | C22 |
| prime radical | C22×C5×D20 | C2 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #394 |
| LCS | G ▷ C23×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×#683 | C2 | semidirect |
| 3. C2×#87778 | C2 | semidirect |
| 4. C2×#87778 | C2 | semidirect |
| 5. #11716698 | C2 | semidirect |
| 35. C2×C5×Dic5 | D4 | semidirect |
| 44. C2×#683 | D5 | semidirect |
| 135. C2×Dic5 | D20 | semidirect |
| 142. C52 | #394 | semidirect |
| 229. C5 | #65280 | semidirect |
| 230. C5 | #65511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C2×C5×#683 | 2 |
| C2×#87778 | 2 |
| #11716698 | 2 |
| #65511 | 5 |
| #65280 | 5 |