Finite Group DatabasebetaFinite Group DatabasebetaOrder 800.
141 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 141 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D25 |
| commutator, cosocle | C22×C25 | C23 |
| Frattini, socle | C22×C5 | C22×D5 |
| Fitting | C22⋊C4×C25 | C2 |
| hypercenter | C22⋊C4 | D25 |
| hypocenter | C25 | #121 |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C22⋊D25 | C2 | semidirect |
| 2. C2×C22⋊D25 | C2 | semidirect |
| 3. C2×D100 | C2 | semidirect |
| 4. C2×C4×D25 | C2 | semidirect |
| 5. C22⋊C4×C25 | C2 | semidirect |
| 6. #87720 | C2 | semidirect |
| 7. #87718 | C2 | semidirect |
| 29. C2×D25 | D4 | semidirect |
| 33. Dic25 | D4 | semidirect |
| 59. C25 | #121 | semidirect |
| 80. C22⋊C4 | D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊D25 | 2 |
| C2×D100 | 2 |
| C2×C4×D25 | 2 |
| C22⋊C4×C25 | 2 |
| #87720 | 2 |
| #87718 | 2 |
| #4030 | 5 |