Finite Group DatabasebetaFinite Group DatabasebetaOrder 200.
48 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×C25 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×D25 | C2 | 1 | 6 | yes | maximal, direct product factor |
| 3 | C2×C25 | C22 | 1 | 3 | yes | complemented |
| 4 | D25 | C22 | 1 | 4 | yes | direct product factor |
| 5 | C22×D5 | — | 5 | 1 | no | maximal |
| 6 | C25 | C23 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 7 | C22×C5 | D5 | 1 | 1 | yes | characteristic |
| 8 | C2×D5 | — | 5 | 6 | no | — |
| 9 | C2×C5 | C2×D5 | 1 | 3 | yes | — |
| 10 | D5 | — | 5 | 4 | no | — |
| 11 | C23 | — | 25 | 1 | no | Sylow |
| 12 | C5 | C22×D5 | 1 | 1 | yes | characteristic |
| 13 | C22 | — | 25 | 6 | no | — |
| 14 | C22 | D25 | 1 | 1 | yes | characteristic, direct product factor |
| 15 | C2 | — | 25 | 4 | no | — |
| 16 | C2 | C2×D25 | 1 | 3 | yes | direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D25 |
| commutator, cosocle, hypocenter | C25 | C23 |
| Frattini | C5 | C22×D5 |
| Fitting | C22×C25 | C2 |
| socle | C22×C5 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C25 | C2 | semidirect |
| 2. C2×D25 | C2 | direct (N × H) |
| 3. C2×C25 | C22 | semidirect |
| 4. D25 | C22 | direct (N × H) |
| 6. C25 | C23 | semidirect |
| 14. C22 | D25 | direct (N × H) |
| 16. C2 | C2×D25 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C25 | 2 |
| C2×D25 | 2 |
| C22×D5 | 5 |