Finite Group DatabasebetaFinite Group DatabasebetaOrder 400.
27 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Q8×C25 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Dic50 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #6014 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C4×C25 | — | 2 | 1 | no | — |
| 5 | C4×C25 | C22 | 1 | 1 | yes | characteristic |
| 6 | Dic25 | — | 2 | 1 | no | — |
| 7 | #689 | — | 5 | 1 | no | maximal |
| 8 | C2×C25 | D4 | 1 | 1 | yes | characteristic |
| 9 | C5×Q8 | D5 | 1 | 1 | yes | characteristic |
| 10 | Dic10 | — | 5 | 1 | no | — |
| 11 | #168 | — | 5 | 1 | no | — |
| 12 | C25 | Q16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | C4×C5 | — | 2 | 1 | no | — |
| 14 | C4×C5 | C2×D5 | 1 | 1 | yes | characteristic |
| 15 | Dic5 | — | 10 | 1 | no | — |
| 16 | Q16 | — | 25 | 1 | no | Sylow |
| 17 | C2×C5 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 18 | Q8 | — | 25 | 1 | no | — |
| 19 | Q8 | D25 | 1 | 1 | yes | characteristic |
| 20 | C8 | — | 25 | 1 | no | — |
| 21 | C5 | #689 | 1 | 1 | yes | characteristic |
| 22 | C4 | — | 2 | 1 | no | — |
| 23 | C4 | — | 50 | 1 | no | — |
| 24 | C4 | C2×D25 | 1 | 1 | yes | characteristic |
| 25 | C2 | C22⋊D25 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D25 |
| commutator, cosocle | C4×C25 | C22 |
| Frattini | C4×C5 | C2×D5 |
| Fitting | Q8×C25 | C2 |
| socle, prime radical | C2×C5 | C22⋊D5 |
| hypercenter | Q8 | D25 |
| hypocenter | C25 | Q16 |
| LCS | G ▷ C4×C25 ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. C25 | Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C25 | 2 |
| Dic50 | 2 |
| #6014 | 2 |
| #689 | 5 |