Finite Group DatabasebetaFinite Group DatabasebetaOrder 400.
124 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D52 |
| commutator, socle, cosocle | C2×C52 | C23 |
| Fitting | C22×C52 | C22 |
| hypercenter | C22 | D52 |
| hypocenter | C52 | C2×D4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×D5 | C2 | semidirect |
| 2. C2×D52 | C2 | semidirect |
| 3. C22⋊(C5⋊D5) | C2 | semidirect |
| 4. C5×C22⋊D5 | C2 | semidirect |
| 5. #6038 | C2 | semidirect |
| 6. #6037 | C2 | semidirect |
| 7. D5×Dic5 | C2 | semidirect |
| 8. C22×C52 | C22 | semidirect |
| 9. C2×C5⋊D5 | C22 | semidirect |
| 12. C2×C5×D5 | C22 | semidirect |
| 13. C2×C5×D5 | C22 | semidirect |
| 15. #1039 | C22 | semidirect |
| 16. C5×Dic5 | C22 | semidirect |
| 24. C5×D5 | D4 | semidirect |
| 28. C22×D5 | D5 | semidirect |
| 36. C22⋊D5 | D5 | direct (N × H) |
| 40. C52 | C2×D4 | semidirect |
| 46. C22×C5 | C2×D5 | semidirect |
| 47. C22×C5 | C2×D5 | semidirect |
| 55. C2×D5 | C2×D5 | semidirect |
| 56. C2×D5 | C2×D5 | semidirect |
| 61. Dic5 | C2×D5 | semidirect |
| 77. D5 | C22⋊D5 | direct (N × H) |
| 86. C5 | D4×D5 | semidirect |
| 87. C5 | C2×C22⋊D5 | semidirect |
| 94. C22 | D52 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D5 | 2 |
| C2×D52 | 2 |
| C22⋊(C5⋊D5) | 2 |
| C5×C22⋊D5 | 2 |
| #6038 | 2 |
| #6037 | 2 |
| D5×Dic5 | 2 |
| C2×C22⋊D5 | 5 |
| D4×D5 | 5 |