Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
574 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C22×C4×C52 | C22 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #538 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11717244 | C2 | semidirect |
| 2. C5×#4076 | C2 | semidirect |
| 3. C2×C5×#685 | C2 | semidirect |
| 4. #11717094 | C2 | semidirect |
| 5. Dic5×C22⋊D5 | C2 | semidirect |
| 6. #11717031 | C2 | semidirect |
| 7. #11717004 | C2 | semidirect |
| 8. #11717003 | C2 | semidirect |
| 9. #11716976 | C2 | semidirect |
| 12. C2×#6045 | C22 | semidirect |
| 15. C2×C5×D20 | C22 | semidirect |
| 18. C2×D5×Dic5 | C22 | semidirect |
| 20. C4⋊#1039 | C22 | semidirect |
| 21. #87806 | C22 | semidirect |
| 24. C5×#685 | C22 | semidirect |
| 25. C5×C4⋊Dic5 | C22 | semidirect |
| 26. #87780 | C22 | semidirect |
| 29. #87778 | C22 | semidirect |
| 30. Dic52 | C22 | semidirect |
| 59. #4076 | D5 | semidirect |
| 61. C2×#685 | D5 | semidirect |
| 104. C2×D20 | C2×D5 | semidirect |
| 124. #685 | C2×D5 | semidirect |
| 129. C4⋊Dic5 | C2×D5 | semidirect |
| 199. C52 | #538 | semidirect |
| 300. C5 | #65828 | semidirect |
| 301. C5 | #65951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717244 | 2 |
| C5×#4076 | 2 |
| C2×C5×#685 | 2 |
| #11717094 | 2 |
| Dic5×C22⋊D5 | 2 |
| #11717031 | 2 |
| #11717004 | 2 |
| #11717003 | 2 |
| #11716976 | 2 |
| #65951 | 5 |
| #65828 | 5 |