Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
904 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 904 conjugacy classes of subgroups — too many to draw. Only its 136 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 | C24×C52 | C22 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | #535 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊(C5⋊D5) | C2 | semidirect |
| 2. C2×#87880 | C2 | semidirect |
| 3. C5×#4099 | C2 | semidirect |
| 4. #11717099 | C2 | semidirect |
| 5. #11717097 | C2 | semidirect |
| 6. #11717089 | C2 | semidirect |
| 7. #11717075 | C2 | semidirect |
| 8. #11717071 | C2 | semidirect |
| 16. C2×C5×C22⋊D5 | C22 | semidirect |
| 17. C2×#6039 | C22 | semidirect |
| 18. C2×#6038 | C22 | semidirect |
| 19. C2×#6037 | C22 | semidirect |
| 21. C2×D5×Dic5 | C22 | semidirect |
| 23. C5×C22⋊Dic5 | C22 | semidirect |
| 24. #87781 | C22 | semidirect |
| 25. #87779 | C22 | semidirect |
| 26. Dic52 | C22 | semidirect |
| 38. C2×#1039 | D4 | semidirect |
| 53. #4099 | D5 | semidirect |
| 91. C2×C22⋊D5 | C2×D5 | semidirect |
| 102. C22⋊Dic5 | C2×D5 | semidirect |
| 162. C52 | #535 | semidirect |
| 247. C5 | #65926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊(C5⋊D5) | 2 |
| C2×#87880 | 2 |
| C5×#4099 | 2 |
| #11717099 | 2 |
| #11717097 | 2 |
| #11717089 | 2 |
| #11717075 | 2 |
| #11717071 | 2 |
| #65926 | 5 |