Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
904 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 904 conjugacy classes of subgroups — too many to draw. Only its 160 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 | #535 |
| 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. C22×C4⋊(C5⋊D5) | C2 | semidirect |
| 2. C2×C5×#709 | C2 | semidirect |
| 3. C5×#4072 | C2 | semidirect |
| 4. #11717099 | C2 | semidirect |
| 5. #11717029 | C2 | semidirect |
| 6. #11717027 | C2 | semidirect |
| 7. #11716982 | C2 | semidirect |
| 15. C2×C5×D20 | C22 | semidirect |
| 16. C2×C4×C5×D5 | C22 | semidirect |
| 17. C2×C5×Dic10 | C22 | semidirect |
| 18. C2×#6038 | C22 | semidirect |
| 20. C5×C4⋊Dic5 | C22 | semidirect |
| 21. C4×C5×Dic5 | C22 | semidirect |
| 22. #87779 | C22 | semidirect |
| 30. C2×C4×C52 | D4 | semidirect |
| 43. C2×#709 | D5 | semidirect |
| 52. #4072 | D5 | semidirect |
| 93. C2×D20 | C2×D5 | semidirect |
| 94. C2×C4×D5 | C2×D5 | semidirect |
| 95. C2×Dic10 | C2×D5 | semidirect |
| 102. C4⋊Dic5 | C2×D5 | semidirect |
| 103. C4×Dic5 | C2×D5 | semidirect |
| 133. C2×C4×C5 | D20 | semidirect |
| 134. C2×C4×C5 | C22⋊D5 | semidirect |
| 160. C52 | #535 | semidirect |
| 236. C2×C4 | #6038 | semidirect |
| 240. C5 | #65859 | semidirect |
| 241. C5 | #66164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C5⋊D5) | 2 |
| C2×C5×#709 | 2 |
| C5×#4072 | 2 |
| #11717099 | 2 |
| #11717029 | 2 |
| #11717027 | 2 |
| #11716982 | 2 |
| #66164 | 5 |
| #65859 | 5 |