Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
616 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 616 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 | C22×C4×C52 | C22 |
| prime radical | C23×C5⋊D5 | C22 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #543 |
| 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 |
|---|---|---|
| 2. C5×#4070 | C2 | semidirect |
| 3. #11717100 | C2 | semidirect |
| 5. #11717009 | C2 | semidirect |
| 6. #11717008 | C2 | semidirect |
| 10. C2×C5×Dic10 | C22 | semidirect |
| 11. C2×#6039 | C22 | semidirect |
| 16. C5×C4⋊Dic5 | C22 | semidirect |
| 17. C5×#683 | C22 | semidirect |
| 18. #87781 | C22 | semidirect |
| 19. #87780 | C22 | semidirect |
| 25. C22×C5⋊D5 | Q8 | semidirect |
| 41. #4070 | D5 | semidirect |
| 69. C2×Dic10 | C2×D5 | semidirect |
| 80. C4⋊Dic5 | C2×D5 | semidirect |
| 83. #683 | C2×D5 | semidirect |
| 124. C52 | #543 | semidirect |
| 190. C5 | #65968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87808 | 2 |
| C5×#4070 | 2 |
| #11717100 | 2 |
| #11717092 | 2 |
| #11717009 | 2 |
| #11717008 | 2 |
| #65968 | 5 |