Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
592 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×#6037 |
| commutator, cosocle | C4×C52 | C24 |
| Frattini | C4 | C22×D52 |
| Fitting | C22×C4×C52 | C22 |
| socle | C2×C52 | C22×D4 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #575 |
| LCS | G ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C4 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#709 | C2 | semidirect |
| 2. C2×#87804 | C2 | semidirect |
| 3. #11716945 | C2 | semidirect |
| 4. #11716941 | C2 | semidirect |
| 5. #11716940 | C2 | semidirect |
| 11. C5×#709 | C22 | semidirect |
| 12. C2×C5×D20 | C22 | semidirect |
| 14. C2×C5×Dic10 | C22 | semidirect |
| 15. #87804 | C22 | semidirect |
| 16. C2×#6029 | C22 | semidirect |
| 17. #87775 | C22 | semidirect |
| 18. #87772 | C22 | semidirect |
| 19. #87770 | C22 | semidirect |
| 38. C2×#709 | D5 | semidirect |
| 69. #709 | C2×D5 | semidirect |
| 70. C2×D20 | C2×D5 | semidirect |
| 72. C2×Dic10 | C2×D5 | semidirect |
| 126. C52 | #575 | semidirect |
| 187. C5 | #66156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| C2×#87804 | 2 |
| #11716945 | 2 |
| #11716941 | 2 |
| #11716940 | 2 |
| #66156 | 5 |