Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
832 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 832 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 | C2×C52×Q8 | C22 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | #535 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87904 | C2 | semidirect |
| 2. C2×#87877 | C2 | semidirect |
| 3. C5×#4093 | C2 | semidirect |
| 4. #11717041 | C2 | semidirect |
| 5. #11717030 | C2 | semidirect |
| 6. #11717029 | C2 | semidirect |
| 7. #11716992 | C2 | semidirect |
| 9. C2×C52×Q8 | C22 | semidirect |
| 12. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 14. C2×C4×C5⋊D5 | C22 | semidirect |
| 16. C2×#6038 | C22 | semidirect |
| 19. C5×#685 | C22 | semidirect |
| 20. C4×C5×Dic5 | C22 | semidirect |
| 21. #87781 | C22 | semidirect |
| 36. C4×C5⋊D5 | D4 | semidirect |
| 45. #4093 | D5 | semidirect |
| 65. C2×C5×Q8 | C2×D5 | semidirect |
| 85. #685 | C2×D5 | semidirect |
| 87. C4×Dic5 | C2×D5 | semidirect |
| 132. C52 | #535 | semidirect |
| 158. C2×Q8 | D52 | semidirect |
| 199. C5 | #66008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87904 | 2 |
| C2×#87877 | 2 |
| C5×#4093 | 2 |
| #11717041 | 2 |
| #11717030 | 2 |
| #11717029 | 2 |
| #11716992 | 2 |
| #66008 | 5 |