Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
584 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D52 |
| commutator, socle | C2×C52 | C23×C4 |
| Fitting | C52×M16 | C22 |
| prime radical | #11717471 | C2 |
| cosocle | C4×C52 | C24 |
| hypercenter | M16 | D52 |
| hypocenter | C52 | #568 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C4 ◁ M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. M16×C5⋊D5 | C2 | semidirect |
| 3. C5×#4053 | C2 | semidirect |
| 4. C2×#87769 | C2 | semidirect |
| 5. #11716932 | C2 | semidirect |
| 6. #11716923 | C2 | semidirect |
| 7. #11716921 | C2 | semidirect |
| 8. D5×#676 | C2 | semidirect |
| 18. C52×M16 | C22 | semidirect |
| 19. #87804 | C22 | semidirect |
| 21. C8×C5⋊D5 | C22 | semidirect |
| 22. C2×C5×#168 | C22 | semidirect |
| 23. C5×#676 | C22 | semidirect |
| 24. C5×C8×D5 | C22 | semidirect |
| 26. #87769 | C22 | semidirect |
| 27. #87769 | C22 | semidirect |
| 28. #87768 | C22 | semidirect |
| 29. D5×#168 | C22 | semidirect |
| 56. #4053 | D5 | semidirect |
| 89. C5×M16 | C2×D5 | semidirect |
| 96. C2×#168 | C2×D5 | semidirect |
| 104. #676 | C2×D5 | semidirect |
| 108. C8×D5 | C2×D5 | semidirect |
| 161. C52 | #568 | semidirect |
| 199. M16 | D52 | semidirect |
| 236. C5 | #66084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717471 | 2 |
| M16×C5⋊D5 | 2 |
| C5×#4053 | 2 |
| C2×#87769 | 2 |
| #11716932 | 2 |
| #11716923 | 2 |
| #11716921 | 2 |
| D5×#676 | 2 |
| #66084 | 5 |