Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
3560 conjugacy classes of subgroups; only the 931 normal subgroups are shown.
This group has 3560 conjugacy classes of subgroups — too many to draw. Only its 931 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×C5⋊D5 |
| commutator, cosocle | C2×C52 | C25 |
| Frattini | C2 | C24×C5⋊D5 |
| Fitting | C22×C52×D4 | C2 |
| socle | C23×C52 | C23 |
| hypercenter | C22×D4 | C5⋊D5 |
| hypocenter | C52 | C22×#41 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C52×D4 | C2 | semidirect |
| 2. C22×C22⋊(C5⋊D5) | C2 | semidirect |
| 3. C23×#1039 | C2 | semidirect |
| 4. C2×#87902 | C2 | direct (N × H) |
| 5. C22×C4×C5⋊D5 | C2 | semidirect |
| 6. C22×#6045 | C2 | semidirect |
| 9. C2×C52×D4 | C22 | semidirect |
| 11. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 14. C22×#1039 | C22 | semidirect |
| 15. #87902 | C22 | direct (N × H) |
| 16. C2×C4×C5⋊D5 | C22 | semidirect |
| 17. C2×#6045 | C22 | semidirect |
| 24. C52×D4 | C23 | semidirect |
| 26. C22⋊(C5⋊D5) | C23 | semidirect |
| 29. C2×#1039 | C23 | semidirect |
| 30. C4×C5⋊D5 | C23 | semidirect |
| 31. #6045 | C23 | semidirect |
| 32. C22×C5×D4 | D5 | semidirect |
| 39. C22×C52 | #41 | semidirect |
| 49. C2×C5×D4 | C2×D5 | semidirect |
| 60. C2×C52 | C2×#41 | semidirect |
| 68. C5×D4 | C22×D5 | semidirect |
| 79. C22×D4 | C5⋊D5 | semidirect |
| 82. C52 | C22×#41 | semidirect |
| 84. C22×C5 | #711 | semidirect |
| 97. C2×D4 | C2×C5⋊D5 | semidirect |
| 104. C2×C5 | C2×#711 | semidirect |
| 114. D4 | C22×C5⋊D5 | semidirect |
| 120. C5 | C22×#711 | semidirect |
| 124. C22 | #87902 | direct (N × H) |
| 132. C2 | C2×#87902 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C22×C22⋊(C5⋊D5) | 2 |
| C23×#1039 | 2 |
| C2×#87902 | 2 |
| C22×C4×C5⋊D5 | 2 |
| C22×#6045 | 2 |
| C22×#711 | 5 |