Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1320 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 323 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Frattini | C22 | C23×C5⋊D5 |
| Fitting | C23×C4×C52 | C2 |
| hypercenter | C23×C4 | C5⋊D5 |
| hypocenter | C52 | #525 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C4×C52 | C2 | semidirect |
| 2. C2×#87900 | C2 | semidirect |
| 3. #11717273 | C2 | semidirect |
| 4. #11717250 | C2 | semidirect |
| 5. #11717249 | C2 | semidirect |
| 6. C4×C22⋊(C5⋊D5) | C2 | semidirect |
| 7. #11717246 | C2 | semidirect |
| 8. #11717244 | C2 | semidirect |
| 18. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 19. C2×C4×C5⋊D5 | C22 | semidirect |
| 20. C2×#6045 | C22 | semidirect |
| 23. #87808 | C22 | semidirect |
| 24. C4⋊#1039 | C22 | semidirect |
| 25. #87806 | C22 | semidirect |
| 26. C4×#1039 | C22 | semidirect |
| 36. C2×C4×C52 | D4 | semidirect |
| 47. C23×C4×C5 | D5 | semidirect |
| 60. C22×C52 | #41 | semidirect |
| 101. C2×C4×C5 | C22⋊D5 | semidirect |
| 113. C23×C4 | C5⋊D5 | semidirect |
| 120. C52 | #525 | semidirect |
| 125. C22×C5 | #709 | semidirect |
| 173. C2×C4 | C22⋊(C5⋊D5) | semidirect |
| 177. C5 | #66125 | semidirect |
| 184. C22 | #87900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C52 | 2 |
| C2×#87900 | 2 |
| #11717273 | 2 |
| #11717250 | 2 |
| #11717249 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| #11717246 | 2 |
| #11717244 | 2 |
| #66125 | 5 |