Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1160 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 293 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 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C2×C52×#41 | C2 |
| hypercenter | C2×#41 | C5⋊D5 |
| hypocenter | C52 | #548 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C52×#41 | C2 | semidirect |
| 2. C2×Q8×C5⋊D5 | C2 | semidirect |
| 3. Q8×#1039 | C2 | semidirect |
| 4. #11717258 | C2 | semidirect |
| 5. #11717256 | C2 | semidirect |
| 6. C4×C22⋊(C5⋊D5) | C2 | semidirect |
| 7. #11717244 | C2 | semidirect |
| 25. C52×Q8 | D4 | semidirect |
| 36. C2×C5×#41 | D5 | semidirect |
| 49. C2×C5⋊D5 | #41 | semidirect |
| 77. C5×Q8 | C22⋊D5 | semidirect |
| 88. C2×#41 | C5⋊D5 | semidirect |
| 95. C52 | #548 | semidirect |
| 130. Q8 | C22⋊(C5⋊D5) | semidirect |
| 140. C5 | #66165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×#41 | 2 |
| C2×Q8×C5⋊D5 | 2 |
| Q8×#1039 | 2 |
| #11717258 | 2 |
| #11717256 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| #11717244 | 2 |
| #66165 | 5 |