Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1176 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1176 conjugacy classes of subgroups — too many to draw. Only its 235 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 | C52×#121 | C2 |
| hypercenter | #121 | C5⋊D5 |
| hypocenter | C52 | #537 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87902 | C2 | semidirect |
| 2. C52×#121 | C2 | semidirect |
| 3. #11717259 | C2 | semidirect |
| 4. #11717259 | C2 | semidirect |
| 5. #11717250 | C2 | semidirect |
| 6. C2×#87806 | C2 | semidirect |
| 7. #11717216 | C2 | semidirect |
| 8. #11717204 | C2 | semidirect |
| 9. #11717198 | C2 | semidirect |
| 47. C2×#1039 | D4 | semidirect |
| 55. C5×#121 | D5 | semidirect |
| 136. #121 | C5⋊D5 | semidirect |
| 138. C52 | #537 | semidirect |
| 204. C5 | #65931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87902 | 2 |
| C52×#121 | 2 |
| #11717259 | 2 |
| #11717250 | 2 |
| C2×#87806 | 2 |
| #11717216 | 2 |
| #11717204 | 2 |
| #11717198 | 2 |
| #65931 | 5 |