Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
952 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 243 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 | #553 |
| 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. C52×#121 | C2 | semidirect |
| 2. #11717259 | C2 | semidirect |
| 3. #11717258 | C2 | semidirect |
| 4. D4×#1039 | C2 | semidirect |
| 5. D4×#1039 | C2 | semidirect |
| 6. C4×C22⋊(C5⋊D5) | C2 | semidirect |
| 7. C2×C4⋊#1039 | C2 | semidirect |
| 8. #11717212 | C2 | semidirect |
| 9. #11717210 | C2 | semidirect |
| 10. #11717206 | C2 | semidirect |
| 11. #11717199 | C2 | semidirect |
| 55. C5×#121 | D5 | semidirect |
| 138. #121 | C5⋊D5 | semidirect |
| 144. C52 | #553 | semidirect |
| 211. C5 | #65952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#121 | 2 |
| #11717259 | 2 |
| #11717258 | 2 |
| D4×#1039 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| C2×C4⋊#1039 | 2 |
| #11717212 | 2 |
| #11717210 | 2 |
| #11717206 | 2 |
| #11717199 | 2 |
| #65952 | 5 |