Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
500 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 132 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 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C2×C52×Q8 | C22 |
| prime radical | C2×C4⋊(C5⋊D5) | C22 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | #556 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×Q8×Dic5 | C2 | semidirect |
| 3. C5×#4090 | C2 | semidirect |
| 4. C4×#6039 | C2 | semidirect |
| 6. #11717009 | C2 | semidirect |
| 7. #11716987 | C2 | semidirect |
| 9. #11716966 | C2 | semidirect |
| 10. #11716961 | C2 | semidirect |
| 11. #11716954 | C2 | semidirect |
| 60. Q8×Dic5 | D5 | semidirect |
| 61. #4090 | D5 | semidirect |
| 196. C52 | #556 | semidirect |
| 285. C5 | #65902 | semidirect |
| 286. C5 | #66066 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717267 | 2 |
| C5×Q8×Dic5 | 2 |
| C5×#4090 | 2 |
| C4×#6039 | 2 |
| #11717013 | 2 |
| #11717009 | 2 |
| #11716987 | 2 |
| #11716982 | 2 |
| #11716966 | 2 |
| #11716961 | 2 |
| #11716954 | 2 |
| #66066 | 5 |
| #65902 | 5 |