Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
744 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 160 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 | C22×C4×C52 | C22 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #535 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#709 | C2 | semidirect |
| 2. C22×C5×D20 | C2 | semidirect |
| 3. #11717246 | C2 | semidirect |
| 4. #11717094 | C2 | semidirect |
| 5. #11717032 | C2 | semidirect |
| 6. #11717026 | C2 | semidirect |
| 7. #11716981 | C2 | semidirect |
| 15. C2×C5×D20 | C22 | semidirect |
| 16. C2×C4×C5×D5 | C22 | semidirect |
| 17. C2×C5×Dic10 | C22 | semidirect |
| 18. C2×#6037 | C22 | semidirect |
| 20. C4⋊#1039 | C22 | semidirect |
| 21. C4×#1039 | C22 | semidirect |
| 22. #87778 | C22 | semidirect |
| 30. C2×C4×C52 | D4 | semidirect |
| 44. C2×#709 | D5 | semidirect |
| 45. C22×D20 | D5 | semidirect |
| 89. C2×D20 | C2×D5 | semidirect |
| 90. C2×C4×D5 | C2×D5 | semidirect |
| 91. C2×Dic10 | C2×D5 | semidirect |
| 130. C2×C4×C5 | C22⋊D5 | semidirect |
| 131. C2×C4×C5 | C22⋊D5 | semidirect |
| 155. C52 | #535 | semidirect |
| 228. C2×C4 | #6037 | semidirect |
| 232. C5 | #66139 | semidirect |
| 233. C5 | #66164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| C22×C5×D20 | 2 |
| #11717246 | 2 |
| #11717094 | 2 |
| #11717032 | 2 |
| #11717026 | 2 |
| #11716981 | 2 |
| #66164 | 5 |
| #66139 | 5 |