Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
736 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Frattini | C22 | C22×D52 |
| Fitting | C22×C4×C52 | C22 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #525 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C4 ◁ 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×C4×C5×D5 | C2 | semidirect |
| 3. #11717246 | C2 | semidirect |
| 4. #11717094 | C2 | semidirect |
| 5. #11717079 | C2 | semidirect |
| 6. #11717026 | C2 | semidirect |
| 7. C4×#6037 | C2 | semidirect |
| 8. #11716974 | C2 | semidirect |
| 14. C2×C5×D20 | C22 | semidirect |
| 18. C2×C4×C5×D5 | C22 | semidirect |
| 19. C2×C5×Dic10 | C22 | semidirect |
| 22. C4⋊#1039 | C22 | semidirect |
| 23. C4×#1039 | C22 | semidirect |
| 24. #87781 | C22 | semidirect |
| 26. #87778 | C22 | semidirect |
| 34. C2×C4×C52 | D4 | semidirect |
| 50. C2×#709 | D5 | semidirect |
| 51. C22×C4×D5 | D5 | semidirect |
| 73. C2×C5×D5 | #41 | semidirect |
| 98. C2×D20 | C2×D5 | semidirect |
| 102. C2×C4×D5 | C2×D5 | semidirect |
| 103. C2×Dic10 | C2×D5 | semidirect |
| 148. C2×C4×C5 | C22⋊D5 | semidirect |
| 149. C2×C4×C5 | C22⋊D5 | semidirect |
| 176. C52 | #525 | semidirect |
| 197. C2×D5 | #709 | semidirect |
| 258. C2×C4 | #6037 | semidirect |
| 262. C5 | #66125 | semidirect |
| 263. C5 | #66162 | 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×C4×C5×D5 | 2 |
| #11717246 | 2 |
| #11717094 | 2 |
| #11717079 | 2 |
| #11717026 | 2 |
| C4×#6037 | 2 |
| #11716974 | 2 |
| #66162 | 5 |
| #66125 | 5 |