Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
824 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 824 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 | C24×C52 | C22 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | #534 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×C22⋊D5 | C2 | semidirect |
| 2. C2×C22⋊#1039 | C2 | semidirect |
| 3. #11717098 | C2 | semidirect |
| 4. #11717094 | C2 | semidirect |
| 5. #11717079 | C2 | semidirect |
| 7. C23×C5×D5 | C22 | semidirect |
| 8. C22×#1039 | C22 | semidirect |
| 11. C2×C5×C22⋊D5 | C22 | semidirect |
| 12. C22×C5×Dic5 | C22 | semidirect |
| 13. C2×#6037 | C22 | semidirect |
| 14. C22⋊#1039 | C22 | semidirect |
| 15. #87781 | C22 | semidirect |
| 16. #87778 | C22 | semidirect |
| 19. C23×C52 | D4 | semidirect |
| 33. C22×C22⋊D5 | D5 | semidirect |
| 55. C23×D5 | C2×D5 | semidirect |
| 63. C2×C22⋊D5 | C2×D5 | semidirect |
| 66. C22×Dic5 | C2×D5 | semidirect |
| 87. C23×C5 | C22⋊D5 | semidirect |
| 112. C52 | #534 | semidirect |
| 163. C23 | #6037 | semidirect |
| 174. C5 | #66138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C22⋊D5 | 2 |
| C2×C22⋊#1039 | 2 |
| #11717098 | 2 |
| #11717094 | 2 |
| #11717079 | 2 |
| #66138 | 5 |