Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
13688 conjugacy classes of subgroups; only the 635 normal subgroups are shown.
This group has 13688 conjugacy classes of subgroups — too many to draw. Only its 635 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×C5⋊D5 |
| commutator, socle, cosocle | C23×C52 | C24 |
| Fitting | C2×C52×#120 | C2 |
| hypercenter | C2×#120 | C5⋊D5 |
| hypocenter | C52 | #2846 |
| LCS | G ▷ C23×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×C5⋊D5 | C2 | semidirect |
| 2. C2×C52×#120 | C2 | semidirect |
| 3. C2×#11717257 | C2 | semidirect |
| 4. #13103110 | C2 | semidirect |
| 5. #13102819 | C2 | semidirect |
| 10. C22×C52×D4 | C22 | semidirect |
| 11. C22×C22⋊(C5⋊D5) | C22 | semidirect |
| 13. C2×C52×C22⋊C4 | C22 | semidirect |
| 14. C2×C22⋊#1039 | C22 | semidirect |
| 16. C2×#87808 | C22 | semidirect |
| 19. C24×C52 | D4 | semidirect |
| 21. C24×C52 | C23 | semidirect |
| 27. C23×C5⋊D5 | D4 | semidirect |
| 31. C22×C4×C52 | C23 | semidirect |
| 33. C22×#1039 | C23 | semidirect |
| 38. C2×C5×#120 | D5 | semidirect |
| 67. C22×C5×D4 | C2×D5 | semidirect |
| 70. C2×C5×C22⋊C4 | C2×D5 | semidirect |
| 80. C22×C52 | #120 | semidirect |
| 86. C2×C5⋊D5 | #120 | semidirect |
| 90. C24×C5 | C22⋊D5 | semidirect |
| 92. C24×C5 | C22×D5 | semidirect |
| 102. C22×C4×C5 | C22×D5 | semidirect |
| 110. C2×#120 | C5⋊D5 | semidirect |
| 144. C22×D4 | C2×C5⋊D5 | semidirect |
| 149. C2×C22⋊C4 | C2×C5⋊D5 | semidirect |
| 150. C52 | #2846 | semidirect |
| 156. C22×C5 | #4083 | semidirect |
| 173. C24 | C22⋊(C5⋊D5) | semidirect |
| 175. C24 | C22×C5⋊D5 | semidirect |
| 180. C22×C4 | C22×C5⋊D5 | semidirect |
| 210. C5 | #10614343 | semidirect |
| 220. C22 | #11717257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C5⋊D5 | 2 |
| C2×C52×#120 | 2 |
| C2×#11717257 | 2 |
| #13103110 | 2 |
| #13102819 | 2 |
| #10614343 | 5 |