Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
384 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×D5⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. D5⋊#700 | C2 | semidirect |
| 4. #11716903 | C2 | semidirect |
| 5. #11716878 | C2 | semidirect |
| 6. #11716770 | C2 | semidirect |
| 7. #11716769 | C2 | semidirect |
| 10. C5×#713 | C4 | semidirect |
| 11. C5×Q8×D5 | C4 | semidirect |
| 13. D5×D20 | C4 | semidirect |
| 17. #87874 | C4 | semidirect |
| 20. C4×#1044 | C22 | semidirect |
| 21. #87863 | C22 | semidirect |
| 22. C4×#1043 | C22 | semidirect |
| 23. #87856 | C22 | semidirect |
| 34. C52×Q8 | C2×C4 | semidirect |
| 36. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 40. C5×D20 | C2×C4 | semidirect |
| 46. C5×Dic10 | C2×C4 | semidirect |
| 98. #713 | AGL(1,𝔽5) | semidirect |
| 99. Q8×D5 | AGL(1,𝔽5) | semidirect |
| 134. C5×D5 | #104 | semidirect |
| 149. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 150. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 173. D20 | C2×AGL(1,𝔽5) | semidirect |
| 192. Dic10 | C2×AGL(1,𝔽5) | semidirect |
| 205. C52 | C2×#104 | semidirect |
| 275. D5 | #4010 | semidirect |
| 280. Q8 | D5⋊AGL(1,𝔽5) | semidirect |
| 305. C5 | C2×#4010 | semidirect |
| 306. C5 | D5⋊#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#713 | 2 |
| C4×D5⋊AGL(1,𝔽5) | 2 |
| D5⋊#700 | 2 |
| #11716903 | 2 |
| #11716878 | 2 |
| #11716770 | 2 |
| #11716769 | 2 |
| D5⋊#104 | 5 |
| C2×#4010 | 5 |