Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×C4×#1042 | C2 | semidirect |
| 3. D5⋊#681 | C2 | semidirect |
| 4. #11716853 | C2 | semidirect |
| 5. #11716851 | C2 | semidirect |
| 7. C52×#41 | C4 | semidirect |
| 9. C5×Q8×D5 | C4 | semidirect |
| 13. C5×D4×D5 | C4 | semidirect |
| 15. C5×#709 | C4 | semidirect |
| 20. C4×#1042 | C22 | semidirect |
| 21. #87849 | C22 | semidirect |
| 29. C52×Q8 | C2×C4 | semidirect |
| 31. C52×D4 | C2×C4 | semidirect |
| 40. C5×D20 | C2×C4 | semidirect |
| 49. C5×Dic10 | C2×C4 | semidirect |
| 82. C5×#41 | Dic5 | semidirect |
| 83. C5×#41 | AGL(1,𝔽5) | semidirect |
| 91. Q8×D5 | Dic5 | semidirect |
| 95. D4×D5 | Dic5 | semidirect |
| 97. #709 | Dic5 | semidirect |
| 116. C5×D5 | #104 | semidirect |
| 126. C5×Q8 | C2×Dic5 | semidirect |
| 127. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 137. C5×D4 | C2×Dic5 | semidirect |
| 138. C5×D4 | C2×AGL(1,𝔽5) | semidirect |
| 162. D20 | C2×Dic5 | semidirect |
| 171. Dic10 | C2×Dic5 | semidirect |
| 179. C52 | C2×#104 | semidirect |
| 218. #41 | #1042 | semidirect |
| 244. D5 | #3969 | semidirect |
| 249. Q8 | C2×#1042 | semidirect |
| 256. D4 | C2×#1042 | semidirect |
| 272. C5 | C2×#3969 | semidirect |
| 273. C5 | D5⋊#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5×#41 | 2 |
| C2×C4×#1042 | 2 |
| D5⋊#681 | 2 |
| #11716853 | 2 |
| #11716851 | 2 |
| D5⋊#104 | 5 |
| C2×#3969 | 5 |