Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
890 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. C4×#87830 | C2 | semidirect |
| 4. #13103904 | C2 | semidirect |
| 6. #13099904 | C2 | semidirect |
| 7. #13099900 | C2 | semidirect |
| 9. Q8×#1044 | C4 | semidirect |
| 11. D4×#1044 | C4 | semidirect |
| 21. #11716878 | C4 | semidirect |
| 22. #11716876 | C4 | semidirect |
| 25. C5×#3969 | C4 | semidirect |
| 26. #11716611 | C4 | semidirect |
| 54. C4×#1043 | C2×C4 | semidirect |
| 55. #87856 | C2×C4 | semidirect |
| 58. C4×C5×Dic5 | C2×C4 | semidirect |
| 59. C5×#681 | C2×C4 | semidirect |
| 80. C52×Q8 | C42 | semidirect |
| 82. C52×D4 | C42 | semidirect |
| 91. C4⋊(C5⋊D5) | C42 | semidirect |
| 100. #6045 | C42 | semidirect |
| 128. #3969 | AGL(1,𝔽5) | semidirect |
| 141. #1044 | #104 | semidirect |
| 200. C4×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 201. #681 | C2×AGL(1,𝔽5) | semidirect |
| 231. C5×Q8 | C4×AGL(1,𝔽5) | semidirect |
| 235. C5×D4 | C4×AGL(1,𝔽5) | semidirect |
| 298. C52 | C4×#104 | semidirect |
| 383. Q8 | #87830 | semidirect |
| 390. D4 | #87830 | semidirect |
| 414. C5 | AGL(1,𝔽5)×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#1044 | 2 |
| #13104804 | 2 |
| C4×#87830 | 2 |
| #13103904 | 2 |
| #13101844 | 2 |
| #13099904 | 2 |
| #13099900 | 2 |
| AGL(1,𝔽5)×#104 | 5 |