Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
942 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 1. #13107619 | C2 | semidirect |
| 3. #13104657 | C2 | semidirect |
| 4. C5×#65767 | C2 | semidirect |
| 5. D5⋊#3955 | C2 | semidirect |
| 6. #13099788 | C2 | semidirect |
| 7. #13099786 | C2 | semidirect |
| 18. #11717260 | C4 | semidirect |
| 19. C5×#4086 | C4 | semidirect |
| 21. #11717032 | C4 | semidirect |
| 22. #11717029 | C4 | semidirect |
| 32. C2×C52×D4 | C2×C4 | semidirect |
| 42. C2×C5×D20 | C2×C4 | semidirect |
| 55. C4⋊#1042 | D4 | semidirect |
| 61. C5×C4⋊AGL(1,𝔽5) | D4 | semidirect |
| 66. C4×#1039 | C2×C4 | semidirect |
| 67. C4×C5×Dic5 | C2×C4 | semidirect |
| 75. #65767 | D5 | semidirect |
| 148. #4086 | AGL(1,𝔽5) | semidirect |
| 202. C2×C5×D4 | C4×D5 | semidirect |
| 203. C2×C5×D4 | C2×AGL(1,𝔽5) | semidirect |
| 234. C2×D20 | C4×D5 | semidirect |
| 245. C4⋊AGL(1,𝔽5) | C22⋊D5 | semidirect |
| 268. C4×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 397. C52 | #1887 | semidirect |
| 474. C2×D4 | D5×AGL(1,𝔽5) | semidirect |
| 556. C5 | #10601116 | semidirect |
| 557. C5 | #10604614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107619 | 2 |
| D5×#4086 | 2 |
| #13104657 | 2 |
| C5×#65767 | 2 |
| D5⋊#3955 | 2 |
| #13099788 | 2 |
| #13099786 | 2 |
| #10604614 | 5 |
| #10601116 | 5 |