Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
502 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 86 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. C52×H(5,𝔽2) | C2 | semidirect |
| 2. C5×#4095 | C2 | semidirect |
| 3. C5×#4086 | C2 | semidirect |
| 4. C5×#3969 | C2 | semidirect |
| 5. C5×#3965 | C2 | semidirect |
| 12. C2×C5×D20 | C22 | semidirect |
| 15. C4×C5×Dic5 | C22 | semidirect |
| 16. C5×#681 | C22 | semidirect |
| 18. #65530 | C5 | direct (N × H) |
| 22. C52×Q8 | D4 | semidirect |
| 26. C52×D4 | D4 | semidirect |
| 35. C5×H(5,𝔽2) | D5 | semidirect |
| 36. C5×H(5,𝔽2) | C2×C5 | semidirect |
| 39. #4095 | C2×C5 | semidirect |
| 40. #4086 | C2×C5 | semidirect |
| 43. #3969 | C2×C5 | semidirect |
| 44. #3965 | C2×C5 | semidirect |
| 73. C2×D20 | C22×C5 | semidirect |
| 80. C4×Dic5 | C22×C5 | semidirect |
| 81. #681 | C22×C5 | semidirect |
| 97. C5×Q8 | C22⋊D5 | semidirect |
| 98. C5×Q8 | C5×D4 | semidirect |
| 111. C5×D4 | C22⋊D5 | semidirect |
| 112. C5×D4 | C5×D4 | semidirect |
| 128. H(5,𝔽2) | C5×D5 | semidirect |
| 133. C52 | #453 | semidirect |
| 189. Q8 | C5×C22⋊D5 | semidirect |
| 195. D4 | C5×C22⋊D5 | semidirect |
| 202. C5 | #65530 | direct (N × H) |
| 203. C5 | C5×#453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×H(5,𝔽2) | 2 |
| C5×#4095 | 2 |
| C5×#4086 | 2 |
| C5×#3969 | 2 |
| C5×#3965 | 2 |
| C5×#453 | 5 |
| #65530 | 5 |