Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
96 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11758758 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×#6039 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11758740 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C5×#1039 | — | 2 | 1 | no | — |
| 5 | C5×#1039 | C22 | 1 | 1 | yes | characteristic |
| 6 | C52×Dic5 | — | 2 | 1 | no | — |
| 7 | #87839 | — | 5 | 1 | no | maximal |
| 8 | C2×C53 | D4 | 1 | 1 | yes | characteristic |
| 9 | C5×Dic10 | — | 10 | 1 | no | — |
| 10 | #6039 | — | 5 | 1 | no | — |
| 11 | #6039 | — | 10 | 1 | no | — |
| 12 | #6039 | D5 | 1 | 1 | yes | characteristic |
| 13 | #6034 | — | 5 | 1 | no | — |
| 14 | #6032 | — | 10 | 1 | no | — |
| 15 | C53 | Q16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | C4×C52 | — | 10 | 1 | no | — |
| 17 | #1039 | — | 2 | 1 | no | — |
| 18 | #1039 | C2×D5 | 1 | 1 | yes | characteristic |
| 19 | C5×Dic5 | — | 2 | 1 | no | — |
| 20 | C5×Dic5 | — | 2 | 1 | no | — |
| 21 | C5×Dic5 | — | 4 | 2 | no | — |
| 22 | C5×Dic5 | — | 10 | 1 | no | — |
| 23 | C5×Dic5 | — | 10 | 1 | no | — |
| 24 | C5×Dic5 | — | 10 | 1 | no | — |
| 25 | C5×Dic5 | — | 10 | 1 | no | — |
| 26 | C5×Dic5 | — | 10 | 1 | no | — |
| 27 | C5×Dic5 | — | 20 | 2 | no | — |
| 28 | #689 | — | 25 | 1 | no | maximal |
| 29 | C2×C52 | — | 2 | 1 | no | — |
| 30 | C2×C52 | — | 2 | 1 | no | — |
| 31 | C2×C52 | — | 2 | 1 | no | — |
| 32 | C2×C52 | — | 4 | 2 | no | — |
| 33 | C2×C52 | — | 4 | 2 | no | — |
| 34 | C2×C52 | — | 8 | 1 | no | — |
| 35 | C2×C52 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 36 | C5×Q8 | — | 25 | 1 | no | — |
| 37 | Dic10 | — | 10 | 1 | no | — |
| 38 | Dic10 | — | 25 | 1 | no | — |
| 39 | Dic10 | — | 50 | 1 | no | — |
| 40 | #170 | — | 50 | 1 | no | — |
| 41 | #168 | — | 25 | 1 | no | — |
| 42 | C52 | — | 2 | 1 | no | — |
| 43 | C52 | — | 2 | 1 | no | — |
| 44 | C52 | — | 2 | 1 | no | — |
| 45 | C52 | — | 4 | 2 | no | — |
| 46 | C52 | — | 4 | 2 | no | — |
| 47 | C52 | — | 8 | 1 | no | — |
| 48 | C52 | #689 | 1 | 1 | yes | characteristic, complemented |
| 49 | C4×C5 | — | 10 | 1 | no | — |
| 50 | C4×C5 | — | 10 | 1 | no | — |
| 51 | C4×C5 | — | 20 | 2 | no | — |
| 52 | C4×C5 | — | 25 | 1 | no | — |
| 53 | C4×C5 | — | 50 | 1 | no | — |
| 54 | Dic5 | — | 2 | 1 | no | — |
| 55 | Dic5 | — | 10 | 1 | no | — |
| 56 | Dic5 | — | 10 | 1 | no | — |
| 57 | Dic5 | — | 10 | 1 | no | — |
| 58 | Dic5 | — | 10 | 1 | no | — |
| 59 | Dic5 | — | 10 | 1 | no | — |
| 60 | Dic5 | — | 20 | 2 | no | — |
| 61 | Q16 | — | 125 | 1 | no | Sylow |
| 62 | C2×C5 | — | 2 | 1 | no | — |
| 63 | C2×C5 | — | 2 | 1 | no | — |
| 64 | C2×C5 | — | 2 | 1 | no | — |
| 65 | C2×C5 | — | 4 | 2 | no | — |
| 66 | C2×C5 | — | 4 | 2 | no | — |
| 67 | C2×C5 | — | 8 | 1 | no | — |
| 68 | C2×C5 | D52⋊C2 | 1 | 1 | yes | characteristic |
| 69 | Q8 | — | 25 | 1 | no | — |
| 70 | Q8 | — | 125 | 1 | no | — |
| 71 | C8 | — | 125 | 1 | no | — |
| 72 | C5 | — | 2 | 1 | no | — |
| 73 | C5 | — | 2 | 1 | no | — |
| 74 | C5 | — | 2 | 1 | no | — |
| 75 | C5 | — | 4 | 2 | no | — |
| 76 | C5 | — | 4 | 2 | no | — |
| 77 | C5 | — | 8 | 1 | no | — |
| 78 | C5 | #87839 | 1 | 1 | yes | characteristic, complemented |
| 79 | C4 | — | 10 | 1 | no | — |
| 80 | C4 | — | 25 | 1 | no | — |
| 81 | C4 | — | 50 | 1 | no | — |
| 82 | C2 | D52⋊D5 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D52⋊D5 |
| commutator, cosocle | C5×#1039 | C22 |
| Fitting, socle, prime radical | C2×C53 | D4 |
| hypocenter | C53 | Q16 |
| LCS | G ▷ C5×#1039 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. C53 | Q16 | semidirect |
| 48. C52 | #689 | semidirect |
| 78. C5 | #87839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11758758 | 2 |
| C5×#6039 | 2 |
| #11758740 | 2 |
| #87839 | 5 |
| #689 | 25 |