Finite Group Databasebeta

← C22×C5×#13133724 #46802172

Subgroups — C22×C5×#13133724 #46802172

Order 34100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#13133724C213yesmaximal, direct product factor
2C5×#13133724C2211yescharacteristic, direct product factor, Hall
3C22×#13133724C515yesmaximal, direct product factor
4C22×C5×C11×C31C511yesmaximal, characteristic, complemented
5C2×#13133724C2×C5115yesdirect product factor
6C2×C5×C11×C31C2×C513yescomplemented
7C22×C5×ΓL(1,𝔽32)—111nomaximal, Hall
8C5×C11×C31C22×C511yescharacteristic, complemented
9#13133724C22×C515yesdirect product factor
10C2×C5×ΓL(1,𝔽32)—113no—
11C22×C11×C31C5211yescharacteristic, complemented, Hall
12C22×C5×C11⋊C5—311nomaximal, Hall
13C5×ΓL(1,𝔽32)—111noHall
14C2×C11×C31C2×C5213yescomplemented
15C22×C5×C31C11⋊C511yescharacteristic, complemented
16C22×ΓL(1,𝔽32)—115no—
17C2×C5×C11⋊C5—313no—
18C11×C31C22×C5211yescharacteristic, complemented, Hall
19C2×C5×C31C2×C11⋊C513yescomplemented
20C2×ΓL(1,𝔽32)—1115no—
21C5×C11⋊C5—311noHall
22C22×C5×C11ΓL(1,𝔽32)11yescharacteristic, complemented
23C22×C11⋊C5—315no—
24C5×C31C22×C11⋊C511yescharacteristic, complemented
25ΓL(1,𝔽32)—115no—
26C22×C31C5×C11⋊C511yescharacteristic, complemented, Hall
27C2×C5×C11C2×ΓL(1,𝔽32)13yescomplemented
28C2×C11⋊C5—3115no—
29C22×C52—3411noHall
30C2×C31C2×C5×C11⋊C513yescomplemented
31C5×C11C22×ΓL(1,𝔽32)11yescharacteristic, complemented
32C11⋊C5—315no—
33C2×C52—3413no—
34C22×C11C5×ΓL(1,𝔽32)11yescharacteristic, complemented, Hall
35C31C22×C5×C11⋊C511yescharacteristic, complemented, Sylow
36C52—3411noSylow
37C2×C11C2×C5×ΓL(1,𝔽32)13yescomplemented
38C22×C5—3415no—
39C22×C5#1313372411yescharacteristic, direct product factor
40C11C22×C5×ΓL(1,𝔽32)11yescharacteristic, complemented, Sylow
41C2×C5—34115no—
42C2×C5C2×#1313372413yesdirect product factor
43C5—3415no—
44C5C22×#1313372411yescharacteristic, direct product factor
45C22C5×#1313372411yescharacteristic, direct product factor, Sylow
46C2C2×C5×#1313372413yesdirect product factor
subgroupG/H
center, hypercenterC22×C5#13133724
commutator, cosocle, hypocenterC11×C31C22×C52
FrattiniC1G
Fitting, socleC22×C5×C11×C31C5
LCSG ▷ C11×C31
UCSC1 ◁ C22×C5

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C5×#13133724C2direct (N × H)
2. C5×#13133724C22direct (N × H)
3. C22×#13133724C5direct (N × H)
4. C22×C5×C11×C31C5semidirect
5. C2×#13133724C2×C5direct (N × H)
6. C2×C5×C11×C31C2×C5semidirect
8. C5×C11×C31C22×C5semidirect
9. #13133724C22×C5direct (N × H)
11. C22×C11×C31C52semidirect
14. C2×C11×C31C2×C52semidirect
15. C22×C5×C31C11⋊C5semidirect
18. C11×C31C22×C52semidirect
19. C2×C5×C31C2×C11⋊C5semidirect
22. C22×C5×C11ΓL(1,𝔽32)semidirect
24. C5×C31C22×C11⋊C5semidirect
26. C22×C31C5×C11⋊C5semidirect
27. C2×C5×C11C2×ΓL(1,𝔽32)semidirect
30. C2×C31C2×C5×C11⋊C5semidirect
31. C5×C11C22×ΓL(1,𝔽32)semidirect
34. C22×C11C5×ΓL(1,𝔽32)semidirect
35. C31C22×C5×C11⋊C5semidirect
37. C2×C11C2×C5×ΓL(1,𝔽32)semidirect
39. C22×C5#13133724direct (N × H)
40. C11C22×C5×ΓL(1,𝔽32)semidirect
42. C2×C5C2×#13133724direct (N × H)
44. C5C22×#13133724direct (N × H)
45. C22C5×#13133724direct (N × H)
46. C2C2×C5×#13133724direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C5×#131337242
C22×#131337245
C22×C5×C11×C315
C22×C5×ΓL(1,𝔽32)11
C22×C5×C11⋊C531