Finite Group Databasebeta

← C3×C5×ΓL(1,𝔽8)×C103 #44570071

Subgroups — C3×C5×ΓL(1,𝔽8)×C103 #44570071

Order 32445.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×ΓL(1,𝔽8)×C103C313yesmaximal, direct product factor
2C3×C5×C7×C103C311yesmaximal, characteristic, complemented
3C3×ΓL(1,𝔽8)×C103C511yesmaximal, characteristic, direct product factor, Hall
4C32×C5×C103—71nomaximal, Hall
5C5×C7×C103C3211yescharacteristic, complemented, Hall
6C3×C7×C103C3×C511yescharacteristic, complemented
7ΓL(1,𝔽8)×C103C3×C513yesdirect product factor
8C3×C5×C103—73no—
9C3×C5×C103ΓL(1,𝔽8)11yescharacteristic, direct product factor
10C32×C103—71noHall
11C7×C103C32×C511yescharacteristic, complemented, Hall
12C5×C103C3×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
13C3×C5×ΓL(1,𝔽8)C10311yesmaximal, characteristic, direct product factor, Hall
14C3×C103—73no—
15C3×C103C5×ΓL(1,𝔽8)11yescharacteristic, direct product factor
16C3×C5×C7C3×C10311yescharacteristic, complemented
17C5×ΓL(1,𝔽8)C3×C10313yesdirect product factor
18C103C3×C5×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Sylow
19C3×ΓL(1,𝔽8)C5×C10311yescharacteristic, direct product factor, Hall
20C32×C5—71noHall
21C5×C7C32×C10311yescharacteristic, complemented, Hall
22C3×C7C3×C5×C10311yescharacteristic, complemented
23ΓL(1,𝔽8)C3×C5×C10313yesdirect product factor
24C3×C5—73no—
25C3×C5ΓL(1,𝔽8)×C10311yescharacteristic, direct product factor
26C32—71noSylow
27C7C32×C5×C10311yescharacteristic, complemented, Sylow
28C5C3×ΓL(1,𝔽8)×C10311yescharacteristic, direct product factor, Sylow
29C3—73no—
30C3C5×ΓL(1,𝔽8)×C10311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC3×C5×C103ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C32×C5×C103
FrattiniC1G
Fitting, socleC3×C5×C7×C103C3
LCSG ▷ C7
UCSC1 ◁ C3×C5×C103

Complements

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

NH ≅ G/Ntype
1. C5×ΓL(1,𝔽8)×C103C3direct (N × H)
2. C3×C5×C7×C103C3semidirect
3. C3×ΓL(1,𝔽8)×C103C5direct (N × H)
5. C5×C7×C103C32semidirect
6. C3×C7×C103C3×C5semidirect
7. ΓL(1,𝔽8)×C103C3×C5direct (N × H)
9. C3×C5×C103ΓL(1,𝔽8)direct (N × H)
11. C7×C103C32×C5semidirect
12. C5×C103C3×ΓL(1,𝔽8)direct (N × H)
13. C3×C5×ΓL(1,𝔽8)C103direct (N × H)
15. C3×C103C5×ΓL(1,𝔽8)direct (N × H)
16. C3×C5×C7C3×C103semidirect
17. C5×ΓL(1,𝔽8)C3×C103direct (N × H)
18. C103C3×C5×ΓL(1,𝔽8)direct (N × H)
19. C3×ΓL(1,𝔽8)C5×C103direct (N × H)
21. C5×C7C32×C103semidirect
22. C3×C7C3×C5×C103semidirect
23. ΓL(1,𝔽8)C3×C5×C103direct (N × H)
25. C3×C5ΓL(1,𝔽8)×C103direct (N × H)
27. C7C32×C5×C103semidirect
28. C5C3×ΓL(1,𝔽8)×C103direct (N × H)
30. C3C5×ΓL(1,𝔽8)×C103direct (N × H)

Maximal subgroups

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

subgroupindex
C5×ΓL(1,𝔽8)×C1033
C3×C5×C7×C1033
C3×ΓL(1,𝔽8)×C1035
C32×C5×C1037
C3×C5×ΓL(1,𝔽8)103