Finite Group Databasebeta

← C5×AGL(1,𝔽7)×C83 #31775239

Subgroups — C5×AGL(1,𝔽7)×C83 #31775239

Order 17430.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×ΓL(1,𝔽8)×C83C211yesmaximal, characteristic, complemented, Hall
2C5×D7×C83C311yesmaximal, characteristic, complemented, Hall
3AGL(1,𝔽7)×C83C511yesmaximal, characteristic, direct product factor, Hall
4C5×C7×C83C2×C311yescharacteristic, complemented, Hall
5C2×C3×C5×C83—71nomaximal, Hall
6ΓL(1,𝔽8)×C83C2×C511yescharacteristic, complemented, Hall
7C3×C5×C83—71noHall
8D7×C83C3×C511yescharacteristic, complemented, Hall
9C2×C5×C83—71noHall
10C7×C83C2×C3×C511yescharacteristic, complemented, Hall
11C2×C3×C83—71noHall
12C5×C83AGL(1,𝔽7)11yescharacteristic, direct product factor, Hall
13C3×C83—71noHall
14C5×AGL(1,𝔽7)C8311yesmaximal, characteristic, direct product factor, Hall
15C2×C83—71noHall
16C5×ΓL(1,𝔽8)C2×C8311yescharacteristic, complemented, Hall
17C83C5×AGL(1,𝔽7)11yescharacteristic, direct product factor, Sylow
18C5×D7C3×C8311yescharacteristic, complemented, Hall
19AGL(1,𝔽7)C5×C8311yescharacteristic, direct product factor, Hall
20C5×C7C2×C3×C8311yescharacteristic, complemented, Hall
21C2×C3×C5—71noHall
22ΓL(1,𝔽8)C2×C5×C8311yescharacteristic, complemented, Hall
23C3×C5—71noHall
24D7C3×C5×C8311yescharacteristic, complemented, Hall
25C2×C5—71noHall
26C7C2×C3×C5×C8311yescharacteristic, complemented, Sylow
27C2×C3—71noHall
28C5AGL(1,𝔽7)×C8311yescharacteristic, direct product factor, Sylow
29C3—71noSylow
30C2—71noSylow
subgroupG/H
center, hypercenterC5×C83AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C5×C83
FrattiniC1G
Fitting, socleC5×C7×C83C2×C3
LCSG ▷ C7
UCSC1 ◁ C5×C83

Complements

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

NH ≅ G/Ntype
1. C5×ΓL(1,𝔽8)×C83C2semidirect
2. C5×D7×C83C3semidirect
3. AGL(1,𝔽7)×C83C5direct (N × H)
4. C5×C7×C83C2×C3semidirect
6. ΓL(1,𝔽8)×C83C2×C5semidirect
8. D7×C83C3×C5semidirect
10. C7×C83C2×C3×C5semidirect
12. C5×C83AGL(1,𝔽7)direct (N × H)
14. C5×AGL(1,𝔽7)C83direct (N × H)
16. C5×ΓL(1,𝔽8)C2×C83semidirect
17. C83C5×AGL(1,𝔽7)direct (N × H)
18. C5×D7C3×C83semidirect
19. AGL(1,𝔽7)C5×C83direct (N × H)
20. C5×C7C2×C3×C83semidirect
22. ΓL(1,𝔽8)C2×C5×C83semidirect
24. D7C3×C5×C83semidirect
26. C7C2×C3×C5×C83semidirect
28. C5AGL(1,𝔽7)×C83direct (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)×C832
C5×D7×C833
AGL(1,𝔽7)×C835
C2×C3×C5×C837
C5×AGL(1,𝔽7)83