Finite Group Databasebeta

← C5×#20259497 #44501289

Subgroups — C5×#20259497 #44501289

Order 30660.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#15690442C211yesmaximal, characteristic
2C5×C7⋊#64408C311yesmaximal, characteristic, complemented, Hall
3C5×#13095276C411yescharacteristic, complemented, Hall
4#20259497C511yesmaximal, characteristic, direct product factor, Hall
5C5×C7×D73C2×C311yescharacteristic
6C5×#64408⋊C3—71nomaximal, Hall
7#15690442C2×C511yescharacteristic
8C5×C7×C73C3×C411yescharacteristic, complemented, Hall
9C5×D73⋊C3—71no—
10C7⋊#64408C3×C511yescharacteristic, complemented, Hall
11#13095276C4×C511yescharacteristic, complemented, Hall
12C5×#64408—71noHall
13C5×C73⋊C3—71noHall
14C7×D73C2×C3×C511yescharacteristic
15#64408⋊C3—71noHall
16C5×D73AGL(1,𝔽7)11yescharacteristic
17C7×C73C3×C4×C511yescharacteristic, complemented, Hall
18D73⋊C3—71no—
19C5×ΓL(1,𝔽8)⋊C4—731nomaximal, Hall
20C5×C73ΓL(1,𝔽8)⋊C411yescharacteristic, complemented, Hall
21#64408—71noHall
22C73⋊C3—71noHall
23C2×C5×ΓL(1,𝔽8)—731no—
24D73C5×AGL(1,𝔽7)11yescharacteristic
25C5×Dic7—731noHall
26C5×ΓL(1,𝔽8)—731noHall
27ΓL(1,𝔽8)⋊C4—731noHall
28C73C5×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented, Sylow
29C2×C5×C7—731no—
30C3×C4×C5—5111noHall
31C2×ΓL(1,𝔽8)—731no—
32C5×C7#64408⋊C311yescharacteristic, complemented, Hall
33C2×C3×C5—5111no—
34Dic7—731noHall
35ΓL(1,𝔽8)—731noHall
36C4×C5—5111noHall
37C3×C5—5111noHall
38C2×C7—731no—
39C3×C4—5111noHall
40C2×C5—731no—
41C7C5×#64408⋊C311yescharacteristic, complemented, Sylow
42C2×C3—5111no—
43C5#2025949711yescharacteristic, direct product factor, Sylow
44C4—5111noSylow
45C3—5111noSylow
46C2—731no—
subgroupG/H
center, hypercenterC5#20259497
commutator, hypocenterC7×C73C3×C4×C5
FrattiniC1G
Fitting, socleC5×C7×C73C3×C4
prime radicalC5×#15690442C2
cosocleC7×D73C2×C3×C5
LCSG ▷ C7×C73
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
2. C5×C7⋊#64408C3semidirect
3. C5×#13095276C4semidirect
4. #20259497C5direct (N × H)
8. C5×C7×C73C3×C4semidirect
10. C7⋊#64408C3×C5semidirect
11. #13095276C4×C5semidirect
17. C7×C73C3×C4×C5semidirect
20. C5×C73ΓL(1,𝔽8)⋊C4semidirect
28. C73C5×ΓL(1,𝔽8)⋊C4semidirect
32. C5×C7#64408⋊C3semidirect
41. C7C5×#64408⋊C3semidirect
43. C5#20259497direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#156904422
C5×C7⋊#644083
#202594975
C5×#64408⋊C37
C5×ΓL(1,𝔽8)⋊C473