Finite Group Databasebeta

← C7×#63122⋊C9 #30655012

Subgroups — C7×#63122⋊C9 #30655012

Order 16380.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C5⋊(D13⋊C9)C211yesmaximal, characteristic
2C3×C7×#63122C311yesmaximal, characteristic
3C5×C7×C13⋊C9C411yescharacteristic, complemented, Hall
4C7×#261⋊C9—51nomaximal, Hall
5C3×C7×D65C2×C311yescharacteristic
6#63122⋊C9C711yesmaximal, characteristic, direct product factor, Hall
7C7×#63122C911yescharacteristic, complemented, Hall
8C7×D13⋊C9—51no—
9C3×C5×C7×C13C3×C411yescharacteristic
10C7×C9×AGL(1,𝔽5)—131nomaximal, Hall
11C5⋊(D13⋊C9)C2×C711yescharacteristic
12C3×C7×#261—51no—
13C7×D65C2×C911yescharacteristic
14C7×C13⋊C9AGL(1,𝔽5)11yescharacteristic, complemented, Hall
15C3×#63122C3×C711yescharacteristic
16C7×C9×D5—131no—
17C5×C13⋊C9C4×C711yescharacteristic, complemented, Hall
18C3×C7×D13—51no—
19#261⋊C9—51noHall
20C5×C7×C13C4×C911yescharacteristic, complemented, Hall
21C3×C7×AGL(1,𝔽5)—391no—
22C3×D65C2×C3×C711yescharacteristic
23C7×#261—51noHall
24C5×C7×C9—131noHall
25C3×C7×C13C3×AGL(1,𝔽5)11yescharacteristic
26#63122C7×C911yescharacteristic, complemented, Hall
27C4×C7×C9—651noHall
28D13⋊C9—51no—
29C3×C7×D5—391no—
30C3×C5×C13C3×C4×C711yescharacteristic
31C7×D13—51no—
32C9×AGL(1,𝔽5)—131noHall
33C3×#261—51no—
34C7×AGL(1,𝔽5)—391noHall
35D65C2×C7×C911yescharacteristic
36C2×C7×C9—651no—
37C13⋊C9C7×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
38C3×C5×C7AGL(1,𝔽13)11yescharacteristic
39C7×C13C9×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
40C9×D5—131no—
41C3×C4×C7—1951no—
42C3×D13—51no—
43C7×D5—391no—
44C5×C13C4×C7×C911yescharacteristic, complemented, Hall
45C7×C9—131noHall
46C3×AGL(1,𝔽5)—391no—
47#261—51noHall
48C5×C9—131noHall
49C2×C3×C7—1951no—
50C3×C13C3×C7×AGL(1,𝔽5)11yescharacteristic
51C4×C9—651noHall
52C5×C7#261⋊C911yescharacteristic, complemented, Hall
53C3×D5—391no—
54C4×C7—1951noHall
55D13—51no—
56C3×C7#63122⋊C311yescharacteristic
57AGL(1,𝔽5)—391noHall
58C2×C9—651no—
59C3×C5C7×AGL(1,𝔽13)11yescharacteristic
60C2×C7—1951no—
61C13C7×C9×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
62C3×C4—1951no—
63D5—391no—
64C9—131noSylow
65C7#63122⋊C911yescharacteristic, direct product factor, Sylow
66C2×C3—1951no—
67C5C7×#261⋊C911yescharacteristic, complemented, Sylow
68C4—1951noSylow
69C3C7×#63122⋊C311yescharacteristic
70C2—1951no—
subgroupG/H
center, hypercenterC3×C7#63122⋊C3
commutator, hypocenterC5×C13C4×C7×C9
FrattiniC3C7×#63122⋊C3
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C7×D65C2×C3
cosocleC3×D65C2×C3×C7
LCSG ▷ C5×C13
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
3. C5×C7×C13⋊C9C4semidirect
6. #63122⋊C9C7direct (N × H)
7. C7×#63122C9semidirect
14. C7×C13⋊C9AGL(1,𝔽5)semidirect
17. C5×C13⋊C9C4×C7semidirect
20. C5×C7×C13C4×C9semidirect
26. #63122C7×C9semidirect
37. C13⋊C9C7×AGL(1,𝔽5)semidirect
39. C7×C13C9×AGL(1,𝔽5)semidirect
44. C5×C13C4×C7×C9semidirect
52. C5×C7#261⋊C9semidirect
61. C13C7×C9×AGL(1,𝔽5)semidirect
65. C7#63122⋊C9direct (N × H)
67. C5C7×#261⋊C9semidirect

Maximal subgroups

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

subgroupindex
C7×C5⋊(D13⋊C9)2
C3×C7×#631223
C7×#261⋊C95
#63122⋊C97
C7×C9×AGL(1,𝔽5)13