Finite Group Databasebeta

← C5×C3⋊#14523129 #44477828

Subgroups — C5×C3⋊#14523129 #44477828

Order 30420.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#92789C211yesmaximal, characteristic
2C5×C3⋊#10621725C311yesmaximal, characteristic, complemented
3C5×#14523129—31nomaximal
4C3×C5×#92789C411yescharacteristic, complemented, Hall
5C3⋊#14523129C511yesmaximal, characteristic, direct product factor, Hall
6C2×C5×#92789—21no—
7C2×C5×#92789D311yescharacteristic
8C2×C3×C5×C132C2×C311yescharacteristic
9C5×#10621725—31noHall
10C2×C3×#92789C2×C511yescharacteristic
11C5×#92789—21no—
12C5×#92789Dic311yescharacteristic, complemented
13C3×C5×C132C3×C411yescharacteristic, complemented
14C5×C3⋊(Dic13⋊C3)—132nomaximal
15C3⋊#10621725C3×C511yescharacteristic, complemented
16#14523129—31no—
17C2×C5×C132C3×D311yescharacteristic
18C3×#92789C4×C511yescharacteristic, complemented, Hall
19C2×C3×C5×C13⋊C3—132no—
20C2×C3×C132C2×C3×C511yescharacteristic
21C2×#92789—21no—
22C2×#92789C5×D311yescharacteristic
23C5×C132C3×Dic311yescharacteristic, complemented, Hall
24C5×Dic39—132no—
25C5×Dic39—394no—
26C5×Dic13⋊C3—392no—
27#10621725—31noHall
28C3×C5×C13⋊C3—132no—
29C3×C132C3×C4×C511yescharacteristic, complemented
30#92789—21no—
31#92789C5×Dic311yescharacteristic, complemented
32C3⋊(Dic13⋊C3)—132no—
33C2×C3×C5×C13—34no—
34C2×C3×C5×C13D13⋊C312yes—
35C2×C5×C13⋊C3—132no—
36C2×C5×C13⋊C3—262no—
37C2×C132C3×C5×D311yescharacteristic
38C5×Dic13—392no—
39C5×Dic13—1174no—
40C2×C3×C13⋊C3—132no—
41C3×C5×C13—34no—
42C3×C5×C13Dic13⋊C312yescomplemented
43C5×C13⋊C3—132no—
44C5×C13⋊C3—262no—
45C3×C5×Dic3—1691noHall
46C132C3×C5×Dic311yescharacteristic, complemented, Sylow
47Dic39—132no—
48Dic39—394no—
49Dic13⋊C3—392no—
50C2×C5×C13—34no—
51C2×C5×C13C3⋊(D13⋊C3)12yes—
52C3×C13⋊C3—132no—
53C2×C32×C5—1691no—
54C2×C3×C13—34no—
55C2×C3×C13C5×D13⋊C312yes—
56C2×C13⋊C3—132no—
57C2×C13⋊C3—262no—
58C5×C13—34no—
59C5×C13C3⋊(Dic13⋊C3)12yescomplemented
60C3×C4×C5—5071no—
61C5×Dic3—1691no—
62Dic13—392no—
63Dic13—1174no—
64C32×C5—1691noHall
65C3×C13—34no—
66C3×C13C5×Dic13⋊C312yescomplemented
67C13⋊C3—132no—
68C13⋊C3—262no—
69C3×Dic3—1691noHall
70C2×C3×C5—3381no—
71C2×C3×C5—1691no—
72C2×C3×C5#1175981611yescharacteristic
73C2×C13—34no—
74C2×C13C5×C3⋊(D13⋊C3)12yes—
75C4×C5—5071noHall
76C2×C32—1691no—
77C3×C5—3381no—
78C3×C5—1691no—
79C3×C5#1452312911yescharacteristic, complemented
80C13—34no—
81C13C5×C3⋊(Dic13⋊C3)12yescomplemented
82C3×C4—5071no—
83Dic3—1691no—
84C2×C5C3⋊#1175981611yescharacteristic
85C32—1691noSylow
86C2×C3—3381no—
87C2×C3—1691no—
88C2×C3C5×#1175981611yescharacteristic
89C5C3⋊#1452312911yescharacteristic, direct product factor, Sylow
90C4—5071noSylow
91C3—3381no—
92C3—1691no—
93C3C5×#1452312911yescharacteristic, complemented
94C2C5×C3⋊#1175981611yescharacteristic
subgroupG/H
center, hypercenterC2×C5C3⋊#11759816
commutator, hypocenterC3×C132C3×C4×C5
FrattiniC2C5×C3⋊#11759816
Fitting, socleC2×C3×C5×C132C2×C3
prime radicalC2×C3×C5×#92789C2
cosocleC2×C3×C132C2×C3×C5
LCSG ▷ C3×C132
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
2. C5×C3⋊#10621725C3semidirect
4. C3×C5×#92789C4semidirect
5. C3⋊#14523129C5direct (N × H)
12. C5×#92789Dic3semidirect
13. C3×C5×C132C3×C4semidirect
15. C3⋊#10621725C3×C5semidirect
18. C3×#92789C4×C5semidirect
23. C5×C132C3×Dic3semidirect
29. C3×C132C3×C4×C5semidirect
31. #92789C5×Dic3semidirect
42. C3×C5×C13Dic13⋊C3semidirect
46. C132C3×C5×Dic3semidirect
59. C5×C13C3⋊(Dic13⋊C3)semidirect
66. C3×C13C5×Dic13⋊C3semidirect
79. C3×C5#14523129semidirect
81. C13C5×C3⋊(Dic13⋊C3)semidirect
89. C5C3⋊#14523129direct (N × H)
93. C3C5×#14523129semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#927892
C5×C3⋊#106217253
C5×#145231293
C3⋊#145231295
C5×C3⋊(Dic13⋊C3)13