Finite Group Databasebeta

← C5×(C3⋊D3)⋊D203 #49141603

Subgroups — C5×(C3⋊D3)⋊D203 #49141603

Order 36540.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×D609C212yesmaximal, complemented
2C5×C7×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3C5×D3×D203—32nomaximal
4C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
5(C3⋊D3)⋊D203C511yesmaximal, characteristic, direct product factor, Hall
6C5×D609D312yescomplemented
7C5×D3×C7×C29—32no—
8C5×D3×C7×C29—61no—
9C3×C5×D203—32no—
10C5×(C3⋊D3)⋊D29—71nomaximal, Hall
11C2×C5×D203—91noHall
12C7×C3⋊D3×C29C2×C511yescharacteristic, complemented
13C3×D609C2×C512yescomplemented
14C3×C5×C7×C29—21no—
15C3×C5×C7×C29C2×D312yescomplemented
16C5×C3⋊D3×C29D711yescharacteristic, complemented
17C3×C5×D87—72no—
18D3×D203—32no—
19C5×D203—32no—
20C2×C5×C7×C29—91no—
21C32×C7×C29C22×C511yescharacteristic, complemented, Hall
22C5×D3×D29—212no—
23C32×C5×C29C2×D711yescharacteristic, complemented, Hall
24C5×(C3⋊D3)⋊D7—291nomaximal, Hall
25D609C5×D312yescomplemented
26D3×C7×C29—32no—
27D3×C7×C29—61no—
28C3×D203—32no—
29(C3⋊D3)⋊D29—71noHall
30C5×C7×C29D3211yescharacteristic, complemented, Hall
31C5×D87—72no—
32C5×D3×C29—32no—
33C5×D3×C29—61no—
34C3×C5×D29—212no—
35C2×D203—91noHall
36C5×C7×C3⋊D3D2911yescharacteristic, complemented
37C3×C5×D21—292no—
38C3×C7×C29—21no—
39C3×C7×C29C2×C5×D312yescomplemented
40C2×C5×D29—631noHall
41C3⋊D3×C29C5×D711yescharacteristic, complemented
42C3×D87—72no—
43C3×C5×C29—21no—
44C3×C5×C29D3×D712yescomplemented
45C5×D3×D7—872no—
46C2×C7×C29—91no—
47D203—32no—
48D3×D29—212no—
49C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
50C2×C5×C29—91no—
51C5×D29—212no—
52C32×C29C2×C5×D711yescharacteristic, complemented, Hall
53(C3⋊D3)⋊D7—291noHall
54C5×D21—292no—
55C5×D3×C7—32no—
56C5×D3×C7—61no—
57C3×C5×D7—872no—
58C7×C29C5×D3211yescharacteristic, complemented, Hall
59C5×D32—2031noHall
60D87—72no—
61C3×D29—212no—
62D3×C29—32no—
63D3×C29—61no—
64C5×C29(C3⋊D3)⋊D711yescharacteristic, complemented, Hall
65C2×C5×D7—2611noHall
66C7×C3⋊D3C5×D2911yescharacteristic, complemented
67C3×D21—292no—
68C2×D29—631noHall
69C3×C5×C7—21no—
70C3×C5×C7D3×D2912yescomplemented
71C5×C3⋊D3D20311yescharacteristic, complemented
72C3×C5×D3—2032no—
73C3×C29—21no—
74C3×C29C5×D3×D712yescomplemented
75D3×D7—872no—
76C2×C5×C7—91no—
77C5×D7—872no—
78C32×C7C2×C5×D2911yescharacteristic, complemented, Hall
79C2×C5×D3—6092no—
80C2×C29—91no—
81D29—212no—
82C32×C5C2×D20311yescharacteristic, complemented, Hall
83D21—292no—
84C3×D7—872no—
85D3×C7—32no—
86D3×C7—61no—
87D32—2031noHall
88C5×C7(C3⋊D3)⋊D2911yescharacteristic, complemented, Hall
89C2×C3×C5—6092no—
90C5×D3—32no—
91C5×D3—61no—
92C5×D3—2032no—
93C29C5×(C3⋊D3)⋊D711yescharacteristic, complemented, Sylow
94C2×D7—2611noHall
95C3×C7—21no—
96C3×C7C5×D3×D2912yescomplemented
97C22×C5—18271noHall
98C3⋊D3C5×D20311yescharacteristic, complemented
99C3×D3—2032no—
100C3×C5—21no—
101C3×C5D3×D20312yescomplemented
102C2×C7—91no—
103D7—872no—
104C2×D3—6092no—
105C2×C5—91no—
106C2×C5—6092no—
107C32C2×C5×D20311yescharacteristic, complemented, Sylow
108C7C5×(C3⋊D3)⋊D2911yescharacteristic, complemented, Sylow
109C2×C3—6092no—
110D3—32no—
111D3—61no—
112D3—2032no—
113C5(C3⋊D3)⋊D20311yescharacteristic, direct product factor, Sylow
114C22—18271noSylow
115C3—21no—
116C3C5×D3×D20312yescomplemented
117C2—91no—
118C2—6092no—
subgroupG/H
center, hypercenterC5(C3⋊D3)⋊D203
commutator, cosocle, hypocenterC32×C7×C29C22×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32×C7×C29
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D609C2semidirect
2. C5×C7×C3⋊D3×C29C2semidirect
4. C32×C5×C7×C29C22semidirect
5. (C3⋊D3)⋊D203C5direct (N × H)
6. C5×D609D3semidirect
12. C7×C3⋊D3×C29C2×C5semidirect
13. C3×D609C2×C5semidirect
15. C3×C5×C7×C29C2×D3semidirect
16. C5×C3⋊D3×C29D7semidirect
21. C32×C7×C29C22×C5semidirect
23. C32×C5×C29C2×D7semidirect
25. D609C5×D3semidirect
30. C5×C7×C29D32semidirect
36. C5×C7×C3⋊D3D29semidirect
39. C3×C7×C29C2×C5×D3semidirect
41. C3⋊D3×C29C5×D7semidirect
44. C3×C5×C29D3×D7semidirect
49. C32×C5×C7C2×D29semidirect
52. C32×C29C2×C5×D7semidirect
58. C7×C29C5×D32semidirect
64. C5×C29(C3⋊D3)⋊D7semidirect
66. C7×C3⋊D3C5×D29semidirect
70. C3×C5×C7D3×D29semidirect
71. C5×C3⋊D3D203semidirect
74. C3×C29C5×D3×D7semidirect
78. C32×C7C2×C5×D29semidirect
82. C32×C5C2×D203semidirect
88. C5×C7(C3⋊D3)⋊D29semidirect
93. C29C5×(C3⋊D3)⋊D7semidirect
96. C3×C7C5×D3×D29semidirect
98. C3⋊D3C5×D203semidirect
101. C3×C5D3×D203semidirect
107. C32C2×C5×D203semidirect
108. C7C5×(C3⋊D3)⋊D29semidirect
113. C5(C3⋊D3)⋊D203direct (N × H)
116. C3C5×D3×D203semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D6092
C5×C7×C3⋊D3×C292
C5×D3×D2033
(C3⋊D3)⋊D2035
C5×(C3⋊D3)⋊D297
C5×(C3⋊D3)⋊D729