Finite Group Databasebeta

← C29×D152 #39908170

Subgroups — C29×D152 #39908170

Order 26100.

224 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 52 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×C29×D15C212yesmaximal, complemented
2C29×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
3D5×C29×D15—32nomaximal
4C32×C52×C29C2211yescharacteristic, complemented, Hall
5D3×C29×D15—52nomaximal
6C29×C3⋊(C5⋊D5)—32no—
7C29×C3⋊(C5⋊D5)—61no—
8C5×C29×D15D312yescomplemented
9C3×C5×D5×C29—32no—
10D52×C29—91noHall
11C29×C3⋊D15—52no—
12C29×C3⋊D15—102no—
13C3×C29×D15D512yescomplemented
14C3×C5×D3×C29—52no—
15C3×C52×C29—21no—
16C3×C52×C29C2×D312yescomplemented
17C2×C29×D15—152no—
18D3×D5×C29—152no—
19C29×C5⋊D5—91no—
20C5×D5×C29—32no—
21C32×C5×C29—22no—
22C32×C5×C29C2×D512yescomplemented
23D32×C29—251noHall
24D152C2911yesmaximal, characteristic, direct product factor, Hall
25C2×C3×C5×C29—152no—
26C29×D15—152no—
27C29×D15—152no—
28C29×D15—302no—
29C29×D15—304no—
30C29×D15—304no—
31C29×D15D1512yesdirect product factor
32C5×D3×C29—52no—
33C3×D5×C29—32no—
34C52×C29D3211yescharacteristic, complemented, Hall
35C2×D5×C29—452no—
36C3⋊D3×C29—251no—
37C3×D3×C29—52no—
38C3⋊(C3⋊(C5⋊D5))C2×C2911yescharacteristic, complemented
39C3×C5×D15C2×C2912yescomplemented
40C3×C5×C29—24no—
41C3×C5×C29—24no—
42C3×C5×C29—22no—
43C3×C5×C29D3×D512yescomplemented
44C3×C5×C29C2×D1512yescomplemented
45C2×D3×C29—752no—
46D5×D15—32no—
47C2×C5×C29—152no—
48D5×C29—32no—
49D5×C29—452no—
50D5×C29—902no—
51C32×C29D5211yescharacteristic, complemented, Hall
52C32×C52C22×C2911yescharacteristic, complemented, Hall
53D3×D15—52no—
54C2×C3×C29—152no—
55D3×C29—52no—
56D3×C29—752no—
57D3×C29—1501no—
58C3⋊(C5⋊D5)—32no—
59C3⋊(C5⋊D5)—61no—
60C5×D15D3×C2912yescomplemented
61C3×C5×D5—32no—
62C5×C29—22no—
63C5×C29D3×D1512yescomplemented
64C22×C29—2251noHall
65D52—91noHall
66C3⋊D15—52no—
67C3⋊D15—102no—
68C3×D15D5×C2912yescomplemented
69C3×C5×D3—52no—
70C3×C29—21no—
71C3×C29D5×D1512yescomplemented
72C3×C52—21no—
73C3×C52C2×D3×C2912yescomplemented
74C2×D15—152no—
75D3×D5—152no—
76C2×C29—152no—
77C2×C29—2251no—
78C5⋊D5—91no—
79C5×D5—32no—
80C32×C5—22no—
81C32×C5C2×D5×C2912yescomplemented
82D32—251noHall
83C2×C3×C5—152no—
84D15—152no—
85D15—152no—
86D15—304no—
87D15—302no—
88D15—304no—
89D15C29×D1512yesdirect product factor
90C3×D5—32no—
91C5×D3—52no—
92C29D15211yescharacteristic, direct product factor, Sylow
93C52D32×C2911yescharacteristic, complemented, Sylow
94C2×D5—452no—
95C3⋊D3—251no—
96C3×D3—52no—
97C3×C5—24no—
98C3×C5—22no—
99C3×C5—24no—
100C3×C5D3×D5×C2912yescomplemented
101C3×C5C2×C29×D1512yescomplemented
102C2×D3—752no—
103C2×C5—152no—
104D5—32no—
105D5—452no—
106D5—902no—
107C32D52×C2911yescharacteristic, complemented, Sylow
108C2×C3—152no—
109D3—52no—
110D3—752no—
111D3—1501no—
112C5—22no—
113C5D3×C29×D1512yescomplemented
114C22—2251noSylow
115C3—21no—
116C3D5×C29×D1512yescomplemented
117C2—152no—
118C2—2251no—
subgroupG/H
center, hypercenterC29D152
commutator, cosocle, hypocenterC32×C52C22×C29
FrattiniC1G
Fitting, socleC32×C52×C29C22
LCSG ▷ C32×C52
UCSC1 ◁ C29

Complements

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

NH ≅ G/Ntype
1. C3×C5×C29×D15C2semidirect
2. C29×C3⋊(C3⋊(C5⋊D5))C2semidirect
4. C32×C52×C29C22semidirect
8. C5×C29×D15D3semidirect
13. C3×C29×D15D5semidirect
16. C3×C52×C29C2×D3semidirect
22. C32×C5×C29C2×D5semidirect
24. D152C29direct (N × H)
31. C29×D15D15direct (N × H)
34. C52×C29D32semidirect
38. C3⋊(C3⋊(C5⋊D5))C2×C29semidirect
39. C3×C5×D15C2×C29semidirect
43. C3×C5×C29D3×D5semidirect
44. C3×C5×C29C2×D15semidirect
51. C32×C29D52semidirect
52. C32×C52C22×C29semidirect
60. C5×D15D3×C29semidirect
63. C5×C29D3×D15semidirect
68. C3×D15D5×C29semidirect
71. C3×C29D5×D15semidirect
73. C3×C52C2×D3×C29semidirect
81. C32×C5C2×D5×C29semidirect
89. D15C29×D15direct (N × H)
92. C29D152direct (N × H)
93. C52D32×C29semidirect
100. C3×C5D3×D5×C29semidirect
101. C3×C5C2×C29×D15semidirect
107. C32D52×C29semidirect
113. C5D3×C29×D15semidirect
116. C3D5×C29×D15semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C29×D152
C29×C3⋊(C3⋊(C5⋊D5))2
D5×C29×D153
D3×C29×D155
D15229