Finite Group Databasebeta

← D3×C29×C3⋊(C5⋊D5) #39908177

Subgroups — D3×C29×C3⋊(C5⋊D5) #39908177

Order 26100.

352 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 104 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×C52×D3×C29C211yesmaximal, characteristic, complemented
2C3×C29×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C29×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
4C2×C29×C3⋊(C5⋊D5)—31nomaximal
5D3×C29×C5⋊D5—31nomaximal
6C32×C52×C29C2211yescharacteristic, complemented, Hall
7D3×C29×D15—56nomaximal
8C29×C3⋊(C5⋊D5)—31no—
9C29×C3⋊(C5⋊D5)—31no—
10C29×C3⋊(C5⋊D5)—61no—
11C29×C3⋊(C5⋊D5)D311yescharacteristic, direct product factor
12C52×D3×C29D311yescharacteristic, complemented
13C3×C29×C5⋊D5—31no—
14C2×C3×C52×C29—31no—
15C2×C29×C5⋊D5—91noHall
16C29×C3⋊D15—56no—
17C3×C29×D15—56no—
18C3×C5×D3×C29D516yescomplemented
19C3×C52×C29—21no—
20C3×C52×C29C2×D311yescharacteristic, complemented
21C3×C52×C29C2×D311yescharacteristic, complemented
22C2×C29×D15—156no—
23D3×D5×C29—156no—
24C2×C52×C29—31no—
25C29×C5⋊D5—31no—
26C29×C5⋊D5—91no—
27C32×C5×C29C2×D516yescomplemented
28D32×C29—251noHall
29D3×C3⋊(C5⋊D5)C2911yesmaximal, characteristic, direct product factor, Hall
30C2×C3×C5×C29—36no—
31C29×D15—56no—
32C29×D15—156no—
33C29×D15—156no—
34C29×D15—306no—
35C5×D3×C29D1516yescomplemented
36C3×D5×C29—156no—
37C52×C29D3211yescharacteristic, complemented, Hall
38C2×D5×C29—456no—
39C3⋊D3×C29—251no—
40C3×D3×C29—251no—
41C3×D3×C29C5⋊D511yescharacteristic, complemented
42C3⋊(C3⋊(C5⋊D5))C2×C2911yescharacteristic, complemented
43C3×C3⋊(C5⋊D5)C2×C2911yescharacteristic, complemented
44C3×C52×D3C2×C2911yescharacteristic, complemented
45C3×C5×C29—26no—
46C3×C5×C29D3×D516yescomplemented
47C3×C5×C29C2×D1516yescomplemented
48C2×D3×C29—751no—
49C2×D3×C29—751no—
50C2×C3⋊(C5⋊D5)—31no—
51D3×C5⋊D5—31no—
52C2×C5×C29—36no—
53D5×C29—156no—
54D5×C29—456no—
55C32×C29C2×C5⋊D511yescharacteristic, complemented, Hall
56C32×C52C22×C2911yescharacteristic, complemented, Hall
57D3×D15—56no—
58C2×C3×C29—31no—
59C2×C3×C29—751no—
60D3×C29—251no—
61D3×C29—751no—
62D3×C29—751no—
63D3×C29—1501no—
64D3×C29C3⋊(C5⋊D5)11yescharacteristic, direct product factor
65C2×C3×C52—31no—
66C3⋊(C5⋊D5)—31no—
67C3⋊(C5⋊D5)—31no—
68C3⋊(C5⋊D5)—61no—
69C3⋊(C5⋊D5)D3×C2911yescharacteristic, direct product factor
70C52×D3D3×C2911yescharacteristic, complemented
71C3×C5⋊D5—31no—
72C5×C29D3×D1516yescomplemented
73C22×C29—2251noHall
74C2×C5⋊D5—91noHall
75C3⋊D15—56no—
76C3×D15—56no—
77C3×C5×D3D5×C2916yescomplemented
78C3×C29—21no—
79C3×C29D3×C5⋊D511yescharacteristic, complemented
80C3×C29C2×C3⋊(C5⋊D5)11yescharacteristic, complemented
81C3×C52—21no—
82C3×C52C2×D3×C2911yescharacteristic, complemented
83C3×C52C2×D3×C2911yescharacteristic, complemented
84C2×D15—156no—
85D3×D5—156no—
86C2×C29—31no—
87C2×C29—751no—
88C2×C29—2251no—
89C2×C52—31no—
90C5⋊D5—31no—
91C5⋊D5—91no—
92C32×C5C2×D5×C2916yescomplemented
93D32—251noHall
94C2×C3×C5—36no—
95D15—56no—
96D15—156no—
97D15—156no—
98D15—306no—
99C3×D5—156no—
100C5×D3C29×D1516yescomplemented
101C29D3×C3⋊(C5⋊D5)11yescharacteristic, direct product factor, Sylow
102C52D32×C2911yescharacteristic, complemented, Sylow
103C2×D5—456no—
104C3⋊D3—251no—
105C3×D3—251no—
106C3×D3C29×C5⋊D511yescharacteristic, complemented
107C3×C5—26no—
108C3×C5D3×D5×C2916yescomplemented
109C3×C5C2×C29×D1516yescomplemented
110C2×D3—751no—
111C2×D3—751no—
112C2×C5—36no—
113D5—156no—
114D5—456no—
115C32C2×C29×C5⋊D511yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—751no—
118D3—251no—
119D3—751no—
120D3—751no—
121D3—1501no—
122D3C29×C3⋊(C5⋊D5)11yescharacteristic, direct product factor
123C5D3×C29×D1516yescomplemented
124C22—2251noSylow
125C3—21no—
126C3D3×C29×C5⋊D511yescharacteristic, complemented
127C3C2×C29×C3⋊(C5⋊D5)11yescharacteristic, complemented
128C2—31no—
129C2—751no—
130C2—2251no—
subgroupG/H
center, hypercenterC29D3×C3⋊(C5⋊D5)
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×C52×D3×C29C2semidirect
2. C3×C29×C3⋊(C5⋊D5)C2semidirect
3. C29×C3⋊(C3⋊(C5⋊D5))C2semidirect
6. C32×C52×C29C22semidirect
11. C29×C3⋊(C5⋊D5)D3direct (N × H)
12. C52×D3×C29D3semidirect
18. C3×C5×D3×C29D5semidirect
20. C3×C52×C29C2×D3semidirect
21. C3×C52×C29C2×D3semidirect
27. C32×C5×C29C2×D5semidirect
29. D3×C3⋊(C5⋊D5)C29direct (N × H)
35. C5×D3×C29D15semidirect
37. C52×C29D32semidirect
41. C3×D3×C29C5⋊D5semidirect
42. C3⋊(C3⋊(C5⋊D5))C2×C29semidirect
43. C3×C3⋊(C5⋊D5)C2×C29semidirect
44. C3×C52×D3C2×C29semidirect
46. C3×C5×C29D3×D5semidirect
47. C3×C5×C29C2×D15semidirect
55. C32×C29C2×C5⋊D5semidirect
56. C32×C52C22×C29semidirect
64. D3×C29C3⋊(C5⋊D5)direct (N × H)
69. C3⋊(C5⋊D5)D3×C29direct (N × H)
70. C52×D3D3×C29semidirect
72. C5×C29D3×D15semidirect
77. C3×C5×D3D5×C29semidirect
79. C3×C29D3×C5⋊D5semidirect
80. C3×C29C2×C3⋊(C5⋊D5)semidirect
82. C3×C52C2×D3×C29semidirect
83. C3×C52C2×D3×C29semidirect
92. C32×C5C2×D5×C29semidirect
100. C5×D3C29×D15semidirect
101. C29D3×C3⋊(C5⋊D5)direct (N × H)
102. C52D32×C29semidirect
106. C3×D3C29×C5⋊D5semidirect
108. C3×C5D3×D5×C29semidirect
109. C3×C5C2×C29×D15semidirect
115. C32C2×C29×C5⋊D5semidirect
122. D3C29×C3⋊(C5⋊D5)direct (N × H)
123. C5D3×C29×D15semidirect
126. C3D3×C29×C5⋊D5semidirect
127. C3C2×C29×C3⋊(C5⋊D5)semidirect

Maximal subgroups

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

subgroupindex
C3×C52×D3×C292
C3×C29×C3⋊(C5⋊D5)2
C29×C3⋊(C3⋊(C5⋊D5))2
C2×C29×C3⋊(C5⋊D5)3
D3×C29×C5⋊D53
D3×C29×D155
D3×C3⋊(C5⋊D5)29