Finite Group Databasebeta

← C3×D87⋊(C5⋊D5) #39908152

Subgroups — C3×D87⋊(C5⋊D5) #39908152

Order 26100.

352 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C32×C5⋊D145C211yesmaximal, characteristic, complemented
2C3×C52×D87C211yesmaximal, characteristic, complemented
3C3×C29×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
4D87⋊(C5⋊D5)C311yesmaximal, characteristic, direct product factor
5C3×C5⋊D5×D29—31nomaximal
6C32×C52×C29C2211yescharacteristic, complemented, Hall
7C3×D15⋊D29—56nomaximal
8C29×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
9C52×D87C2×C311yescharacteristic, complemented
10C3×C5⋊D145—21no—
11C3×C5⋊D145D311yescharacteristic, complemented
12C3×C5⋊D145C2×C311yescharacteristic, complemented
13C3×C29×C5⋊D5—31no—
14C3×C52×D29—31no—
15C5⋊D5×D29—31noHall
16C3×C29×D15—56no—
17C3×C5×D87D516yescomplemented
18C32×D145—56no—
19C3×C52×C29—21no—
20C3×C52×C29C2×D311yescharacteristic, complemented
21C3×C52×C29C22×C311yescharacteristic, complemented
22D15⋊D29—56no—
23C3×D5×D29—156no—
24C5⋊D145C3×D311yescharacteristic, complemented
25C29×C5⋊D5—31no—
26C52×D29—31no—
27C32×C5×C29C2×D516yescomplemented
28C3×D3×D29—251noHall
29C3×D3×C5⋊D5—291nomaximal, Hall
30C29×D15—56no—
31C5×D87C3×D516yescomplemented
32C3×D145—56no—
33C3×D145—56no—
34C3×D145—106no—
35C3×D5×C29—156no—
36C3×C5×D29—36no—
37C52×C29C2×C3×D311yescharacteristic, complemented, Hall
38D5×D29—156no—
39C3×D87C5⋊D511yescharacteristic, complemented
40C3×D3×C29—251no—
41C32×D29—251no—
42C3×C3⋊(C5⋊D5)D2911yescharacteristic, complemented
43C3×C52×D3—291no—
44C32×C5⋊D5—291no—
45C3×C5×C29—26no—
46C3×C5×C29D3×D516yescomplemented
47C3×C5×C29C2×C3×D516yescomplemented
48C2×C3×D29—751no—
49D3×D29—251no—
50C2×C3×C5⋊D5—871no—
51D3×C5⋊D5—291no—
52D145—56no—
53C5×D29—36no—
54D5×C29—156no—
55C32×C29C2×C5⋊D511yescharacteristic, complemented, Hall
56C32×C52C2×D2911yescharacteristic, complemented, Hall
57C3×D3×D5—1456no—
58C2×C3×C29—751no—
59D87C3×C5⋊D511yescharacteristic, complemented
60C3×D29—31no—
61C3×D29—251no—
62C3×D29—251no—
63C3×D29—501no—
64D3×C29—251no—
65C2×C3×C52—871no—
66C3⋊(C5⋊D5)C3×D2911yescharacteristic, complemented
67C52×D3—291no—
68C3×C5⋊D5—31no—
69C3×C5⋊D5—291no—
70C3×C5⋊D5—291no—
71C3×C5⋊D5—581no—
72C5×C29C3×D3×D516yescomplemented
73C2×D29—751noHall
74C2×C5⋊D5—871noHall
75C3×D15—56no—
76C3×C5×D3—296no—
77C32×D5—1456no—
78C3×C29—21no—
79C3×C29D3×C5⋊D511yescharacteristic, complemented
80C3×C29C2×C3×C5⋊D511yescharacteristic, complemented
81C3×C52—21no—
82C3×C52D3×D2911yescharacteristic, complemented
83C3×C52C2×C3×D2911yescharacteristic, complemented
84C2×C3×D5—4356no—
85D3×D5—1456no—
86C2×C29—751no—
87D29—31no—
88D29—251no—
89C2×C52—871no—
90C5⋊D5—31no—
91C5⋊D5—291no—
92C32×C5D5×D2916yescomplemented
93C2×C3×D3—7251noHall
94C2×C3×C5—876no—
95D15—56no—
96C3×D5—156no—
97C3×D5—2906no—
98C3×D5—1456no—
99C3×D5—1456no—
100C5×D3—296no—
101C29C3×D3×C5⋊D511yescharacteristic, complemented, Sylow
102C52C3×D3×D2911yescharacteristic, complemented, Sylow
103C2×D5—4356no—
104C2×C32—7251no—
105C3×D3—251no—
106C3×D3—291no—
107C3×C5—26no—
108C3×C5C3×D5×D2916yescomplemented
109C3×C5D15⋊D2916yescomplemented
110C22×C3—21751no—
111C2×D3—7251no—
112C2×C5—876no—
113D5—156no—
114D5—1456no—
115C32C5⋊D5×D2911yescharacteristic, complemented, Sylow
116C2×C3—751no—
117C2×C3—871no—
118C2×C3—14501no—
119C2×C3—7251no—
120C2×C3—7251no—
121D3—251no—
122D3—291no—
123C5C3×D15⋊D2916yescomplemented
124C22—21751noSylow
125C3—21no—
126C3C3×C5⋊D5×D2911yescharacteristic, complemented
127C3D87⋊(C5⋊D5)11yescharacteristic, direct product factor
128C2—751no—
129C2—871no—
130C2—7251no—
subgroupG/H
center, hypercenterC3D87⋊(C5⋊D5)
commutator, cosocle, hypocenterC3×C52×C29C22×C3
FrattiniC1G
Fitting, socleC32×C52×C29C22
LCSG ▷ C3×C52×C29
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C5⋊D145C2semidirect
2. C3×C52×D87C2semidirect
3. C3×C29×C3⋊(C5⋊D5)C2semidirect
4. D87⋊(C5⋊D5)C3direct (N × H)
6. C32×C52×C29C22semidirect
8. C29×C3⋊(C5⋊D5)C2×C3semidirect
9. C52×D87C2×C3semidirect
11. C3×C5⋊D145D3semidirect
12. C3×C5⋊D145C2×C3semidirect
17. C3×C5×D87D5semidirect
20. C3×C52×C29C2×D3semidirect
21. C3×C52×C29C22×C3semidirect
24. C5⋊D145C3×D3semidirect
27. C32×C5×C29C2×D5semidirect
31. C5×D87C3×D5semidirect
37. C52×C29C2×C3×D3semidirect
39. C3×D87C5⋊D5semidirect
42. C3×C3⋊(C5⋊D5)D29semidirect
46. C3×C5×C29D3×D5semidirect
47. C3×C5×C29C2×C3×D5semidirect
55. C32×C29C2×C5⋊D5semidirect
56. C32×C52C2×D29semidirect
59. D87C3×C5⋊D5semidirect
66. C3⋊(C5⋊D5)C3×D29semidirect
72. C5×C29C3×D3×D5semidirect
79. C3×C29D3×C5⋊D5semidirect
80. C3×C29C2×C3×C5⋊D5semidirect
82. C3×C52D3×D29semidirect
83. C3×C52C2×C3×D29semidirect
92. C32×C5D5×D29semidirect
101. C29C3×D3×C5⋊D5semidirect
102. C52C3×D3×D29semidirect
108. C3×C5C3×D5×D29semidirect
109. C3×C5D15⋊D29semidirect
115. C32C5⋊D5×D29semidirect
123. C5C3×D15⋊D29semidirect
126. C3C3×C5⋊D5×D29semidirect
127. C3D87⋊(C5⋊D5)direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5⋊D1452
C3×C52×D872
C3×C29×C3⋊(C5⋊D5)2
D87⋊(C5⋊D5)3
C3×C5⋊D5×D293
C3×D15⋊D295
C3×D3×C5⋊D529