Finite Group Databasebeta

← C3⋊(C5⋊D5)×D87 #39908180

Subgroups — C3⋊(C5⋊D5)×D87 #39908180

Order 26100.

352 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 86 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×D87C211yesmaximal, characteristic, complemented
2C3×C29×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C5⋊D145))C211yesmaximal, characteristic, complemented
4C5⋊D5×D87—31nomaximal
5D29×C3⋊(C5⋊D5)—31nomaximal
6C32×C52×C29C2211yescharacteristic, complemented, Hall
7D15×D87—56nomaximal
8C3⋊(C5⋊D145)—31no—
9C3⋊(C5⋊D145)—31no—
10C3⋊(C5⋊D145)—61no—
11C29×C3⋊(C5⋊D5)D311yescharacteristic, complemented
12C52×D87D311yescharacteristic, complemented
13C3×C29×C5⋊D5—31no—
14C3×C52×D29—31no—
15C5⋊D5×D29—91noHall
16C3⋊D435—56no—
17C3×C29×D15—56no—
18C3×C5×D87D516yescomplemented
19C3×C52×C29—21no—
20C3×C52×C29C2×D311yescharacteristic, complemented
21C3×C52×C29C2×D311yescharacteristic, complemented
22D5×D87—156no—
23D15×D29—156no—
24C5⋊D145—91no—
25C29×C5⋊D5—31no—
26C52×D29—31no—
27C32×C5×C29C2×D516yescomplemented
28D3×D87—251noHall
29D3×C3⋊(C5⋊D5)—291nomaximal, Hall
30D435—156no—
31D435—156no—
32D435—306no—
33C29×D15—56no—
34C5×D87D1516yescomplemented
35C3×D5×C29—156no—
36C3×C5×D29—36no—
37C52×C29D3211yescharacteristic, complemented, Hall
38D5×D29—456no—
39C3⋊D87—251no—
40C3×D87C5⋊D511yescharacteristic, complemented
41C3×D3×C29—251no—
42C3⋊(C3⋊(C5⋊D5))—291no—
43C3×C3⋊(C5⋊D5)D2911yescharacteristic, complemented
44C3×C52×D3—291no—
45C3×C5×C29—26no—
46C3×C5×C29D3×D516yescomplemented
47C3×C5×C29C2×D1516yescomplemented
48C2×D87—751no—
49D3×D29—751no—
50C2×C3⋊(C5⋊D5)—871no—
51D3×C5⋊D5—871no—
52D145—456no—
53C5×D29—36no—
54D5×C29—156no—
55C32×C29C2×C5⋊D511yescharacteristic, complemented, Hall
56C32×C52C2×D2911yescharacteristic, complemented, Hall
57D3×D15—1456no—
58C2×C3×C29—751no—
59D87—751no—
60D87—751no—
61D87—1501no—
62D87C3⋊(C5⋊D5)11yescharacteristic, direct product factor
63C3×D29—31no—
64D3×C29—251no—
65C2×C3×C52—871no—
66C3⋊(C5⋊D5)—871no—
67C3⋊(C5⋊D5)—871no—
68C3⋊(C5⋊D5)—1741no—
69C3⋊(C5⋊D5)D8711yescharacteristic, direct product factor
70C52×D3—291no—
71C3×C5⋊D5—31no—
72C5×C29D3×D1516yescomplemented
73C2×D29—2251noHall
74C2×C5⋊D5—2611noHall
75C3⋊D15—1456no—
76C3×D15—56no—
77C3×C5×D3—296no—
78C3×C29—21no—
79C3×C29D3×C5⋊D511yescharacteristic, complemented
80C3×C29C2×C3⋊(C5⋊D5)11yescharacteristic, complemented
81C3×C52—21no—
82C3×C52D3×D2911yescharacteristic, complemented
83C3×C52C2×D8711yescharacteristic, complemented
84C2×D15—4356no—
85D3×D5—4356no—
86C2×C29—751no—
87D29—31no—
88D29—2251no—
89C2×C52—871no—
90C5⋊D5—31no—
91C5⋊D5—2611no—
92C32×C5D5×D2916yescomplemented
93D32—7251noHall
94C2×C3×C5—876no—
95D15—56no—
96D15—8706no—
97D15—4356no—
98D15—4356no—
99C3×D5—156no—
100C5×D3—296no—
101C29D3×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
102C52D3×D8711yescharacteristic, complemented, Sylow
103C2×D5—13056no—
104C3⋊D3—7251no—
105C3×D3—251no—
106C3×D3—291no—
107C3×C5—26no—
108C3×C5D15×D2916yescomplemented
109C3×C5D5×D8716yescomplemented
110C2×D3—21751no—
111C2×D3—21751no—
112C2×C5—876no—
113D5—156no—
114D5—13056no—
115C32C5⋊D5×D2911yescharacteristic, complemented, Sylow
116C2×C3—751no—
117C2×C3—871no—
118D3—251no—
119D3—291no—
120D3—21751no—
121D3—21751no—
122D3—43501no—
123C5D15×D8716yescomplemented
124C22—65251noSylow
125C3—21no—
126C3D29×C3⋊(C5⋊D5)11yescharacteristic, complemented
127C3C5⋊D5×D8711yescharacteristic, complemented
128C2—751no—
129C2—871no—
130C2—65251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C29C22
LCSG ▷ C32×C52×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C52×D87C2semidirect
2. C3×C29×C3⋊(C5⋊D5)C2semidirect
3. C3⋊(C3⋊(C5⋊D145))C2semidirect
6. C32×C52×C29C22semidirect
11. C29×C3⋊(C5⋊D5)D3semidirect
12. C52×D87D3semidirect
18. C3×C5×D87D5semidirect
20. C3×C52×C29C2×D3semidirect
21. C3×C52×C29C2×D3semidirect
27. C32×C5×C29C2×D5semidirect
34. C5×D87D15semidirect
37. C52×C29D32semidirect
40. C3×D87C5⋊D5semidirect
43. C3×C3⋊(C5⋊D5)D29semidirect
46. C3×C5×C29D3×D5semidirect
47. C3×C5×C29C2×D15semidirect
55. C32×C29C2×C5⋊D5semidirect
56. C32×C52C2×D29semidirect
62. D87C3⋊(C5⋊D5)direct (N × H)
69. C3⋊(C5⋊D5)D87direct (N × H)
72. C5×C29D3×D15semidirect
79. C3×C29D3×C5⋊D5semidirect
80. C3×C29C2×C3⋊(C5⋊D5)semidirect
82. C3×C52D3×D29semidirect
83. C3×C52C2×D87semidirect
92. C32×C5D5×D29semidirect
101. C29D3×C3⋊(C5⋊D5)semidirect
102. C52D3×D87semidirect
108. C3×C5D15×D29semidirect
109. C3×C5D5×D87semidirect
115. C32C5⋊D5×D29semidirect
123. C5D15×D87semidirect
126. C3D29×C3⋊(C5⋊D5)semidirect
127. C3C5⋊D5×D87semidirect

Maximal subgroups

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

subgroupindex
C3×C52×D872
C3×C29×C3⋊(C5⋊D5)2
C3⋊(C3⋊(C5⋊D145))2
C5⋊D5×D873
D29×C3⋊(C5⋊D5)3
D15×D875
D3×C3⋊(C5⋊D5)29