Finite Group Databasebeta

← D69×C3⋊(C5⋊D5) #35208206

Subgroups — D69×C3⋊(C5⋊D5) #35208206

Order 20700.

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×D69C211yesmaximal, characteristic, complemented
2C3×C23×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C5⋊D115))C211yesmaximal, characteristic, complemented
4C5⋊D5×D69—31nomaximal
5D23×C3⋊(C5⋊D5)—31nomaximal
6C32×C52×C23C2211yescharacteristic, complemented, Hall
7D15×D69—56nomaximal
8C3⋊(C5⋊D115)—31no—
9C3⋊(C5⋊D115)—31no—
10C3⋊(C5⋊D115)—61no—
11C23×C3⋊(C5⋊D5)D311yescharacteristic, complemented
12C52×D69D311yescharacteristic, complemented
13C3×C23×C5⋊D5—31no—
14C3×C52×D23—31no—
15D23×C5⋊D5—91noHall
16C3⋊D345—56no—
17C3×C23×D15—56no—
18C3×C5×D69D516yescomplemented
19C3×C52×C23—21no—
20C3×C52×C23C2×D311yescharacteristic, complemented
21C3×C52×C23C2×D311yescharacteristic, complemented
22D5×D69—156no—
23D15×D23—156no—
24C5⋊D115—91no—
25C23×C5⋊D5—31no—
26C52×D23—31no—
27C32×C5×C23C2×D516yescomplemented
28D3×C3⋊(C5⋊D5)—231nomaximal, Hall
29D3×D69—251noHall
30D345—156no—
31D345—156no—
32D345—306no—
33C23×D15—56no—
34C5×D69D1516yescomplemented
35C3×D5×C23—156no—
36C3×C5×D23—36no—
37C52×C23D3211yescharacteristic, complemented, Hall
38D5×D23—456no—
39C3⋊(C3⋊(C5⋊D5))—231no—
40C3×C3⋊(C5⋊D5)D2311yescharacteristic, complemented
41C3×C52×D3—231no—
42C3⋊D69—251no—
43C3×D69C5⋊D511yescharacteristic, complemented
44C3×D3×C23—251no—
45C3×C5×C23—26no—
46C3×C5×C23D3×D516yescomplemented
47C3×C5×C23C2×D1516yescomplemented
48C2×C3⋊(C5⋊D5)—691no—
49D3×C5⋊D5—691no—
50C2×D69—751no—
51D3×D23—751no—
52D115—456no—
53C5×D23—36no—
54D5×C23—156no—
55C32×C52C2×D2311yescharacteristic, complemented, Hall
56C32×C23C2×C5⋊D511yescharacteristic, complemented, Hall
57D3×D15—1156no—
58C2×C3×C52—691no—
59C3⋊(C5⋊D5)—691no—
60C3⋊(C5⋊D5)—691no—
61C3⋊(C5⋊D5)—1381no—
62C3⋊(C5⋊D5)D6911yescharacteristic, direct product factor
63C52×D3—231no—
64C3×C5⋊D5—31no—
65C2×C3×C23—751no—
66D69—751no—
67D69—751no—
68D69—1501no—
69D69C3⋊(C5⋊D5)11yescharacteristic, direct product factor
70C3×D23—31no—
71D3×C23—251no—
72C5×C23D3×D1516yescomplemented
73C2×C5⋊D5—2071noHall
74C2×D23—2251noHall
75C3⋊D15—1156no—
76C3×D15—56no—
77C3×C5×D3—236no—
78C3×C52—21no—
79C3×C52D3×D2311yescharacteristic, complemented
80C3×C52C2×D6911yescharacteristic, complemented
81C3×C23—21no—
82C3×C23D3×C5⋊D511yescharacteristic, complemented
83C3×C23C2×C3⋊(C5⋊D5)11yescharacteristic, complemented
84C2×D15—3456no—
85D3×D5—3456no—
86C2×C52—691no—
87C5⋊D5—31no—
88C5⋊D5—2071no—
89C2×C23—751no—
90D23—31no—
91D23—2251no—
92C32×C5D5×D2316yescomplemented
93D32—5751noHall
94C2×C3×C5—696no—
95D15—56no—
96D15—3456no—
97D15—3456no—
98D15—6906no—
99C3×D5—156no—
100C5×D3—236no—
101C52D3×D6911yescharacteristic, complemented, Sylow
102C23D3×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
103C2×D5—10356no—
104C3⋊D3—5751no—
105C3×D3—231no—
106C3×D3—251no—
107C3×C5—26no—
108C3×C5D15×D2316yescomplemented
109C3×C5D5×D6916yescomplemented
110C2×D3—17251no—
111C2×D3—17251no—
112C2×C5—696no—
113D5—10356no—
114D5—156no—
115C32D23×C5⋊D511yescharacteristic, complemented, Sylow
116C2×C3—691no—
117C2×C3—751no—
118D3—231no—
119D3—251no—
120D3—34501no—
121D3—17251no—
122D3—17251no—
123C5D15×D6916yescomplemented
124C22—51751noSylow
125C3—21no—
126C3D23×C3⋊(C5⋊D5)11yescharacteristic, complemented
127C3C5⋊D5×D6911yescharacteristic, complemented
128C2—51751no—
129C2—691no—
130C2—751no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C23C22
LCSG ▷ C32×C52×C23
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C52×D69C2semidirect
2. C3×C23×C3⋊(C5⋊D5)C2semidirect
3. C3⋊(C3⋊(C5⋊D115))C2semidirect
6. C32×C52×C23C22semidirect
11. C23×C3⋊(C5⋊D5)D3semidirect
12. C52×D69D3semidirect
18. C3×C5×D69D5semidirect
20. C3×C52×C23C2×D3semidirect
21. C3×C52×C23C2×D3semidirect
27. C32×C5×C23C2×D5semidirect
34. C5×D69D15semidirect
37. C52×C23D32semidirect
40. C3×C3⋊(C5⋊D5)D23semidirect
43. C3×D69C5⋊D5semidirect
46. C3×C5×C23D3×D5semidirect
47. C3×C5×C23C2×D15semidirect
55. C32×C52C2×D23semidirect
56. C32×C23C2×C5⋊D5semidirect
62. C3⋊(C5⋊D5)D69direct (N × H)
69. D69C3⋊(C5⋊D5)direct (N × H)
72. C5×C23D3×D15semidirect
79. C3×C52D3×D23semidirect
80. C3×C52C2×D69semidirect
82. C3×C23D3×C5⋊D5semidirect
83. C3×C23C2×C3⋊(C5⋊D5)semidirect
92. C32×C5D5×D23semidirect
101. C52D3×D69semidirect
102. C23D3×C3⋊(C5⋊D5)semidirect
108. C3×C5D15×D23semidirect
109. C3×C5D5×D69semidirect
115. C32D23×C5⋊D5semidirect
123. C5D15×D69semidirect
126. C3D23×C3⋊(C5⋊D5)semidirect
127. C3C5⋊D5×D69semidirect

Maximal subgroups

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

subgroupindex
C3×C52×D692
C3×C23×C3⋊(C5⋊D5)2
C3⋊(C3⋊(C5⋊D115))2
C5⋊D5×D693
D23×C3⋊(C5⋊D5)3
D15×D695
D3×C3⋊(C5⋊D5)23