Finite Group Databasebeta

← D57⋊(C3⋊(C5⋊D5)) #30685932

Subgroups — D57⋊(C3⋊(C5⋊D5)) #30685932

Order 17100.

352 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C19×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
2C3×C3⋊(C5⋊D95)C211yesmaximal, characteristic, complemented
3C3×C52×D57C211yesmaximal, characteristic, complemented
4D57⋊(C5⋊D5)—31nomaximal
5D19×C3⋊(C5⋊D5)—31nomaximal
6C32×C52×C19C2211yescharacteristic, complemented, Hall
7D57⋊D15—56nomaximal
8C3⋊(C5⋊D95)D311yescharacteristic, complemented
9C19×C3⋊(C5⋊D5)—31no—
10C19×C3⋊(C5⋊D5)—31no—
11C19×C3⋊(C5⋊D5)—61no—
12C52×D57D311yescharacteristic, complemented
13C3×C5⋊D95—31no—
14C3×C52×D19—31no—
15D19×C5⋊D5—91noHall
16C19×C3⋊D15—56no—
17C3×D285—56no—
18C3×C5×D57D516yescomplemented
19C3×C52×C19—21no—
20C3×C52×C19C2×D311yescharacteristic, complemented
21C3×C52×C19C2×D311yescharacteristic, complemented
22D15⋊D19—156no—
23D15×D19—156no—
24C5⋊D95—31no—
25C19×C5⋊D5—91no—
26C52×D19—31no—
27D3×C3⋊(C5⋊D5)—191nomaximal, Hall
28C32×C5×C19C2×D516yescomplemented
29(C3⋊D3)⋊D19—251noHall
30D285—56no—
31C19×D15—156no—
32C19×D15—156no—
33C19×D15—306no—
34C5×D57D1516yescomplemented
35C3×D95—156no—
36C3×C5×D19—36no—
37C52×C19D3211yescharacteristic, complemented, Hall
38C3⋊(C3⋊(C5⋊D5))D1911yescharacteristic, complemented
39C3×C3⋊(C5⋊D5)—191no—
40C3×C52×D3—191no—
41D5×D19—456no—
42C3⋊D3×C19—251no—
43C3×D57—251no—
44C3×D57C5⋊D511yescharacteristic, complemented
45C2×C3⋊(C5⋊D5)—571no—
46D3×C5⋊D5—571no—
47C3×C5×C19—26no—
48C3×C5×C19D3×D516yescomplemented
49C3×C5×C19C2×D1516yescomplemented
50D3×D19—751no—
51D3×D19—751no—
52C32×C52C2×D1911yescharacteristic, complemented, Hall
53D95—156no—
54C5×D19—36no—
55D5×C19—456no—
56D3×D15—956no—
57C32×C19C2×C5⋊D511yescharacteristic, complemented, Hall
58C2×C3×C52—571no—
59C3⋊(C5⋊D5)—31no—
60C3⋊(C5⋊D5)—31no—
61C3⋊(C5⋊D5)—61no—
62C3⋊(C5⋊D5)—191no—
63C52×D3—191no—
64C3×C5⋊D5—571no—
65D57—251no—
66D57C3⋊(C5⋊D5)11yescharacteristic, complemented
67C3×D19—31no—
68C3×D19—751no—
69D3×C19—751no—
70D3×C19—751no—
71D3×C19—1501no—
72C2×C5⋊D5—1711noHall
73C5×C19D3×D1516yescomplemented
74C3⋊D15—56no—
75C3×D15—956no—
76C3×C5×D3—196no—
77C2×D19—2251noHall
78C3×C52—21no—
79C3×C52D3×D1911yescharacteristic, complemented
80C3×C52D3×D1911yescharacteristic, complemented
81C2×D15—2856no—
82D3×D5—2856no—
83C3×C19—21no—
84C3×C19D3×C5⋊D511yescharacteristic, complemented
85C3×C19C2×C3⋊(C5⋊D5)11yescharacteristic, complemented
86C2×C52—571no—
87C5⋊D5—91no—
88C5⋊D5—571no—
89C32×C5D5×D1916yescomplemented
90C2×C19—2251no—
91D19—31no—
92D19—751no—
93D32—4751noHall
94C2×C3×C5—576no—
95D15—156no—
96D15—156no—
97D15—306no—
98D15—956no—
99C3×D5—2856no—
100C5×D3—196no—
101C52(C3⋊D3)⋊D1911yescharacteristic, complemented, Sylow
102C2×D5—8556no—
103C19D3×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
104C3⋊D3—251no—
105C3×D3—191no—
106C3×D3—4751no—
107C3×C5—26no—
108C3×C5D15×D1916yescomplemented
109C3×C5D15⋊D1916yescomplemented
110C2×D3—14251no—
111C2×D3—14251no—
112C2×C5—576no—
113D5—2856no—
114D5—456no—
115C32D19×C5⋊D511yescharacteristic, complemented, Sylow
116C2×C3—571no—
117C2×C3—14251no—
118D3—191no—
119D3—751no—
120D3—751no—
121D3—1501no—
122D3—4751no—
123C5D57⋊D1516yescomplemented
124C22—42751noSylow
125C3—21no—
126C3D19×C3⋊(C5⋊D5)11yescharacteristic, complemented
127C3D57⋊(C5⋊D5)11yescharacteristic, complemented
128C2—571no—
129C2—14251no—
130C2—2251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C19C22
LCSG ▷ C32×C52×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. C19×C3⋊(C3⋊(C5⋊D5))C2semidirect
2. C3×C3⋊(C5⋊D95)C2semidirect
3. C3×C52×D57C2semidirect
6. C32×C52×C19C22semidirect
8. C3⋊(C5⋊D95)D3semidirect
12. C52×D57D3semidirect
18. C3×C5×D57D5semidirect
20. C3×C52×C19C2×D3semidirect
21. C3×C52×C19C2×D3semidirect
28. C32×C5×C19C2×D5semidirect
34. C5×D57D15semidirect
37. C52×C19D32semidirect
38. C3⋊(C3⋊(C5⋊D5))D19semidirect
44. C3×D57C5⋊D5semidirect
48. C3×C5×C19D3×D5semidirect
49. C3×C5×C19C2×D15semidirect
52. C32×C52C2×D19semidirect
57. C32×C19C2×C5⋊D5semidirect
66. D57C3⋊(C5⋊D5)semidirect
73. C5×C19D3×D15semidirect
79. C3×C52D3×D19semidirect
80. C3×C52D3×D19semidirect
84. C3×C19D3×C5⋊D5semidirect
85. C3×C19C2×C3⋊(C5⋊D5)semidirect
89. C32×C5D5×D19semidirect
101. C52(C3⋊D3)⋊D19semidirect
103. C19D3×C3⋊(C5⋊D5)semidirect
108. C3×C5D15×D19semidirect
109. C3×C5D15⋊D19semidirect
115. C32D19×C5⋊D5semidirect
123. C5D57⋊D15semidirect
126. C3D19×C3⋊(C5⋊D5)semidirect
127. C3D57⋊(C5⋊D5)semidirect

Maximal subgroups

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

subgroupindex
C19×C3⋊(C3⋊(C5⋊D5))2
C3×C3⋊(C5⋊D95)2
C3×C52×D572
D57⋊(C5⋊D5)3
D19×C3⋊(C5⋊D5)3
D57⋊D155
D3×C3⋊(C5⋊D5)19