Finite Group Databasebeta

← C3×D57⋊(C5⋊D5) #30685886

Subgroups — C3×D57⋊(C5⋊D5) #30685886

Order 17100.

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
1C3×C19×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
2C3×C52×D57C211yesmaximal, characteristic, complemented
3C32×C5⋊D95C211yesmaximal, characteristic, complemented
4D57⋊(C5⋊D5)C311yesmaximal, characteristic, direct product factor
5C3×D19×C5⋊D5—31nomaximal
6C32×C52×C19C2211yescharacteristic, complemented, Hall
7C3×D15⋊D19—56nomaximal
8C19×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
9C52×D57C2×C311yescharacteristic, complemented
10C3×C5⋊D95—21no—
11C3×C5⋊D95D311yescharacteristic, complemented
12C3×C5⋊D95C2×C311yescharacteristic, complemented
13C3×C19×C5⋊D5—31no—
14C3×C52×D19—31no—
15D19×C5⋊D5—31noHall
16C3×C19×D15—56no—
17C3×C5×D57D516yescomplemented
18C32×D95—56no—
19C3×C52×C19—21no—
20C3×C52×C19C2×D311yescharacteristic, complemented
21C3×C52×C19C22×C311yescharacteristic, complemented
22D15⋊D19—56no—
23C3×D5×D19—156no—
24C5⋊D95C3×D311yescharacteristic, complemented
25C19×C5⋊D5—31no—
26C52×D19—31no—
27C3×D3×C5⋊D5—191nomaximal, Hall
28C32×C5×C19C2×D516yescomplemented
29C3×D3×D19—251noHall
30C19×D15—56no—
31C5×D57C3×D516yescomplemented
32C3×D95—56no—
33C3×D95—56no—
34C3×D95—106no—
35C3×D5×C19—156no—
36C3×C5×D19—36no—
37C52×C19C2×C3×D311yescharacteristic, complemented, Hall
38C3×C3⋊(C5⋊D5)D1911yescharacteristic, complemented
39C3×C52×D3—191no—
40C32×C5⋊D5—191no—
41D5×D19—156no—
42C3×D57C5⋊D511yescharacteristic, complemented
43C3×D3×C19—251no—
44C32×D19—251no—
45C2×C3×C5⋊D5—571no—
46D3×C5⋊D5—191no—
47C3×C5×C19—26no—
48C3×C5×C19D3×D516yescomplemented
49C3×C5×C19C2×C3×D516yescomplemented
50C2×C3×D19—751no—
51D3×D19—251no—
52C32×C52C2×D1911yescharacteristic, complemented, Hall
53D95—56no—
54C5×D19—36no—
55D5×C19—156no—
56C3×D3×D5—956no—
57C32×C19C2×C5⋊D511yescharacteristic, complemented, Hall
58C2×C3×C52—571no—
59C3⋊(C5⋊D5)C3×D1911yescharacteristic, complemented
60C52×D3—191no—
61C3×C5⋊D5—31no—
62C3×C5⋊D5—191no—
63C3×C5⋊D5—191no—
64C3×C5⋊D5—381no—
65C2×C3×C19—751no—
66D57C3×C5⋊D511yescharacteristic, complemented
67C3×D19—31no—
68C3×D19—251no—
69C3×D19—251no—
70C3×D19—501no—
71D3×C19—251no—
72C2×C5⋊D5—571noHall
73C5×C19C3×D3×D516yescomplemented
74C3×D15—56no—
75C3×C5×D3—196no—
76C32×D5—956no—
77C2×D19—751noHall
78C3×C52—21no—
79C3×C52D3×D1911yescharacteristic, complemented
80C3×C52C2×C3×D1911yescharacteristic, complemented
81C2×C3×D5—2856no—
82D3×D5—956no—
83C3×C19—21no—
84C3×C19D3×C5⋊D511yescharacteristic, complemented
85C3×C19C2×C3×C5⋊D511yescharacteristic, complemented
86C2×C52—571no—
87C5⋊D5—31no—
88C5⋊D5—191no—
89C32×C5D5×D1916yescomplemented
90C2×C19—751no—
91D19—31no—
92D19—251no—
93C2×C3×D3—4751noHall
94C2×C3×C5—576no—
95D15—56no—
96C3×D5—156no—
97C3×D5—956no—
98C3×D5—956no—
99C3×D5—1906no—
100C5×D3—196no—
101C52C3×D3×D1911yescharacteristic, complemented, Sylow
102C2×D5—2856no—
103C19C3×D3×C5⋊D511yescharacteristic, complemented, Sylow
104C2×C32—4751no—
105C3×D3—191no—
106C3×D3—251no—
107C3×C5—26no—
108C3×C5C3×D5×D1916yescomplemented
109C3×C5D15⋊D1916yescomplemented
110C22×C3—14251no—
111C2×D3—4751no—
112C2×C5—576no—
113D5—156no—
114D5—956no—
115C32D19×C5⋊D511yescharacteristic, complemented, Sylow
116C2×C3—571no—
117C2×C3—751no—
118C2×C3—9501no—
119C2×C3—4751no—
120C2×C3—4751no—
121D3—191no—
122D3—251no—
123C5C3×D15⋊D1916yescomplemented
124C22—14251noSylow
125C3—21no—
126C3C3×D19×C5⋊D511yescharacteristic, complemented
127C3D57⋊(C5⋊D5)11yescharacteristic, direct product factor
128C2—571no—
129C2—751no—
130C2—4751no—
subgroupG/H
center, hypercenterC3D57⋊(C5⋊D5)
commutator, cosocle, hypocenterC3×C52×C19C22×C3
FrattiniC1G
Fitting, socleC32×C52×C19C22
LCSG ▷ C3×C52×C19
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C19×C3⋊(C5⋊D5)C2semidirect
2. C3×C52×D57C2semidirect
3. C32×C5⋊D95C2semidirect
4. D57⋊(C5⋊D5)C3direct (N × H)
6. C32×C52×C19C22semidirect
8. C19×C3⋊(C5⋊D5)C2×C3semidirect
9. C52×D57C2×C3semidirect
11. C3×C5⋊D95D3semidirect
12. C3×C5⋊D95C2×C3semidirect
17. C3×C5×D57D5semidirect
20. C3×C52×C19C2×D3semidirect
21. C3×C52×C19C22×C3semidirect
24. C5⋊D95C3×D3semidirect
28. C32×C5×C19C2×D5semidirect
31. C5×D57C3×D5semidirect
37. C52×C19C2×C3×D3semidirect
38. C3×C3⋊(C5⋊D5)D19semidirect
42. C3×D57C5⋊D5semidirect
48. C3×C5×C19D3×D5semidirect
49. C3×C5×C19C2×C3×D5semidirect
52. C32×C52C2×D19semidirect
57. C32×C19C2×C5⋊D5semidirect
59. C3⋊(C5⋊D5)C3×D19semidirect
66. D57C3×C5⋊D5semidirect
73. C5×C19C3×D3×D5semidirect
79. C3×C52D3×D19semidirect
80. C3×C52C2×C3×D19semidirect
84. C3×C19D3×C5⋊D5semidirect
85. C3×C19C2×C3×C5⋊D5semidirect
89. C32×C5D5×D19semidirect
101. C52C3×D3×D19semidirect
103. C19C3×D3×C5⋊D5semidirect
108. C3×C5C3×D5×D19semidirect
109. C3×C5D15⋊D19semidirect
115. C32D19×C5⋊D5semidirect
123. C5C3×D15⋊D19semidirect
126. C3C3×D19×C5⋊D5semidirect
127. C3D57⋊(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
C3×C19×C3⋊(C5⋊D5)2
C3×C52×D572
C32×C5⋊D952
D57⋊(C5⋊D5)3
C3×D19×C5⋊D53
C3×D15⋊D195
C3×D3×C5⋊D519