Finite Group Databasebeta

← C3×D51⋊(C5⋊D5) #29505976

Subgroups — C3×D51⋊(C5⋊D5) #29505976

Order 15300.

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×C17×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
2C3×C52×D51C211yesmaximal, characteristic, complemented
3C32×C5⋊D85C211yesmaximal, characteristic, complemented
4D51⋊(C5⋊D5)C311yesmaximal, characteristic, direct product factor
5C3×D17×C5⋊D5—31nomaximal
6C32×C52×C17C2211yescharacteristic, complemented, Hall
7C3×D15⋊D17—56nomaximal
8C17×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
9C52×D51C2×C311yescharacteristic, complemented
10C3×C5⋊D85—21no—
11C3×C5⋊D85D311yescharacteristic, complemented
12C3×C5⋊D85C2×C311yescharacteristic, complemented
13C3×C17×C5⋊D5—31no—
14C3×C52×D17—31no—
15D17×C5⋊D5—31noHall
16C3×C17×D15—56no—
17C3×C5×D51D516yescomplemented
18C32×D85—56no—
19C3×C52×C17—21no—
20C3×C52×C17C2×D311yescharacteristic, complemented
21C3×C52×C17C22×C311yescharacteristic, complemented
22D15⋊D17—56no—
23C3×D5×D17—156no—
24C3×D3×C5⋊D5—171nomaximal, Hall
25C5⋊D85C3×D311yescharacteristic, complemented
26C17×C5⋊D5—31no—
27C52×D17—31no—
28C32×C5×C17C2×D516yescomplemented
29C3×D3×D17—251noHall
30C17×D15—56no—
31C5×D51C3×D516yescomplemented
32C3×D85—56no—
33C3×D85—56no—
34C3×D85—106no—
35C3×D5×C17—156no—
36C3×C5×D17—36no—
37C3×C3⋊(C5⋊D5)D1711yescharacteristic, complemented
38C3×C52×D3—171no—
39C32×C5⋊D5—171no—
40C52×C17C2×C3×D311yescharacteristic, complemented, Hall
41D5×D17—156no—
42C3×D51C5⋊D511yescharacteristic, complemented
43C3×D3×C17—251no—
44C32×D17—251no—
45C2×C3×C5⋊D5—511no—
46D3×C5⋊D5—171no—
47C3×C5×C17—26no—
48C3×C5×C17D3×D516yescomplemented
49C3×C5×C17C2×C3×D516yescomplemented
50C32×C52C2×D1711yescharacteristic, complemented, Hall
51C2×C3×D17—751no—
52D3×D17—251no—
53C3×D3×D5—856no—
54D85—56no—
55C5×D17—36no—
56D5×C17—156no—
57C32×C17C2×C5⋊D511yescharacteristic, complemented, Hall
58C2×C3×C52—511no—
59C3⋊(C5⋊D5)C3×D1711yescharacteristic, complemented
60C52×D3—171no—
61C3×C5⋊D5—31no—
62C3×C5⋊D5—171no—
63C3×C5⋊D5—171no—
64C3×C5⋊D5—341no—
65C2×C3×C17—751no—
66D51C3×C5⋊D511yescharacteristic, complemented
67C3×D17—31no—
68C3×D17—251no—
69C3×D17—251no—
70C3×D17—501no—
71D3×C17—251no—
72C2×C5⋊D5—511noHall
73C3×D15—56no—
74C3×C5×D3—176no—
75C32×D5—856no—
76C5×C17C3×D3×D516yescomplemented
77C3×C52—21no—
78C3×C52D3×D1711yescharacteristic, complemented
79C3×C52C2×C3×D1711yescharacteristic, complemented
80C2×D17—751noHall
81C2×C3×D5—2556no—
82D3×D5—856no—
83C3×C17—21no—
84C3×C17D3×C5⋊D511yescharacteristic, complemented
85C3×C17C2×C3×C5⋊D511yescharacteristic, complemented
86C2×C52—511no—
87C5⋊D5—31no—
88C5⋊D5—171no—
89C32×C5D5×D1716yescomplemented
90C2×C3×D3—4251noHall
91C2×C17—751no—
92D17—31no—
93D17—251no—
94C2×C3×C5—516no—
95D15—56no—
96C3×D5—156no—
97C3×D5—856no—
98C3×D5—856no—
99C3×D5—1706no—
100C5×D3—176no—
101C52C3×D3×D1711yescharacteristic, complemented, Sylow
102C2×D5—2556no—
103C2×C32—4251no—
104C3×D3—171no—
105C3×D3—251no—
106C17C3×D3×C5⋊D511yescharacteristic, complemented, Sylow
107C3×C5—26no—
108C3×C5C3×D5×D1716yescomplemented
109C3×C5D15⋊D1716yescomplemented
110C22×C3—12751no—
111C2×D3—4251no—
112C2×C5—516no—
113D5—156no—
114D5—856no—
115C32D17×C5⋊D511yescharacteristic, complemented, Sylow
116C2×C3—511no—
117C2×C3—751no—
118C2×C3—8501no—
119C2×C3—4251no—
120C2×C3—4251no—
121D3—171no—
122D3—251no—
123C5C3×D15⋊D1716yescomplemented
124C22—12751noSylow
125C3—21no—
126C3C3×D17×C5⋊D511yescharacteristic, complemented
127C3D51⋊(C5⋊D5)11yescharacteristic, direct product factor
128C2—511no—
129C2—751no—
130C2—4251no—
subgroupG/H
center, hypercenterC3D51⋊(C5⋊D5)
commutator, cosocle, hypocenterC3×C52×C17C22×C3
FrattiniC1G
Fitting, socleC32×C52×C17C22
LCSG ▷ C3×C52×C17
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C17×C3⋊(C5⋊D5)C2semidirect
2. C3×C52×D51C2semidirect
3. C32×C5⋊D85C2semidirect
4. D51⋊(C5⋊D5)C3direct (N × H)
6. C32×C52×C17C22semidirect
8. C17×C3⋊(C5⋊D5)C2×C3semidirect
9. C52×D51C2×C3semidirect
11. C3×C5⋊D85D3semidirect
12. C3×C5⋊D85C2×C3semidirect
17. C3×C5×D51D5semidirect
20. C3×C52×C17C2×D3semidirect
21. C3×C52×C17C22×C3semidirect
25. C5⋊D85C3×D3semidirect
28. C32×C5×C17C2×D5semidirect
31. C5×D51C3×D5semidirect
37. C3×C3⋊(C5⋊D5)D17semidirect
40. C52×C17C2×C3×D3semidirect
42. C3×D51C5⋊D5semidirect
48. C3×C5×C17D3×D5semidirect
49. C3×C5×C17C2×C3×D5semidirect
50. C32×C52C2×D17semidirect
57. C32×C17C2×C5⋊D5semidirect
59. C3⋊(C5⋊D5)C3×D17semidirect
66. D51C3×C5⋊D5semidirect
76. C5×C17C3×D3×D5semidirect
78. C3×C52D3×D17semidirect
79. C3×C52C2×C3×D17semidirect
84. C3×C17D3×C5⋊D5semidirect
85. C3×C17C2×C3×C5⋊D5semidirect
89. C32×C5D5×D17semidirect
101. C52C3×D3×D17semidirect
106. C17C3×D3×C5⋊D5semidirect
108. C3×C5C3×D5×D17semidirect
109. C3×C5D15⋊D17semidirect
115. C32D17×C5⋊D5semidirect
123. C5C3×D15⋊D17semidirect
126. C3C3×D17×C5⋊D5semidirect
127. C3D51⋊(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×C17×C3⋊(C5⋊D5)2
C3×C52×D512
C32×C5⋊D852
D51⋊(C5⋊D5)3
C3×D17×C5⋊D53
C3×D15⋊D175
C3×D3×C5⋊D517