Finite Group Databasebeta

← D3×C3⋊(C5⋊D85) #29506031

Subgroups — D3×C3⋊(C5⋊D85) #29506031

Order 15300.

352 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 100 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⋊(C3⋊(C5⋊D85))C211yesmaximal, characteristic, complemented
2C3×C3⋊(C5⋊D85)C211yesmaximal, characteristic, complemented
3C3×C52×D3×C17C211yesmaximal, characteristic, complemented
4C2×C3⋊(C5⋊D85)—31nomaximal
5D3×C5⋊D85—31nomaximal
6C32×C52×C17C2211yescharacteristic, complemented, Hall
7D3×D255—56nomaximal
8C3⋊(C5⋊D85)—31no—
9C3⋊(C5⋊D85)—31no—
10C3⋊(C5⋊D85)—61no—
11C3⋊(C5⋊D85)D311yescharacteristic, direct product factor
12C52×D3×C17D311yescharacteristic, complemented
13C3×C5⋊D85—31no—
14C2×C3×C52×C17—31no—
15C2×C5⋊D85—91noHall
16C3⋊D255—56no—
17C3×D255—56no—
18C3×C5×D3×C17D516yescomplemented
19C3×C52×C17—21no—
20C3×C52×C17C2×D311yescharacteristic, complemented
21C3×C52×C17C2×D311yescharacteristic, complemented
22C2×D255—156no—
23D3×D85—156no—
24D3×C3⋊(C5⋊D5)—171nomaximal, Hall
25C2×C52×C17—31no—
26C5⋊D85—31no—
27C5⋊D85—91no—
28C32×C5×C17C2×D516yescomplemented
29D3×D51—251noHall
30C2×C3×C5×C17—36no—
31D255—56no—
32D255—156no—
33D255—156no—
34D255—306no—
35C5×D3×C17D1516yescomplemented
36C3×D85—156no—
37C3⋊(C3⋊(C5⋊D5))—171no—
38C3×C3⋊(C5⋊D5)—171no—
39C3×C52×D3D1711yescharacteristic, complemented
40C52×C17D3211yescharacteristic, complemented, Hall
41C2×D85—456no—
42C3⋊D51—251no—
43C3×D51—251no—
44C3×D3×C17C5⋊D511yescharacteristic, complemented
45C2×C3⋊(C5⋊D5)—511no—
46D3×C5⋊D5—511no—
47C3×C5×C17—26no—
48C3×C5×C17D3×D516yescomplemented
49C3×C5×C17C2×D1516yescomplemented
50C32×C52C2×D1711yescharacteristic, complemented, Hall
51C2×D51—751no—
52D3×D17—751no—
53D3×D15—856no—
54C2×C5×C17—36no—
55D85—156no—
56D85—456no—
57C32×C17C2×C5⋊D511yescharacteristic, complemented, Hall
58C2×C3×C52—31no—
59C3⋊(C5⋊D5)—171no—
60C3⋊(C5⋊D5)—511no—
61C3⋊(C5⋊D5)—511no—
62C3⋊(C5⋊D5)—1021no—
63C52×D3D5111yescharacteristic, complemented
64C3×C5⋊D5—511no—
65C2×C3×C17—31no—
66D51—251no—
67D51—751no—
68D51—751no—
69D51—1501no—
70C3×D17—751no—
71D3×C17C3⋊(C5⋊D5)11yescharacteristic, complemented
72C2×C5⋊D5—1531noHall
73C3⋊D15—856no—
74C3×D15—856no—
75C3×C5×D3D8516yescomplemented
76C5×C17D3×D1516yescomplemented
77C3×C52—21no—
78C3×C52D3×D1711yescharacteristic, complemented
79C3×C52C2×D5111yescharacteristic, complemented
80C2×D17—2251noHall
81C2×D15—2556no—
82D3×D5—2556no—
83C3×C17—21no—
84C3×C17D3×C5⋊D511yescharacteristic, complemented
85C3×C17C2×C3⋊(C5⋊D5)11yescharacteristic, complemented
86C2×C52—31no—
87C5⋊D5—511no—
88C5⋊D5—1531no—
89C32×C5C2×D8516yescomplemented
90D32—4251noHall
91C2×C17—31no—
92D17—751no—
93D17—2251no—
94C2×C3×C5—36no—
95D15—856no—
96D15—5106no—
97D15—2556no—
98D15—2556no—
99C3×D5—2556no—
100C5×D3D25516yescomplemented
101C52D3×D5111yescharacteristic, complemented, Sylow
102C2×D5—7656no—
103C3⋊D3—4251no—
104C3×D3—4251no—
105C3×D3C5⋊D8511yescharacteristic, complemented
106C17D3×C3⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
107C3×C5—26no—
108C3×C5D3×D8516yescomplemented
109C3×C5C2×D25516yescomplemented
110C2×D3—12751no—
111C2×D3—12751no—
112C2×C5—36no—
113D5—7656no—
114D5—2556no—
115C32C2×C5⋊D8511yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—12751no—
118D3—4251no—
119D3—25501no—
120D3—12751no—
121D3—12751no—
122D3C3⋊(C5⋊D85)11yescharacteristic, direct product factor
123C5D3×D25516yescomplemented
124C22—38251noSylow
125C3—21no—
126C3D3×C5⋊D8511yescharacteristic, complemented
127C3C2×C3⋊(C5⋊D85)11yescharacteristic, complemented
128C2—31no—
129C2—38251no—
130C2—12751no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C17C22
LCSG ▷ C32×C52×C17
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C3⋊(C5⋊D85))C2semidirect
2. C3×C3⋊(C5⋊D85)C2semidirect
3. C3×C52×D3×C17C2semidirect
6. C32×C52×C17C22semidirect
11. C3⋊(C5⋊D85)D3direct (N × H)
12. C52×D3×C17D3semidirect
18. C3×C5×D3×C17D5semidirect
20. C3×C52×C17C2×D3semidirect
21. C3×C52×C17C2×D3semidirect
28. C32×C5×C17C2×D5semidirect
35. C5×D3×C17D15semidirect
39. C3×C52×D3D17semidirect
40. C52×C17D32semidirect
44. C3×D3×C17C5⋊D5semidirect
48. C3×C5×C17D3×D5semidirect
49. C3×C5×C17C2×D15semidirect
50. C32×C52C2×D17semidirect
57. C32×C17C2×C5⋊D5semidirect
63. C52×D3D51semidirect
71. D3×C17C3⋊(C5⋊D5)semidirect
75. C3×C5×D3D85semidirect
76. C5×C17D3×D15semidirect
78. C3×C52D3×D17semidirect
79. C3×C52C2×D51semidirect
84. C3×C17D3×C5⋊D5semidirect
85. C3×C17C2×C3⋊(C5⋊D5)semidirect
89. C32×C5C2×D85semidirect
100. C5×D3D255semidirect
101. C52D3×D51semidirect
105. C3×D3C5⋊D85semidirect
106. C17D3×C3⋊(C5⋊D5)semidirect
108. C3×C5D3×D85semidirect
109. C3×C5C2×D255semidirect
115. C32C2×C5⋊D85semidirect
122. D3C3⋊(C5⋊D85)direct (N × H)
123. C5D3×D255semidirect
126. C3D3×C5⋊D85semidirect
127. C3C2×C3⋊(C5⋊D85)semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊(C5⋊D85))2
C3×C3⋊(C5⋊D85)2
C3×C52×D3×C172
C2×C3⋊(C5⋊D85)3
D3×C5⋊D853
D3×D2555
D3×C3⋊(C5⋊D5)17