Finite Group Databasebeta

← C52×D3×D51 #29506021

Subgroups — C52×D3×D51 #29506021

Order 15300.

352 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 128 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
1C52×C3⋊D51C211yesmaximal, characteristic, complemented
2C3×C52×D51C211yesmaximal, characteristic, complemented
3C3×C52×D3×C17C211yesmaximal, characteristic, complemented
4C2×C52×D51—31nomaximal
5C52×D3×D17—31nomaximal
6C32×C52×C17C2211yescharacteristic, complemented, Hall
7C5×D3×D51C516yesmaximal, direct product factor
8C52×D51—31no—
9C52×D51—31no—
10C52×D51—61no—
11C52×D51D311yescharacteristic, direct product factor
12C52×D3×C17D311yescharacteristic, complemented
13C3×C52×D17—31no—
14C2×C3×C52×C17—31no—
15C2×C52×D17—91noHall
16C5×C3⋊D51C2×C516yescomplemented
17C3×C5×D51C2×C516yescomplemented
18C3×C5×D3×C17C2×C516yescomplemented
19C3×C52×C17—21no—
20C3×C52×C17C2×D311yescharacteristic, complemented
21C3×C52×C17C2×D311yescharacteristic, complemented
22C2×C5×D51—36no—
23C5×D3×D17—36no—
24C52×D32—171nomaximal, Hall
25C2×C52×C17—31no—
26C52×D17—31no—
27C52×D17—91no—
28C32×C5×C17C22×C516yescomplemented
29D3×D51C5211yescharacteristic, direct product factor, Hall
30C2×C3×C5×C17—36no—
31C5×D51—36no—
32C5×D51—36no—
33C5×D51—66no—
34C5×D51C5×D316yesdirect product factor
35C5×D3×C17C5×D316yescomplemented
36C3×C5×D17—36no—
37C52×C3⋊D3—171no—
38C3×C52×D3—171no—
39C3×C52×D3D1711yescharacteristic, complemented
40C52×C17D3211yescharacteristic, complemented, Hall
41C2×C5×D17—96no—
42C3⋊D51C2×C5211yescharacteristic, complemented
43C3×D51C2×C5211yescharacteristic, complemented
44C3×D3×C17C2×C5211yescharacteristic, complemented
45C2×C52×D3—511no—
46C2×C52×D3—511no—
47C3×C5×C17—26no—
48C3×C5×C17C2×C5×D316yescomplemented
49C3×C5×C17C2×C5×D316yescomplemented
50C32×C52C2×D1711yescharacteristic, complemented, Hall
51C2×D51—31no—
52D3×D17—31no—
53C5×D32—176no—
54C2×C5×C17—36no—
55C5×D17—36no—
56C5×D17—96no—
57C32×C17C22×C5211yescharacteristic, complemented, Hall
58C2×C3×C52—31no—
59C2×C3×C52—511no—
60C52×D3—171no—
61C52×D3—511no—
62C52×D3—511no—
63C52×D3—1021no—
64C52×D3D5111yescharacteristic, direct product factor
65C2×C3×C17—31no—
66D51—31no—
67D51—31no—
68D51—61no—
69D51C52×D311yescharacteristic, direct product factor
70C3×D17—31no—
71D3×C17C52×D311yescharacteristic, complemented
72C22×C52—1531noHall
73C5×C3⋊D3—176no—
74C3×C5×D3—176no—
75C3×C5×D3C5×D1716yescomplemented
76C5×C17C5×D3216yescomplemented
77C3×C52—21no—
78C3×C52D3×D1711yescharacteristic, complemented
79C3×C52C2×D5111yescharacteristic, complemented
80C2×D17—91noHall
81C2×C5×D3—516no—
82C2×C5×D3—516no—
83C3×C17—21no—
84C3×C17C2×C52×D311yescharacteristic, complemented
85C3×C17C2×C52×D311yescharacteristic, complemented
86C2×C52—31no—
87C2×C52—511no—
88C2×C52—1531no—
89C32×C5C2×C5×D1716yescomplemented
90D32—171noHall
91C2×C17—31no—
92D17—31no—
93D17—91no—
94C2×C3×C5—36no—
95C2×C3×C5—516no—
96C5×D3—176no—
97C5×D3—516no—
98C5×D3—516no—
99C5×D3—1026no—
100C5×D3C5×D5116yesdirect product factor
101C52D3×D5111yescharacteristic, direct product factor, Sylow
102C22×C5—1536no—
103C3⋊D3—171no—
104C3×D3—171no—
105C3×D3C52×D1711yescharacteristic, complemented
106C17C52×D3211yescharacteristic, complemented, Sylow
107C3×C5—26no—
108C3×C5C5×D3×D1716yescomplemented
109C3×C5C2×C5×D5116yescomplemented
110C2×D3—511no—
111C2×D3—511no—
112C2×C5—36no—
113C2×C5—516no—
114C2×C5—1536no—
115C32C2×C52×D1711yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—511no—
118D3—171no—
119D3—511no—
120D3—511no—
121D3—1021no—
122D3C52×D5111yescharacteristic, direct product factor
123C5C5×D3×D5116yesdirect product factor
124C22—1531noSylow
125C3—21no—
126C3C52×D3×D1711yescharacteristic, complemented
127C3C2×C52×D5111yescharacteristic, complemented
128C2—31no—
129C2—511no—
130C2—1531no—
subgroupG/H
center, hypercenterC52D3×D51
commutator, cosocle, hypocenterC32×C17C22×C52
FrattiniC1G
Fitting, socleC32×C52×C17C22
LCSG ▷ C32×C17
UCSC1 ◁ C52

Complements

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

NH ≅ G/Ntype
1. C52×C3⋊D51C2semidirect
2. C3×C52×D51C2semidirect
3. C3×C52×D3×C17C2semidirect
6. C32×C52×C17C22semidirect
7. C5×D3×D51C5direct (N × H)
11. C52×D51D3direct (N × H)
12. C52×D3×C17D3semidirect
16. C5×C3⋊D51C2×C5semidirect
17. C3×C5×D51C2×C5semidirect
18. C3×C5×D3×C17C2×C5semidirect
20. C3×C52×C17C2×D3semidirect
21. C3×C52×C17C2×D3semidirect
28. C32×C5×C17C22×C5semidirect
29. D3×D51C52direct (N × H)
34. C5×D51C5×D3direct (N × H)
35. C5×D3×C17C5×D3semidirect
39. C3×C52×D3D17semidirect
40. C52×C17D32semidirect
42. C3⋊D51C2×C52semidirect
43. C3×D51C2×C52semidirect
44. C3×D3×C17C2×C52semidirect
48. C3×C5×C17C2×C5×D3semidirect
49. C3×C5×C17C2×C5×D3semidirect
50. C32×C52C2×D17semidirect
57. C32×C17C22×C52semidirect
64. C52×D3D51direct (N × H)
69. D51C52×D3direct (N × H)
71. D3×C17C52×D3semidirect
75. C3×C5×D3C5×D17semidirect
76. C5×C17C5×D32semidirect
78. C3×C52D3×D17semidirect
79. C3×C52C2×D51semidirect
84. C3×C17C2×C52×D3semidirect
85. C3×C17C2×C52×D3semidirect
89. C32×C5C2×C5×D17semidirect
100. C5×D3C5×D51direct (N × H)
101. C52D3×D51direct (N × H)
105. C3×D3C52×D17semidirect
106. C17C52×D32semidirect
108. C3×C5C5×D3×D17semidirect
109. C3×C5C2×C5×D51semidirect
115. C32C2×C52×D17semidirect
122. D3C52×D51direct (N × H)
123. C5C5×D3×D51direct (N × H)
126. C3C52×D3×D17semidirect
127. C3C2×C52×D51semidirect

Maximal subgroups

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

subgroupindex
C52×C3⋊D512
C3×C52×D512
C3×C52×D3×C172
C2×C52×D513
C52×D3×D173
C5×D3×D515
C52×D3217