Finite Group Databasebeta

← C52×D3×D39 #26043813

Subgroups — C52×D3×D39 #26043813

Order 11700.

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⋊D39C211yesmaximal, characteristic, complemented
2C3×C52×D39C211yesmaximal, characteristic, complemented
3C3×C52×D3×C13C211yesmaximal, characteristic, complemented
4C2×C52×D39—31nomaximal
5C52×D3×D13—31nomaximal
6C32×C52×C13C2211yescharacteristic, complemented, Hall
7C5×D3×D39C516yesmaximal, direct product factor
8C2×C3×C52×C13—31no—
9C52×D39—31no—
10C52×D39—31no—
11C52×D39—61no—
12C52×D39D311yescharacteristic, direct product factor
13C52×D3×C13D311yescharacteristic, complemented
14C3×C52×D13—31no—
15C2×C52×D13—91noHall
16C5×C3⋊D39C2×C516yescomplemented
17C3×C5×D39C2×C516yescomplemented
18C3×C5×D3×C13C2×C516yescomplemented
19C3×C52×C13—21no—
20C3×C52×C13C2×D311yescharacteristic, complemented
21C3×C52×C13C2×D311yescharacteristic, complemented
22C52×D32—131nomaximal, Hall
23C2×C5×D39—36no—
24C5×D3×D13—36no—
25C2×C52×C13—31no—
26C52×D13—31no—
27C52×D13—91no—
28C32×C5×C13C22×C516yescomplemented
29D3×D39C5211yescharacteristic, direct product factor, Hall
30C52×C3⋊D3—131no—
31C3×C52×D3—131no—
32C3×C52×D3D1311yescharacteristic, complemented
33C2×C3×C5×C13—36no—
34C5×D39—36no—
35C5×D39—36no—
36C5×D39—66no—
37C5×D39C5×D316yesdirect product factor
38C5×D3×C13C5×D316yescomplemented
39C3×C5×D13—36no—
40C52×C13D3211yescharacteristic, complemented, Hall
41C2×C52×D3—391no—
42C2×C52×D3—391no—
43C2×C5×D13—96no—
44C3⋊D39C2×C5211yescharacteristic, complemented
45C3×D39C2×C5211yescharacteristic, complemented
46C3×D3×C13C2×C5211yescharacteristic, complemented
47C32×C52C2×D1311yescharacteristic, complemented, Hall
48C3×C5×C13—26no—
49C3×C5×C13C2×C5×D316yescomplemented
50C3×C5×C13C2×C5×D316yescomplemented
51C5×D32—136no—
52C2×D39—31no—
53D3×D13—31no—
54C2×C3×C52—31no—
55C2×C3×C52—391no—
56C52×D3—131no—
57C52×D3—391no—
58C52×D3—391no—
59C52×D3—781no—
60C52×D3D3911yescharacteristic, direct product factor
61C2×C5×C13—36no—
62C5×D13—36no—
63C5×D13—96no—
64C32×C13C22×C5211yescharacteristic, complemented, Hall
65C22×C52—1171noHall
66C5×C3⋊D3—136no—
67C3×C5×D3—136no—
68C3×C5×D3C5×D1316yescomplemented
69C2×C3×C13—31no—
70D39—31no—
71D39—31no—
72D39—61no—
73D39C52×D311yescharacteristic, direct product factor
74C3×D13—31no—
75D3×C13C52×D311yescharacteristic, complemented
76C3×C52—21no—
77C3×C52D3×D1311yescharacteristic, complemented
78C3×C52C2×D3911yescharacteristic, complemented
79C5×C13C5×D3216yescomplemented
80C2×C5×D3—396no—
81C2×C5×D3—396no—
82C2×D13—91noHall
83C2×C52—31no—
84C2×C52—391no—
85C2×C52—1171no—
86C32×C5C2×C5×D1316yescomplemented
87C3×C13—21no—
88C3×C13C2×C52×D311yescharacteristic, complemented
89C3×C13C2×C52×D311yescharacteristic, complemented
90D32—131noHall
91C2×C3×C5—36no—
92C2×C3×C5—396no—
93C5×D3—136no—
94C5×D3—396no—
95C5×D3—396no—
96C5×D3—786no—
97C5×D3C5×D3916yesdirect product factor
98C2×C13—31no—
99D13—31no—
100D13—91no—
101C52D3×D3911yescharacteristic, direct product factor, Sylow
102C22×C5—1176no—
103C3⋊D3—131no—
104C3×D3—131no—
105C3×D3C52×D1311yescharacteristic, complemented
106C3×C5—26no—
107C3×C5C5×D3×D1316yescomplemented
108C3×C5C2×C5×D3916yescomplemented
109C13C52×D3211yescharacteristic, complemented, Sylow
110C2×D3—391no—
111C2×D3—391no—
112C2×C5—36no—
113C2×C5—396no—
114C2×C5—1176no—
115C32C2×C52×D1311yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—391no—
118D3—131no—
119D3—391no—
120D3—391no—
121D3—781no—
122D3C52×D3911yescharacteristic, direct product factor
123C5C5×D3×D3916yesdirect product factor
124C22—1171noSylow
125C3—21no—
126C3C52×D3×D1311yescharacteristic, complemented
127C3C2×C52×D3911yescharacteristic, complemented
128C2—31no—
129C2—391no—
130C2—1171no—
subgroupG/H
center, hypercenterC52D3×D39
commutator, cosocle, hypocenterC32×C13C22×C52
FrattiniC1G
Fitting, socleC32×C52×C13C22
LCSG ▷ C32×C13
UCSC1 ◁ C52

Complements

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

NH ≅ G/Ntype
1. C52×C3⋊D39C2semidirect
2. C3×C52×D39C2semidirect
3. C3×C52×D3×C13C2semidirect
6. C32×C52×C13C22semidirect
7. C5×D3×D39C5direct (N × H)
12. C52×D39D3direct (N × H)
13. C52×D3×C13D3semidirect
16. C5×C3⋊D39C2×C5semidirect
17. C3×C5×D39C2×C5semidirect
18. C3×C5×D3×C13C2×C5semidirect
20. C3×C52×C13C2×D3semidirect
21. C3×C52×C13C2×D3semidirect
28. C32×C5×C13C22×C5semidirect
29. D3×D39C52direct (N × H)
32. C3×C52×D3D13semidirect
37. C5×D39C5×D3direct (N × H)
38. C5×D3×C13C5×D3semidirect
40. C52×C13D32semidirect
44. C3⋊D39C2×C52semidirect
45. C3×D39C2×C52semidirect
46. C3×D3×C13C2×C52semidirect
47. C32×C52C2×D13semidirect
49. C3×C5×C13C2×C5×D3semidirect
50. C3×C5×C13C2×C5×D3semidirect
60. C52×D3D39direct (N × H)
64. C32×C13C22×C52semidirect
68. C3×C5×D3C5×D13semidirect
73. D39C52×D3direct (N × H)
75. D3×C13C52×D3semidirect
77. C3×C52D3×D13semidirect
78. C3×C52C2×D39semidirect
79. C5×C13C5×D32semidirect
86. C32×C5C2×C5×D13semidirect
88. C3×C13C2×C52×D3semidirect
89. C3×C13C2×C52×D3semidirect
97. C5×D3C5×D39direct (N × H)
101. C52D3×D39direct (N × H)
105. C3×D3C52×D13semidirect
107. C3×C5C5×D3×D13semidirect
108. C3×C5C2×C5×D39semidirect
109. C13C52×D32semidirect
115. C32C2×C52×D13semidirect
122. D3C52×D39direct (N × H)
123. C5C5×D3×D39direct (N × H)
126. C3C52×D3×D13semidirect
127. C3C2×C52×D39semidirect

Maximal subgroups

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

subgroupindex
C52×C3⋊D392
C3×C52×D392
C3×C52×D3×C132
C2×C52×D393
C52×D3×D133
C5×D3×D395
C52×D3213