Finite Group Databasebeta

← C5×D7×C3⋊D39 #30655679

Subgroups — C5×D7×C3⋊D39 #30655679

Order 16380.

240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C5×C3⋊D273C211yesmaximal, characteristic, complemented
2C5×C7×C3⋊D39C211yesmaximal, characteristic, complemented
3C32×C5×C13×D7C211yesmaximal, characteristic, complemented
4C5×D7×D39—34nomaximal
5C32×C5×C7×C13C2211yescharacteristic, complemented, Hall
6D7×C3⋊D39C511yesmaximal, characteristic, direct product factor, Hall
7C5×D273—34no—
8C5×C7×D39—34no—
9C3×C5×C13×D7D314yescomplemented
10C2×C5×C3⋊D39—71nomaximal, Hall
11C5×D7×D13—91noHall
12C3⋊D273C2×C511yescharacteristic, complemented
13C7×C3⋊D39C2×C511yescharacteristic, complemented
14C32×C13×D7C2×C511yescharacteristic, complemented
15C3×C5×C7×C13C2×D314yescomplemented
16C5×D7×C3⋊D3—131nomaximal, Hall
17C2×C32×C5×C13—71no—
18C5×C3⋊D39—71no—
19C5×C3⋊D39D711yescharacteristic, direct product factor
20D7×D39—34no—
21C5×D91—91no—
22C5×C13×D7C3⋊D311yescharacteristic, complemented
23C5×C7×D13—91no—
24C32×C7×C13C22×C511yescharacteristic, complemented, Hall
25C2×C5×D39—214no—
26C5×C3⋊D21—131no—
27C5×C7×C3⋊D3—131no—
28C32×C5×D7D1311yescharacteristic, complemented
29C32×C5×C13C2×D711yescharacteristic, complemented, Hall
30D273—34no—
31C7×D39—34no—
32C3×C13×D7C5×D314yescomplemented
33C2×C3⋊D39—71noHall
34C5×C7×C13C2×C3⋊D311yescharacteristic, complemented, Hall
35C5×D3×D7—394no—
36C2×C3×C5×C13—74no—
37C5×D39—34no—
38C5×D39—214no—
39D7×D13—91noHall
40C32×C5×C7C2×D1311yescharacteristic, complemented, Hall
41C3×C7×C13C2×C5×D314yescomplemented
42C2×C5×D13—631noHall
43D7×C3⋊D3—131noHall
44C2×C32×C13—71no—
45C3⋊D39—71no—
46C3⋊D39C5×D711yescharacteristic, direct product factor
47C5×D21—394no—
48C5×D3×C7—394no—
49C3×C5×D7D3914yescomplemented
50C3×C5×C13D3×D714yescomplemented
51D91—91no—
52C7×D13—91no—
53C13×D7C5×C3⋊D311yescharacteristic, complemented
54C2×C5×C3⋊D3—911noHall
55C2×D39—214no—
56C2×C5×D7—1171noHall
57C2×C5×C13—71no—
58C5×D13—91no—
59C5×D13—631no—
60C3⋊D21—131no—
61C7×C3⋊D3—131no—
62C32×D7C5×D1311yescharacteristic, complemented
63C32×C13C2×C5×D711yescharacteristic, complemented, Hall
64C3×C5×C7C2×D3914yescomplemented
65C7×C13C2×C5×C3⋊D311yescharacteristic, complemented, Hall
66C2×C32×C5—71no—
67C5×C3⋊D3—131no—
68C5×C3⋊D3—911no—
69D3×D7—394no—
70C2×C3×C13—74no—
71D39—34no—
72D39—214no—
73C2×C5×C7—1171no—
74C5×D7—1171no—
75C5×D7C3⋊D3911yescharacteristic, direct product factor
76C5×C13D7×C3⋊D311yescharacteristic, complemented, Hall
77C32×C7C2×C5×D1311yescharacteristic, complemented, Hall
78C2×C5×D3—2734no—
79C2×D13—631noHall
80C32×C5D7×D1311yescharacteristic, complemented, Hall
81D21—394no—
82C3×D7C5×D3914yescomplemented
83D3×C7—394no—
84C3×C13C5×D3×D714yescomplemented
85C2×C3⋊D3—911noHall
86C5×C7C2×C3⋊D3911yescharacteristic, complemented, Hall
87C2×C3×C5—74no—
88C5×D3—2734no—
89C5×D3—394no—
90C2×D7—1171noHall
91C2×C13—71no—
92D13—91no—
93D13—631no—
94C3×C7C2×C5×D3914yescomplemented
95C22×C5—8191noHall
96C2×C32—71no—
97C3⋊D3—131no—
98C3⋊D3—911no—
99C3×C5D7×D3914yescomplemented
100C2×C7—1171no—
101D7—1171no—
102D7C5×C3⋊D3911yescharacteristic, direct product factor
103C13C5×D7×C3⋊D311yescharacteristic, complemented, Sylow
104C2×D3—2734no—
105C2×C5—71no—
106C2×C5—8191no—
107C2×C5—1171no—
108C32C5×D7×D1311yescharacteristic, complemented, Sylow
109C7C2×C5×C3⋊D3911yescharacteristic, complemented, Sylow
110C2×C3—74no—
111D3—2734no—
112D3—394no—
113C5D7×C3⋊D3911yescharacteristic, direct product factor, Sylow
114C22—8191noSylow
115C3C5×D7×D3914yescomplemented
116C2—71no—
117C2—8191no—
118C2—1171no—
subgroupG/H
center, hypercenterC5D7×C3⋊D39
commutator, cosocle, hypocenterC32×C7×C13C22×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C13C22
LCSG ▷ C32×C7×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊D273C2semidirect
2. C5×C7×C3⋊D39C2semidirect
3. C32×C5×C13×D7C2semidirect
5. C32×C5×C7×C13C22semidirect
6. D7×C3⋊D39C5direct (N × H)
9. C3×C5×C13×D7D3semidirect
12. C3⋊D273C2×C5semidirect
13. C7×C3⋊D39C2×C5semidirect
14. C32×C13×D7C2×C5semidirect
15. C3×C5×C7×C13C2×D3semidirect
19. C5×C3⋊D39D7direct (N × H)
22. C5×C13×D7C3⋊D3semidirect
24. C32×C7×C13C22×C5semidirect
28. C32×C5×D7D13semidirect
29. C32×C5×C13C2×D7semidirect
32. C3×C13×D7C5×D3semidirect
34. C5×C7×C13C2×C3⋊D3semidirect
40. C32×C5×C7C2×D13semidirect
41. C3×C7×C13C2×C5×D3semidirect
46. C3⋊D39C5×D7direct (N × H)
49. C3×C5×D7D39semidirect
50. C3×C5×C13D3×D7semidirect
53. C13×D7C5×C3⋊D3semidirect
62. C32×D7C5×D13semidirect
63. C32×C13C2×C5×D7semidirect
64. C3×C5×C7C2×D39semidirect
65. C7×C13C2×C5×C3⋊D3semidirect
75. C5×D7C3⋊D39direct (N × H)
76. C5×C13D7×C3⋊D3semidirect
77. C32×C7C2×C5×D13semidirect
80. C32×C5D7×D13semidirect
82. C3×D7C5×D39semidirect
84. C3×C13C5×D3×D7semidirect
86. C5×C7C2×C3⋊D39semidirect
94. C3×C7C2×C5×D39semidirect
99. C3×C5D7×D39semidirect
102. D7C5×C3⋊D39direct (N × H)
103. C13C5×D7×C3⋊D3semidirect
108. C32C5×D7×D13semidirect
109. C7C2×C5×C3⋊D39semidirect
113. C5D7×C3⋊D39direct (N × H)
115. C3C5×D7×D39semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊D2732
C5×C7×C3⋊D392
C32×C5×C13×D72
C5×D7×D393
D7×C3⋊D395
C2×C5×C3⋊D397
C5×D7×C3⋊D313