Finite Group Databasebeta

← D65⋊(C3⋊D39) #44478325

Subgroups — D65⋊(C3⋊D39) #44478325

Order 30420.

384 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C32×C13×D65C211yesmaximal, characteristic, complemented
2C5×C3⋊(C3⋊(C13⋊D13))C211yesmaximal, characteristic, complemented
3C13×C3⋊D195C211yesmaximal, characteristic, complemented
4D65⋊D39—34nomaximal
5C32×C5×C132C2211yescharacteristic, complemented, Hall
6D13×C3⋊D39—51nomaximal, Hall
7C13×D195—34no—
8C5×C3⋊(C13⋊D13)—34no—
9C3×C13×D65D314yescomplemented
10D65⋊D13—91noHall
11C3⋊(C3⋊(C13⋊D13))D511yescharacteristic, complemented
12C13×C3⋊D39—51no—
13C32×C13×D13—51no—
14C3×C5×C132C2×D314yescomplemented
15D65⋊(C3⋊D3)—131nomaximal
16D5×C3⋊D39—131nomaximal
17D13×D39—154no—
18C13×D65—91no—
19C13×D65C3⋊D311yescharacteristic, complemented
20C5×C13⋊D13—91no—
21C32×C132C2×D511yescharacteristic, complemented, Hall
22C3⋊D195D1311yescharacteristic, complemented
23C13×C3⋊D15—131no—
24C5×C3⋊D39—131no—
25C5×C3⋊D39—131no—
26C5×C3⋊D39—266no—
27C32×D65D1311yescharacteristic, complemented
28C32×D5×C13—131no—
29C3⋊(C13⋊D13)—34no—
30C13×D39—154no—
31C3×C13×D13—54no—
32C5×C132C2×C3⋊D311yescharacteristic, complemented, Hall
33D15⋊D13—394no—
34D5×D39—394no—
35D132—451noHall
36C32×C5×C13—26no—
37C32×C5×C13C2×D1311yescharacteristic, complemented
38C32×C5×C13C2×D1311yescharacteristic, complemented
39C3×C132D3×D514yescomplemented
40C2×C3⋊D39—651no—
41C3⋊D3×D13—651no—
42D195—34no—
43C13×D15—394no—
44C5×D39—394no—
45C5×D39—394no—
46C5×D39—7824no—
47C3×D65D3914yescomplemented
48C3×D5×C13—134no—
49C13⋊D13—91no—
50C13×D13—51no—
51C13×D13—451no—
52D5×D13—1171no—
53D5×D13—1171no—
54C2×C32×C13—651no—
55C3⋊D39—51no—
56C3⋊D39—131no—
57C3⋊D39—131no—
58C3⋊D39—266no—
59C13×C3⋊D3—651no—
60C32×D13—51no—
61C3×C5×C13—224no—
62C3×C5×C13D3×D1314yescomplemented
63C3×C5×C13C2×D3914yescomplemented
64D5×C3⋊D3—1691noHall
65C132D5×C3⋊D311yescharacteristic, complemented, Sylow
66C2×D39—1954no—
67D3×D13—1954no—
68D65—91no—
69D65C3⋊D3911yescharacteristic, complemented
70C5×D13—1171no—
71C5×D13—1171no—
72C5×D13—2346no—
73D5×C13—131no—
74D5×C13—1171no—
75C32×C13—26no—
76C32×C13D5×D1311yescharacteristic, complemented
77C32×C13D5×D1311yescharacteristic, complemented
78C3⋊D15—131no—
79C5×C3⋊D3—1691no—
80C32×D5—131no—
81C2×C3×C13—654no—
82D39—154no—
83D39—394no—
84D39—394no—
85D39—7824no—
86C3×D13—54no—
87D3×C13—1954no—
88C5×C13—26no—
89C5×C13C3⋊D3×D1311yescharacteristic, complemented
90C5×C13C2×C3⋊D3911yescharacteristic, complemented
91D3×D5—5074no—
92C2×D13—5851no—
93C2×D13—5851no—
94C32×C5D13211yescharacteristic, complemented, Hall
95C3×C13—224no—
96C3×C13D5×D3914yescomplemented
97C3×C13D15⋊D1314yescomplemented
98C2×C3⋊D3—8451noHall
99D15—394no—
100C3×D5—134no—
101C5×D3—5074no—
102C2×C13—651no—
103C2×C13—5851no—
104D13—51no—
105D13—451no—
106D13—1171no—
107D13—1171no—
108D13—2346no—
109C2×D5—15211noHall
110C2×C32—651no—
111C3⋊D3—651no—
112C3⋊D3—1691no—
113C3×C5D13×D3914yescomplemented
114C13—26no—
115C13D5×C3⋊D3911yescharacteristic, complemented
116C13D65⋊(C3⋊D3)11yescharacteristic, complemented
117C2×D3—25354no—
118C2×C5—15211no—
119D5—131no—
120D5—1171no—
121C32D65⋊D1311yescharacteristic, complemented, Sylow
122C2×C3—654no—
123D3—1954no—
124D3—5074no—
125C5D13×C3⋊D3911yescharacteristic, complemented, Sylow
126C22—76051noSylow
127C3D65⋊D3914yescomplemented
128C2—651no—
129C2—5851no—
130C2—15211no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C132C22
LCSG ▷ C32×C5×C132
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C13×D65C2semidirect
2. C5×C3⋊(C3⋊(C13⋊D13))C2semidirect
3. C13×C3⋊D195C2semidirect
5. C32×C5×C132C22semidirect
9. C3×C13×D65D3semidirect
11. C3⋊(C3⋊(C13⋊D13))D5semidirect
14. C3×C5×C132C2×D3semidirect
19. C13×D65C3⋊D3semidirect
21. C32×C132C2×D5semidirect
22. C3⋊D195D13semidirect
27. C32×D65D13semidirect
32. C5×C132C2×C3⋊D3semidirect
37. C32×C5×C13C2×D13semidirect
38. C32×C5×C13C2×D13semidirect
39. C3×C132D3×D5semidirect
47. C3×D65D39semidirect
62. C3×C5×C13D3×D13semidirect
63. C3×C5×C13C2×D39semidirect
65. C132D5×C3⋊D3semidirect
69. D65C3⋊D39semidirect
76. C32×C13D5×D13semidirect
77. C32×C13D5×D13semidirect
89. C5×C13C3⋊D3×D13semidirect
90. C5×C13C2×C3⋊D39semidirect
94. C32×C5D132semidirect
96. C3×C13D5×D39semidirect
97. C3×C13D15⋊D13semidirect
113. C3×C5D13×D39semidirect
115. C13D5×C3⋊D39semidirect
116. C13D65⋊(C3⋊D3)semidirect
121. C32D65⋊D13semidirect
125. C5D13×C3⋊D39semidirect
127. C3D65⋊D39semidirect

Maximal subgroups

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

subgroupindex
C32×C13×D652
C5×C3⋊(C3⋊(C13⋊D13))2
C13×C3⋊D1952
D65⋊D393
D13×C3⋊D395
D65⋊(C3⋊D3)13
D5×C3⋊D3913