Finite Group Databasebeta

← #44478326

Subgroups — #44478326

Order 30420.

384 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 61 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×C5⋊(C13⋊D13)C211yesmaximal, characteristic, complemented
2C5×C13×C3⋊D39C211yesmaximal, characteristic, complemented
3C13×C3⋊D195C211yesmaximal, characteristic, complemented
4D39⋊D65—34nomaximal
5C32×C5×C132C2211yescharacteristic, complemented, Hall
6#20258962—51nomaximal, Hall
7C13×D195—34no—
8C5×C13×D39—34no—
9C3×C5⋊(C13⋊D13)D314yescomplemented
10D13×D65—91noHall
11C13×C3⋊D39—51no—
12C13×C3⋊D39D511yescharacteristic, complemented
13C32×C13⋊D13—51no—
14C3×C5×C132C2×D314yescomplemented
15D65⋊(C3⋊D3)—131nomaximal
16C3⋊D3×D65—131nomaximal
17D39⋊D13—154no—
18C5⋊(C13⋊D13)C3⋊D311yescharacteristic, complemented
19C13×D65—91no—
20C5×C13×D13—91no—
21C32×C132C2×D511yescharacteristic, complemented, Hall
22C3⋊D195D1311yescharacteristic, complemented
23C13×C3⋊D15—131no—
24C5×C3⋊D39D1311yescharacteristic, complemented
25C5×C13×C3⋊D3—131no—
26C32×D65—131no—
27C32×D65—131no—
28C32×D65—266no—
29C13×D39—34no—
30C13×D39—154no—
31C3×C13⋊D13—54no—
32C5×C132C2×C3⋊D311yescharacteristic, complemented, Hall
33D15⋊D13—394no—
34D3×D65—394no—
35D132—451noHall
36C32×C5×C13—26no—
37C32×C5×C13C2×D1311yescharacteristic, complemented
38C32×C5×C13C2×D1311yescharacteristic, complemented
39C3×C132D3×D514yescomplemented
40C3⋊D3×D13—651no—
41C3⋊D3×D13—651no—
42D195—34no—
43C13×D15—394no—
44C5×D39—34no—
45C5×D3×C13—394no—
46C3×D65—134no—
47C3×D65—134no—
48C3×D65—2624no—
49C13⋊D13—51no—
50C13×D13—91no—
51C13×D13—451no—
52C2×D65—1171no—
53D5×D13—1171no—
54C3⋊D39—51no—
55C3⋊D39D6511yescharacteristic, complemented
56C13×C3⋊D3—131no—
57C13×C3⋊D3—651no—
58C32×D13—651no—
59C32×D13—651no—
60C32×D13—1306no—
61C3×C5×C13—224no—
62C3×C5×C13D3×D1314yescomplemented
63C3×C5×C13D3×D1314yescomplemented
64D5×C3⋊D3—1691noHall
65C132D5×C3⋊D311yescharacteristic, complemented, Sylow
66D3×D13—1954no—
67D3×D13—1954no—
68C2×C5×C13—1171no—
69D65—91no—
70D65—131no—
71D65—131no—
72D65—266no—
73C5×D13—91no—
74D5×C13—1171no—
75C32×C13—26no—
76C32×C13D5×D1311yescharacteristic, complemented
77C32×C13C2×D6511yescharacteristic, complemented
78C3⋊D15—131no—
79C5×C3⋊D3—131no—
80C32×D5—1691no—
81D39—34no—
82D39—154no—
83C3×D13—654no—
84C3×D13—654no—
85C3×D13—13024no—
86D3×C13—394no—
87D3×C13—1954no—
88C5×C13—26no—
89C5×C13C3⋊D3×D1311yescharacteristic, complemented
90C5×C13C3⋊D3×D1311yescharacteristic, complemented
91D3×D5—5074no—
92C2×D13—5851no—
93C2×D13—5851no—
94C32×C5D13211yescharacteristic, complemented, Hall
95C3×C13—224no—
96C3×C13D3×D6514yescomplemented
97C3×C13D15⋊D1314yescomplemented
98C2×C3⋊D3—8451noHall
99D15—394no—
100C3×D5—1694no—
101C5×D3—394no—
102C2×C13—5851no—
103C2×C13—1171no—
104D13—91no—
105D13—451no—
106D13—651no—
107D13—651no—
108D13—1306no—
109C2×D5—15211noHall
110C2×C32—8451no—
111C3⋊D3—131no—
112C3⋊D3—651no—
113C3×C5D39⋊D1314yescomplemented
114C13—26no—
115C13C3⋊D3×D6511yescharacteristic, complemented
116C13D65⋊(C3⋊D3)11yescharacteristic, complemented
117C2×D3—25354no—
118C2×C5—1171no—
119D5—1171no—
120D5—1691no—
121C32D13×D6511yescharacteristic, complemented, Sylow
122C2×C3—8454no—
123D3—394no—
124D3—1954no—
125C5#2025896211yescharacteristic, complemented, Sylow
126C22—76051noSylow
127C3D39⋊D6514yescomplemented
128C2—5851no—
129C2—8451no—
130C2—1171no—
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×C5⋊(C13⋊D13)C2semidirect
2. C5×C13×C3⋊D39C2semidirect
3. C13×C3⋊D195C2semidirect
5. C32×C5×C132C22semidirect
9. C3×C5⋊(C13⋊D13)D3semidirect
12. C13×C3⋊D39D5semidirect
14. C3×C5×C132C2×D3semidirect
18. C5⋊(C13⋊D13)C3⋊D3semidirect
21. C32×C132C2×D5semidirect
22. C3⋊D195D13semidirect
24. C5×C3⋊D39D13semidirect
32. C5×C132C2×C3⋊D3semidirect
37. C32×C5×C13C2×D13semidirect
38. C32×C5×C13C2×D13semidirect
39. C3×C132D3×D5semidirect
55. C3⋊D39D65semidirect
62. C3×C5×C13D3×D13semidirect
63. C3×C5×C13D3×D13semidirect
65. C132D5×C3⋊D3semidirect
76. C32×C13D5×D13semidirect
77. C32×C13C2×D65semidirect
89. C5×C13C3⋊D3×D13semidirect
90. C5×C13C3⋊D3×D13semidirect
94. C32×C5D132semidirect
96. C3×C13D3×D65semidirect
97. C3×C13D15⋊D13semidirect
113. C3×C5D39⋊D13semidirect
115. C13C3⋊D3×D65semidirect
116. C13D65⋊(C3⋊D3)semidirect
121. C32D13×D65semidirect
125. C5#20258962semidirect
127. C3D39⋊D65semidirect

Maximal subgroups

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

subgroupindex
C32×C5⋊(C13⋊D13)2
C5×C13×C3⋊D392
C13×C3⋊D1952
D39⋊D653
#202589625
D65⋊(C3⋊D3)13
C3⋊D3×D6513