Finite Group Databasebeta

← C32×D13×D65 #44478229

Subgroups — C32×D13×D65 #44478229

Order 30420.

384 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 96 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×D13C211yesmaximal, characteristic, complemented
2C32×C13×D65C211yesmaximal, characteristic, complemented
3C32×C5⋊(C13⋊D13)C211yesmaximal, characteristic, complemented
4C3×D13×D65C314yesmaximal, direct product factor
5C32×C5×C132C2211yescharacteristic, complemented, Hall
6C32×D132—51nomaximal, Hall
7C3×C5⋊(C13⋊D13)C2×C314yescomplemented
8C3×C13×D65C2×C314yescomplemented
9C3×C5×C13×D13C2×C314yescomplemented
10D13×D65C3211yescharacteristic, direct product factor, Hall
11C32×C13⋊D13—51no—
12C32×C13×D13—51no—
13C32×C13×D13D511yescharacteristic, complemented
14C3×C5×C132C22×C314yescomplemented
15C2×C32×D65—131nomaximal
16C32×D5×D13—131nomaximal
17C3×D132—54no—
18C5⋊(C13⋊D13)C2×C3211yescharacteristic, complemented
19C13×D65C2×C3211yescharacteristic, complemented
20C5×C13×D13C2×C3211yescharacteristic, complemented
21C32×C132C2×D511yescharacteristic, complemented, Hall
22C2×C32×C5×C13—131no—
23C32×D65—131no—
24C32×D65—131no—
25C32×D65—266no—
26C32×D65D1311yescharacteristic, direct product factor
27C32×D5×C13—131no—
28C32×C5×D13D1311yescharacteristic, complemented
29C3×C13⋊D13—54no—
30C3×C13×D13—54no—
31C3×C13×D13C3×D514yescomplemented
32C5×C132C22×C3211yescharacteristic, complemented, Hall
33C2×C3×D65—134no—
34C3×D5×D13—134no—
35D132—51noHall
36C32×C5×C13—26no—
37C32×C5×C13C2×D1311yescharacteristic, complemented
38C32×C5×C13C2×D1311yescharacteristic, complemented
39C3×C132C2×C3×D514yescomplemented
40C2×C32×D13—651no—
41C2×C32×D13—651no—
42C2×C3×C5×C13—134no—
43C3×D65—134no—
44C3×D65—134no—
45C3×D65—2624no—
46C3×D65C3×D1314yesdirect product factor
47C3×D5×C13—134no—
48C3×C5×D13C3×D1314yescomplemented
49C13⋊D13—51no—
50C13×D13—51no—
51C13×D13C32×D511yescharacteristic, complemented
52C2×D65—131no—
53D5×D13—131no—
54C2×C32×C13—131no—
55C2×C32×C13—651no—
56C32×D13—51no—
57C32×D13—651no—
58C32×D13—651no—
59C32×D13—1306no—
60C32×D13D6511yescharacteristic, direct product factor
61C3×C5×C13—224no—
62C3×C5×C13C2×C3×D1314yescomplemented
63C3×C5×C13C2×C3×D1314yescomplemented
64C2×C32×D5—1691noHall
65C132C2×C32×D511yescharacteristic, complemented, Sylow
66C2×C3×D13—654no—
67C2×C3×D13—654no—
68C2×C5×C13—131no—
69D65—131no—
70D65—131no—
71D65—266no—
72D65C32×D1311yescharacteristic, direct product factor
73C5×D13C32×D1311yescharacteristic, complemented
74D5×C13—131no—
75C32×C13—26no—
76C32×C13D5×D1311yescharacteristic, complemented
77C32×C13C2×D6511yescharacteristic, complemented
78C2×C32×C5—131no—
79C32×D5—131no—
80C32×D5—1691no—
81C2×C3×C13—134no—
82C2×C3×C13—654no—
83C3×D13—54no—
84C3×D13—654no—
85C3×D13—654no—
86C3×D13—13024no—
87C3×D13C3×D6514yesdirect product factor
88C5×C13—26no—
89C5×C13C2×C32×D1311yescharacteristic, complemented
90C5×C13C2×C32×D1311yescharacteristic, complemented
91C2×C3×D5—1694no—
92C2×D13—651no—
93C2×D13—651no—
94C32×C5D13211yescharacteristic, complemented, Hall
95C3×C13—224no—
96C3×C13C3×D5×D1314yescomplemented
97C3×C13C2×C3×D6514yescomplemented
98C22×C32—8451noHall
99C2×C3×C5—134no—
100C3×D5—134no—
101C3×D5—1694no—
102C2×C13—131no—
103C2×C13—651no—
104D13—51no—
105D13—651no—
106D13—651no—
107D13—1306no—
108D13C32×D6511yescharacteristic, direct product factor
109C2×D5—1691noHall
110C2×C32—131no—
111C2×C32—651no—
112C2×C32—8451no—
113C3×C5C3×D13214yescomplemented
114C13—26no—
115C13C32×D5×D1311yescharacteristic, complemented
116C13C2×C32×D6511yescharacteristic, complemented
117C22×C3—8454no—
118C2×C5—131no—
119D5—131no—
120D5—1691no—
121C32D13×D6511yescharacteristic, direct product factor, Sylow
122C2×C3—134no—
123C2×C3—654no—
124C2×C3—8454no—
125C5C32×D13211yescharacteristic, complemented, Sylow
126C22—8451noSylow
127C3C3×D13×D6514yesdirect product factor
128C2—131no—
129C2—651no—
130C2—8451no—
subgroupG/H
center, hypercenterC32D13×D65
commutator, cosocle, hypocenterC5×C132C22×C32
FrattiniC1G
Fitting, socleC32×C5×C132C22
LCSG ▷ C5×C132
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C32×C5×C13×D13C2semidirect
2. C32×C13×D65C2semidirect
3. C32×C5⋊(C13⋊D13)C2semidirect
4. C3×D13×D65C3direct (N × H)
5. C32×C5×C132C22semidirect
7. C3×C5⋊(C13⋊D13)C2×C3semidirect
8. C3×C13×D65C2×C3semidirect
9. C3×C5×C13×D13C2×C3semidirect
10. D13×D65C32direct (N × H)
13. C32×C13×D13D5semidirect
14. C3×C5×C132C22×C3semidirect
18. C5⋊(C13⋊D13)C2×C32semidirect
19. C13×D65C2×C32semidirect
20. C5×C13×D13C2×C32semidirect
21. C32×C132C2×D5semidirect
26. C32×D65D13direct (N × H)
28. C32×C5×D13D13semidirect
31. C3×C13×D13C3×D5semidirect
32. C5×C132C22×C32semidirect
37. C32×C5×C13C2×D13semidirect
38. C32×C5×C13C2×D13semidirect
39. C3×C132C2×C3×D5semidirect
46. C3×D65C3×D13direct (N × H)
48. C3×C5×D13C3×D13semidirect
51. C13×D13C32×D5semidirect
60. C32×D13D65direct (N × H)
62. C3×C5×C13C2×C3×D13semidirect
63. C3×C5×C13C2×C3×D13semidirect
65. C132C2×C32×D5semidirect
72. D65C32×D13direct (N × H)
73. C5×D13C32×D13semidirect
76. C32×C13D5×D13semidirect
77. C32×C13C2×D65semidirect
87. C3×D13C3×D65direct (N × H)
89. C5×C13C2×C32×D13semidirect
90. C5×C13C2×C32×D13semidirect
94. C32×C5D132semidirect
96. C3×C13C3×D5×D13semidirect
97. C3×C13C2×C3×D65semidirect
108. D13C32×D65direct (N × H)
113. C3×C5C3×D132semidirect
115. C13C32×D5×D13semidirect
116. C13C2×C32×D65semidirect
121. C32D13×D65direct (N × H)
125. C5C32×D132semidirect
127. C3C3×D13×D65direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C13×D132
C32×C13×D652
C32×C5⋊(C13⋊D13)2
C3×D13×D653
C32×D1325
C2×C32×D6513
C32×D5×D1313