Finite Group Databasebeta

← C13×#15668837 #50304442

Subgroups — C13×#15668837 #50304442

Order 38220.

208 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C3×C5×C13×C7⋊D7C211yesmaximal, characteristic, complemented
2C7×C13×D105C212yesmaximal, complemented
3C13×D35⋊D7—31nomaximal, Hall
4C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
5C13×D21⋊D7—51nomaximal, Hall
6C7×C13×D35—32no—
7C5×C13×C7⋊D7D311yescharacteristic, complemented
8C13×D7×D15—72nomaximal
9C7×C13×D21—52no—
10C3×C13×C7⋊D7D511yescharacteristic, complemented
11C5×C72×C13C2×D311yescharacteristic, complemented, Hall
12#15668837C1311yesmaximal, characteristic, direct product factor, Hall
13C13×D105D712yescomplemented
14C7×C13×D15—72no—
15C3×C5×C13×D7—72no—
16C3×C5×C13×D7—143no—
17C13×D72—151noHall
18C3×C72×C13C2×D511yescharacteristic, complemented, Hall
19D5×C13×D7—212no—
20C7×D105C2×C1312yescomplemented
21C3×C5×C7⋊D7C2×C1311yescharacteristic, complemented
22C3×C5×C7×C13—23no—
23C3×C5×C7×C13C2×D712yescomplemented
24C13×C7⋊D7D1511yescharacteristic, complemented
25C7×C13×D7—152no—
26D3×C13×D7—352no—
27D35⋊D7—31noHall
28C13×D35—32no—
29C7×D5×C13—212no—
30C5×C13×D7—72no—
31C5×C13×D7—143no—
32C2×C13×D15—491noHall
33C3×C5×C72C22×C1311yescharacteristic, complemented, Hall
34C72×C13C2×D1511yescharacteristic, complemented, Hall
35D21⋊D7—51noHall
36C13×D21—52no—
37D3×C7×C13—352no—
38C3×C13×D7—72no—
39C3×C13×D7—143no—
40C7×D35—32no—
41C5×C7⋊D7D3×C1311yescharacteristic, complemented
42C5×C7×C13—23no—
43C5×C7×C13D3×D712yescomplemented
44D7×D15—72no—
45C2×C3×C5×C13—491no—
46C13×D15—72no—
47C2×C13×D7—1052no—
48C7×D21—52no—
49C3×C7⋊D7D5×C1311yescharacteristic, complemented
50C3×C7×C13—23no—
51C3×C7×C13D5×D712yescomplemented
52C2×D5×C13—1471noHall
53C5×C72C2×D3×C1311yescharacteristic, complemented, Hall
54D105C13×D712yescomplemented
55C7×D15—72no—
56C3×C5×D7—72no—
57C3×C5×D7—143no—
58D72—151noHall
59C3×C5×C13D7211yescharacteristic, complemented, Hall
60C2×C7×C13—1052no—
61C13×D7—72no—
62C13×D7—143no—
63C13×D7—152no—
64C2×D3×C13—2451noHall
65C3×C72C2×D5×C1311yescharacteristic, complemented, Hall
66D5×D7—212no—
67C2×C5×C13—491no—
68D5×C13—212no—
69C3×C5×C7—23no—
70C3×C5×C7C2×C13×D712yescomplemented
71C7⋊D7C13×D1511yescharacteristic, complemented
72C7×D7—152no—
73C7×C13—23no—
74C7×C13D7×D1512yescomplemented
75D3×D7—352no—
76C2×C3×C13—491no—
77D3×C13—352no—
78D35—32no—
79C5×D7—72no—
80C5×D7—143no—
81C7×D5—212no—
82C5×C13D21⋊D711yescharacteristic, complemented, Hall
83C2×D15—491noHall
84C22×C13—7351noHall
85C72C2×C13×D1511yescharacteristic, complemented, Sylow
86D21—52no—
87C3×D7—72no—
88C3×D7—143no—
89D3×C7—352no—
90C3×C13D35⋊D711yescharacteristic, complemented, Hall
91C5×C7—23no—
92C5×C7D3×C13×D712yescomplemented
93C2×C3×C5—491no—
94D15—72no—
95C2×D7—1052no—
96C2×C13—491no—
97C2×C13—1052no—
98C3×C7—23no—
99C3×C7D5×C13×D712yescomplemented
100C2×D5—1471noHall
101C3×C5C13×D7211yescharacteristic, complemented, Hall
102C2×C7—1052no—
103D7—72no—
104D7—143no—
105D7—152no—
106C13#1566883711yescharacteristic, direct product factor, Sylow
107C2×D3—2451noHall
108C2×C5—491no—
109D5—212no—
110C7—23no—
111C7C13×D7×D1512yescomplemented
112C2×C3—491no—
113D3—352no—
114C5C13×D21⋊D711yescharacteristic, complemented, Sylow
115C22—7351noSylow
116C3C13×D35⋊D711yescharacteristic, complemented, Sylow
117C2—491no—
118C2—1052no—
subgroupG/H
center, hypercenterC13#15668837
commutator, cosocle, hypocenterC3×C5×C72C22×C13
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C3×C5×C72
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C3×C5×C13×C7⋊D7C2semidirect
2. C7×C13×D105C2semidirect
4. C3×C5×C72×C13C22semidirect
7. C5×C13×C7⋊D7D3semidirect
10. C3×C13×C7⋊D7D5semidirect
11. C5×C72×C13C2×D3semidirect
12. #15668837C13direct (N × H)
13. C13×D105D7semidirect
18. C3×C72×C13C2×D5semidirect
20. C7×D105C2×C13semidirect
21. C3×C5×C7⋊D7C2×C13semidirect
23. C3×C5×C7×C13C2×D7semidirect
24. C13×C7⋊D7D15semidirect
33. C3×C5×C72C22×C13semidirect
34. C72×C13C2×D15semidirect
41. C5×C7⋊D7D3×C13semidirect
43. C5×C7×C13D3×D7semidirect
49. C3×C7⋊D7D5×C13semidirect
51. C3×C7×C13D5×D7semidirect
53. C5×C72C2×D3×C13semidirect
54. D105C13×D7semidirect
59. C3×C5×C13D72semidirect
65. C3×C72C2×D5×C13semidirect
70. C3×C5×C7C2×C13×D7semidirect
71. C7⋊D7C13×D15semidirect
74. C7×C13D7×D15semidirect
82. C5×C13D21⋊D7semidirect
85. C72C2×C13×D15semidirect
90. C3×C13D35⋊D7semidirect
92. C5×C7D3×C13×D7semidirect
99. C3×C7D5×C13×D7semidirect
101. C3×C5C13×D72semidirect
106. C13#15668837direct (N × H)
111. C7C13×D7×D15semidirect
114. C5C13×D21⋊D7semidirect
116. C3C13×D35⋊D7semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C13×C7⋊D72
C7×C13×D1052
C13×D35⋊D73
C13×D21⋊D75
C13×D7×D157
#1566883713