Finite Group Databasebeta

← C3×C5×(C7⋊D7)⋊D13 #50304344

Subgroups — C3×C5×(C7⋊D7)⋊D13 #50304344

Order 38220.

208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 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×C7×D91C212yesmaximal, complemented
2C3×C5×C13×C7⋊D7C211yesmaximal, characteristic, complemented
3C5×(C7⋊D7)⋊D13C311yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
5C3×(C7⋊D7)⋊D13C511yesmaximal, characteristic, direct product factor, Hall
6C5×C13×C7⋊D7C2×C311yescharacteristic, complemented
7C5×C7×D91C2×C312yescomplemented
8C3×C5×D7×D13—72nomaximal
9C3×C13×C7⋊D7C2×C511yescharacteristic, complemented
10C3×C7×D91C2×C512yescomplemented
11C5×C72×C13C22×C311yescharacteristic, complemented, Hall
12C3×C5×D72—131nomaximal, Hall
13C3×C5×D91D712yescomplemented
14C3×C5×C13×D7—72no—
15C3×C5×C13×D7—143no—
16C3×C5×C7×D13—72no—
17(C7⋊D7)⋊D13C3×C511yescharacteristic, direct product factor, Hall
18C3×C72×C13C22×C511yescharacteristic, complemented, Hall
19C5×D7×D13—72no—
20C3×C5×C7⋊D7D1311yescharacteristic, complemented
21C3×C5×C7×D7—132no—
22C3×C5×C7×C13—23no—
23C3×C5×C7×C13C2×D712yescomplemented
24C13×C7⋊D7C2×C3×C511yescharacteristic, complemented
25C7×D91C2×C3×C512yescomplemented
26C3×D7×D13—72no—
27C5×D72—131noHall
28C5×D91C3×D712yescomplemented
29C5×C13×D7—72no—
30C5×C13×D7—143no—
31C5×C7×D13—72no—
32C2×C3×C5×D13—491noHall
33C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
34C72×C13C22×C3×C511yescharacteristic, complemented, Hall
35C3×D72—131noHall
36C3×D91C5×D712yescomplemented
37C3×C13×D7—72no—
38C3×C13×D7—143no—
39C3×C7×D13—72no—
40C5×C7⋊D7C3×D1311yescharacteristic, complemented
41C5×C7×D7—132no—
42C5×C7×C13—23no—
43C5×C7×C13C2×C3×D712yescomplemented
44C2×C3×C5×D7—912no—
45C2×C3×C5×C13—491no—
46C3×C5×D13—72no—
47D7×D13—72no—
48C3×C7⋊D7C5×D1311yescharacteristic, complemented
49C3×C7×D7—132no—
50C3×C7×C13—23no—
51C3×C7×C13C2×C5×D712yescomplemented
52C2×C5×D13—491noHall
53C5×C72C2×C3×D1311yescharacteristic, complemented, Hall
54C2×C3×C5×C7—912no—
55C3×C5×D7—72no—
56C3×C5×D7—132no—
57C3×C5×D7—143no—
58D72—131noHall
59C3×C5×C13D7211yescharacteristic, complemented, Hall
60D91C3×C5×D712yescomplemented
61C7×D13—72no—
62C13×D7—72no—
63C13×D7—143no—
64C2×C3×D13—491noHall
65C3×C72C2×C5×D1311yescharacteristic, complemented, Hall
66C2×C5×D7—912no—
67C2×C5×C13—491no—
68C5×D13—72no—
69C3×C5×C7—23no—
70C3×C5×C7D7×D1312yescomplemented
71C7⋊D7C3×C5×D1311yescharacteristic, complemented
72C7×D7—132no—
73C7×C13—23no—
74C7×C13C2×C3×C5×D712yescomplemented
75C2×C3×D7—912no—
76C2×C3×C13—491no—
77C3×D13—72no—
78C2×C5×C7—912no—
79C5×D7—72no—
80C5×D7—132no—
81C5×D7—143no—
82C5×C13C3×D7211yescharacteristic, complemented, Hall
83C22×C3×C5—6371noHall
84C2×D13—491noHall
85C72C2×C3×C5×D1311yescharacteristic, complemented, Sylow
86C2×C3×C7—912no—
87C3×D7—72no—
88C3×D7—132no—
89C3×D7—143no—
90C3×C13C5×D7211yescharacteristic, complemented, Hall
91C5×C7—23no—
92C5×C7C3×D7×D1312yescomplemented
93C2×C3×C5—491no—
94C2×C3×C5—912no—
95C2×D7—912no—
96C2×C13—491no—
97D13—72no—
98C3×C7—23no—
99C3×C7C5×D7×D1312yescomplemented
100C22×C5—6371noHall
101C3×C5(C7⋊D7)⋊D1311yescharacteristic, direct product factor, Hall
102C2×C7—912no—
103D7—72no—
104D7—132no—
105D7—143no—
106C13C3×C5×D7211yescharacteristic, complemented, Sylow
107C22×C3—6371noHall
108C2×C5—491no—
109C2×C5—912no—
110C7—23no—
111C7C3×C5×D7×D1312yescomplemented
112C2×C3—491no—
113C2×C3—912no—
114C5C3×(C7⋊D7)⋊D1311yescharacteristic, direct product factor, Sylow
115C22—6371noSylow
116C3C5×(C7⋊D7)⋊D1311yescharacteristic, direct product factor, Sylow
117C2—491no—
118C2—912no—
subgroupG/H
center, hypercenterC3×C5(C7⋊D7)⋊D13
commutator, cosocle, hypocenterC72×C13C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C72×C13
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D91C2semidirect
2. C3×C5×C13×C7⋊D7C2semidirect
3. C5×(C7⋊D7)⋊D13C3direct (N × H)
4. C3×C5×C72×C13C22semidirect
5. C3×(C7⋊D7)⋊D13C5direct (N × H)
6. C5×C13×C7⋊D7C2×C3semidirect
7. C5×C7×D91C2×C3semidirect
9. C3×C13×C7⋊D7C2×C5semidirect
10. C3×C7×D91C2×C5semidirect
11. C5×C72×C13C22×C3semidirect
13. C3×C5×D91D7semidirect
17. (C7⋊D7)⋊D13C3×C5direct (N × H)
18. C3×C72×C13C22×C5semidirect
20. C3×C5×C7⋊D7D13semidirect
23. C3×C5×C7×C13C2×D7semidirect
24. C13×C7⋊D7C2×C3×C5semidirect
25. C7×D91C2×C3×C5semidirect
28. C5×D91C3×D7semidirect
33. C3×C5×C72C2×D13semidirect
34. C72×C13C22×C3×C5semidirect
36. C3×D91C5×D7semidirect
40. C5×C7⋊D7C3×D13semidirect
43. C5×C7×C13C2×C3×D7semidirect
48. C3×C7⋊D7C5×D13semidirect
51. C3×C7×C13C2×C5×D7semidirect
53. C5×C72C2×C3×D13semidirect
59. C3×C5×C13D72semidirect
60. D91C3×C5×D7semidirect
65. C3×C72C2×C5×D13semidirect
70. C3×C5×C7D7×D13semidirect
71. C7⋊D7C3×C5×D13semidirect
74. C7×C13C2×C3×C5×D7semidirect
82. C5×C13C3×D72semidirect
85. C72C2×C3×C5×D13semidirect
90. C3×C13C5×D72semidirect
92. C5×C7C3×D7×D13semidirect
99. C3×C7C5×D7×D13semidirect
101. C3×C5(C7⋊D7)⋊D13direct (N × H)
106. C13C3×C5×D72semidirect
111. C7C3×C5×D7×D13semidirect
114. C5C3×(C7⋊D7)⋊D13direct (N × H)
116. C3C5×(C7⋊D7)⋊D13direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7×D912
C3×C5×C13×C7⋊D72
C5×(C7⋊D7)⋊D133
C3×(C7⋊D7)⋊D135
C3×C5×D7×D137
C3×C5×D7213