Finite Group Databasebeta

← C5×D39⋊(C7⋊D7) #50304410

Subgroups — C5×D39⋊(C7⋊D7) #50304410

Order 38220.

400 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 110 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⋊D91C211yesmaximal, characteristic, complemented
2C5×C72×D39C211yesmaximal, characteristic, complemented
3C5×C13×C3⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
4C5×D13×C7⋊D7—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6D39⋊(C7⋊D7)C511yesmaximal, characteristic, direct product factor, Hall
7C5×C7⋊D91D311yescharacteristic, complemented
8C5×C13×C7⋊D7—31no—
9C5×C72×D13—31no—
10C5×D21⋊D13—78nomaximal
11C13×C3⋊(C7⋊D7)C2×C511yescharacteristic, complemented
12C72×D39C2×C511yescharacteristic, complemented
13C3×C7⋊D91C2×C511yescharacteristic, complemented
14C5×C72×C13C2×D311yescharacteristic, complemented, Hall
15C5×D3×C7⋊D7—131nomaximal, Hall
16C5×C13×D21—78no—
17C5×C7×D39D718yescomplemented
18C3×C5×D91—78no—
19D13×C7⋊D7—31noHall
20C3×C72×C13C22×C511yescharacteristic, complemented, Hall
21C5×D7×D13—218no—
22C5×C3⋊(C7⋊D7)D1311yescharacteristic, complemented
23C5×D3×C72—131no—
24C3×C5×C7⋊D7—131no—
25C3×C5×C7×C13C2×D718yescomplemented
26C7⋊D91C5×D311yescharacteristic, complemented
27C13×C7⋊D7—31no—
28C72×D13—31no—
29D21⋊D13—78no—
30C2×C5×C7⋊D7—391noHall
31C5×D91—78no—
32C5×C13×D7—218no—
33C5×C7×D13—38no—
34C5×D3×D13—491noHall
35C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
36C72×C13C2×C5×D311yescharacteristic, complemented, Hall
37D3×C7⋊D7—131noHall
38C13×D21—78no—
39C7×D39C5×D718yescomplemented
40C3×D91—78no—
41C2×C5×C72—391no—
42C5×C7⋊D7—31no—
43C5×C7⋊D7—131no—
44C5×C7×C13D3×D718yescomplemented
45C5×D3×D7—918no—
46C5×D39C7⋊D711yescharacteristic, complemented
47C5×D3×C13—491no—
48C3×C5×D13—491no—
49D7×D13—218no—
50C3⋊(C7⋊D7)C5×D1311yescharacteristic, complemented
51D3×C72—131no—
52C3×C7⋊D7—131no—
53C3×C7×C13C2×C5×D718yescomplemented
54C2×C5×D13—1471noHall
55C5×C72D3×D1311yescharacteristic, complemented, Hall
56C5×D21—78no—
57C5×D3×C7—138no—
58C3×C5×D7—918no—
59C2×C7⋊D7—391noHall
60C3×C5×C13C2×C7⋊D711yescharacteristic, complemented, Hall
61D91—78no—
62C7×D13—38no—
63C13×D7—218no—
64D3×D13—491noHall
65C3×C72C2×C5×D1311yescharacteristic, complemented, Hall
66C2×C5×D7—2738no—
67C2×C5×C13—1471no—
68C5×D13—31no—
69C5×D13—491no—
70C3×C5×C7D7×D1318yescomplemented
71C2×C72—391no—
72C7⋊D7—31no—
73C7⋊D7—131no—
74C7×C13C5×D3×D718yescomplemented
75D3×D7—918no—
76D39C5×C7⋊D711yescharacteristic, complemented
77C3×D13—491no—
78D3×C13—491no—
79C2×C5×C7—398no—
80C5×D7—218no—
81C5×D7—918no—
82C5×C13D3×C7⋊D711yescharacteristic, complemented, Hall
83C2×C5×D3—6371noHall
84C2×D13—1471noHall
85C72C5×D3×D1311yescharacteristic, complemented, Sylow
86D21—78no—
87C3×D7—918no—
88D3×C7—138no—
89C3×C13C2×C5×C7⋊D711yescharacteristic, complemented, Hall
90C5×C7D21⋊D1318yescomplemented
91C2×C3×C5—6371no—
92C5×D3—131no—
93C5×D3—491no—
94C2×D7—2738no—
95C2×C13—1471no—
96D13—31no—
97D13—491no—
98C3×C7C5×D7×D1318yescomplemented
99C22×C5—19111noHall
100C3×C5D13×C7⋊D711yescharacteristic, complemented, Hall
101C2×C7—398no—
102D7—218no—
103D7—918no—
104C13C5×D3×C7⋊D711yescharacteristic, complemented, Sylow
105C2×D3—6371noHall
106C2×C5—391no—
107C2×C5—6371no—
108C2×C5—1471no—
109C7C5×D21⋊D1318yescomplemented
110C2×C3—6371no—
111D3—131no—
112D3—491no—
113C5D39⋊(C7⋊D7)11yescharacteristic, direct product factor, Sylow
114C22—19111noSylow
115C3C5×D13×C7⋊D711yescharacteristic, complemented, Sylow
116C2—391no—
117C2—6371no—
118C2—1471no—
subgroupG/H
center, hypercenterC5D39⋊(C7⋊D7)
commutator, cosocle, hypocenterC3×C72×C13C22×C5
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C3×C72×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7⋊D91C2semidirect
2. C5×C72×D39C2semidirect
3. C5×C13×C3⋊(C7⋊D7)C2semidirect
5. C3×C5×C72×C13C22semidirect
6. D39⋊(C7⋊D7)C5direct (N × H)
7. C5×C7⋊D91D3semidirect
11. C13×C3⋊(C7⋊D7)C2×C5semidirect
12. C72×D39C2×C5semidirect
13. C3×C7⋊D91C2×C5semidirect
14. C5×C72×C13C2×D3semidirect
17. C5×C7×D39D7semidirect
20. C3×C72×C13C22×C5semidirect
22. C5×C3⋊(C7⋊D7)D13semidirect
25. C3×C5×C7×C13C2×D7semidirect
26. C7⋊D91C5×D3semidirect
35. C3×C5×C72C2×D13semidirect
36. C72×C13C2×C5×D3semidirect
39. C7×D39C5×D7semidirect
44. C5×C7×C13D3×D7semidirect
46. C5×D39C7⋊D7semidirect
50. C3⋊(C7⋊D7)C5×D13semidirect
53. C3×C7×C13C2×C5×D7semidirect
55. C5×C72D3×D13semidirect
60. C3×C5×C13C2×C7⋊D7semidirect
65. C3×C72C2×C5×D13semidirect
70. C3×C5×C7D7×D13semidirect
74. C7×C13C5×D3×D7semidirect
76. D39C5×C7⋊D7semidirect
82. C5×C13D3×C7⋊D7semidirect
85. C72C5×D3×D13semidirect
89. C3×C13C2×C5×C7⋊D7semidirect
90. C5×C7D21⋊D13semidirect
98. C3×C7C5×D7×D13semidirect
100. C3×C5D13×C7⋊D7semidirect
104. C13C5×D3×C7⋊D7semidirect
109. C7C5×D21⋊D13semidirect
113. C5D39⋊(C7⋊D7)direct (N × H)
115. C3C5×D13×C7⋊D7semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7⋊D912
C5×C72×D392
C5×C13×C3⋊(C7⋊D7)2
C5×D13×C7⋊D73
D39⋊(C7⋊D7)5
C5×D21⋊D137
C5×D3×C7⋊D713