Finite Group Databasebeta

← C7⋊D7×D195 #50304448

Subgroups — C7⋊D7×D195 #50304448

Order 38220.

400 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 100 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
2C72×D195C211yesmaximal, characteristic, complemented
3C3⋊(C5⋊(C7⋊D91))C211yesmaximal, characteristic, complemented
4C7⋊D7×D65—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6D39×C7⋊D7—51nomaximal, Hall
7C5⋊(C7⋊D91)—31no—
8C72×D65—31no—
9C5×C13×C7⋊D7D311yescharacteristic, complemented
10D7×D195—78nomaximal
11C3⋊(C7⋊D91)—51no—
12C72×D39—51no—
13C3×C13×C7⋊D7D511yescharacteristic, complemented
14C5×C72×C13C2×D311yescharacteristic, complemented, Hall
15D15×C7⋊D7—131nomaximal, Hall
16D1365—78no—
17C7×D195D718yescomplemented
18C3×C5×C13×D7—78no—
19D13×C7⋊D7—151noHall
20C3×C72×C13C2×D511yescharacteristic, complemented, Hall
21D7×D65—218no—
22C3⋊(C5⋊(C7⋊D7))—131no—
23C72×D15—131no—
24C3×C5×C7⋊D7D1311yescharacteristic, complemented
25C3×C5×C7×C13C2×D718yescomplemented
26C7⋊D91—151no—
27C13×C7⋊D7D1511yescharacteristic, complemented
28C72×D13—151no—
29D7×D39—358no—
30D5×C7⋊D7—391noHall
31D455—218no—
32C7×D65—38no—
33C5×C13×D7—78no—
34C2×D195—491noHall
35C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
36C72×C13C2×D1511yescharacteristic, complemented, Hall
37D3×C7⋊D7—651noHall
38D273—358no—
39C7×D39—58no—
40C3×C13×D7—78no—
41C5⋊(C7⋊D7)—391no—
42C72×D5—391no—
43C5×C7⋊D7D3911yescharacteristic, complemented
44C5×C7×C13D3×D718yescomplemented
45D7×D15—918no—
46C2×C3×C5×C13—491no—
47D195—491no—
48D195C7⋊D711yescharacteristic, direct product factor
49D7×D13—1058no—
50C3⋊(C7⋊D7)—651no—
51D3×C72—651no—
52C3×C7⋊D7D6511yescharacteristic, complemented
53C3×C7×C13D5×D718yescomplemented
54C2×D65—1471noHall
55C5×C72C2×D3911yescharacteristic, complemented, Hall
56D105—918no—
57C7×D15—138no—
58C3×C5×D7—78no—
59C2×C7⋊D7—1951noHall
60C3×C5×C13C2×C7⋊D711yescharacteristic, complemented, Hall
61D91—1058no—
62C7×D13—158no—
63C13×D7—78no—
64C2×D39—2451noHall
65C3×C72C2×D6511yescharacteristic, complemented, Hall
66D5×D7—2738no—
67C2×C5×C13—491no—
68D65—31no—
69D65—1471no—
70C3×C5×C7D7×D1318yescomplemented
71C2×C72—1951no—
72C7⋊D7—1951no—
73C7⋊D7D19511yescharacteristic, direct product factor
74C7×C13D7×D1518yescomplemented
75D3×D7—4558no—
76C2×C3×C13—491no—
77D39—51no—
78D39—2451no—
79D35—2738no—
80C5×D7—78no—
81C7×D5—398no—
82C5×C13D3×C7⋊D711yescharacteristic, complemented, Hall
83C2×D15—6371noHall
84C2×D13—7351noHall
85C72C2×D19511yescharacteristic, complemented, Sylow
86D21—4558no—
87C3×D7—78no—
88D3×C7—658no—
89C3×C13D5×C7⋊D711yescharacteristic, complemented, Hall
90C5×C7D7×D3918yescomplemented
91C2×C3×C5—491no—
92D15—131no—
93D15—6371no—
94C2×D7—13658no—
95C2×C13—491no—
96D13—151no—
97D13—7351no—
98C3×C7D7×D6518yescomplemented
99C2×D5—19111noHall
100C3×C5D13×C7⋊D711yescharacteristic, complemented, Hall
101C2×C7—1958no—
102D7—78no—
103D7—13658no—
104C13D15×C7⋊D711yescharacteristic, complemented, Sylow
105C2×D3—31851noHall
106C2×C5—491no—
107D5—391no—
108D5—19111no—
109C7D7×D19518yescomplemented
110C2×C3—491no—
111D3—651no—
112D3—31851no—
113C5D39×C7⋊D711yescharacteristic, complemented, Sylow
114C22—95551noSylow
115C3C7⋊D7×D6511yescharacteristic, complemented, Sylow
116C2—491no—
117C2—95551no—
118C2—1951no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C13C22
LCSG ▷ C3×C5×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×C13×C7⋊D7C2semidirect
2. C72×D195C2semidirect
3. C3⋊(C5⋊(C7⋊D91))C2semidirect
5. C3×C5×C72×C13C22semidirect
9. C5×C13×C7⋊D7D3semidirect
13. C3×C13×C7⋊D7D5semidirect
14. C5×C72×C13C2×D3semidirect
17. C7×D195D7semidirect
20. C3×C72×C13C2×D5semidirect
24. C3×C5×C7⋊D7D13semidirect
25. C3×C5×C7×C13C2×D7semidirect
27. C13×C7⋊D7D15semidirect
35. C3×C5×C72C2×D13semidirect
36. C72×C13C2×D15semidirect
43. C5×C7⋊D7D39semidirect
44. C5×C7×C13D3×D7semidirect
48. D195C7⋊D7direct (N × H)
52. C3×C7⋊D7D65semidirect
53. C3×C7×C13D5×D7semidirect
55. C5×C72C2×D39semidirect
60. C3×C5×C13C2×C7⋊D7semidirect
65. C3×C72C2×D65semidirect
70. C3×C5×C7D7×D13semidirect
73. C7⋊D7D195direct (N × H)
74. C7×C13D7×D15semidirect
82. C5×C13D3×C7⋊D7semidirect
85. C72C2×D195semidirect
89. C3×C13D5×C7⋊D7semidirect
90. C5×C7D7×D39semidirect
98. C3×C7D7×D65semidirect
100. C3×C5D13×C7⋊D7semidirect
104. C13D15×C7⋊D7semidirect
109. C7D7×D195semidirect
113. C5D39×C7⋊D7semidirect
115. C3C7⋊D7×D65semidirect

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
C72×D1952
C3⋊(C5⋊(C7⋊D91))2
C7⋊D7×D653
D39×C7⋊D75
D7×D1957
D15×C7⋊D713