Finite Group Databasebeta

← (C5⋊(D13⋊C3))⋊(C7⋊D7) #50304215

Subgroups — (C5⋊(D13⋊C3))⋊(C7⋊D7) #50304215

Order 38220.

400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C13⋊C3×C5⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
2C72×C5⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
3C5×(C13⋊C3)⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
4D65⋊(C7⋊D7)C311yesmaximal, characteristic, complemented, Hall
5C5×C72×C13⋊C3C2211yescharacteristic, complemented, Hall
6D13⋊C3×C7⋊D7—51nomaximal, Hall
7C13×C5⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C72×D65C2×C311yescharacteristic, complemented
9C5×C7⋊D91C2×C311yescharacteristic, complemented
10(C5⋊(D13⋊C3))⋊D7—78nomaximal
11C13⋊C3×C7⋊D7—51no—
12(C13⋊C3)⋊(C7⋊D7)D511yescharacteristic, complemented
13C72×D13⋊C3—51no—
14C5×C72×C13C22×C311yescharacteristic, complemented, Hall
15C3×D5×C7⋊D7—131nomaximal, Hall
16C13⋊C3×D35—78no—
17C7×C5⋊(D13⋊C3)D718yescomplemented
18C5×(C13⋊C3)⋊D7—78no—
19D13×C7⋊D7—51noHall
20C72×C13⋊C3C2×D511yescharacteristic, complemented, Hall
21D35⋊D13—78no—
22C3×C5⋊(C7⋊D7)—131no—
23C3×C72×D5—131no—
24C3×C5×C7⋊D7—131no—
25C5×C7×C13⋊C3C2×D718yescomplemented
26C7⋊D91C3×D511yescharacteristic, complemented
27C13×C7⋊D7—51no—
28C72×D13—51no—
29D7×D13⋊C3—358no—
30D5×C7⋊D7—131noHall
31C13×D35—78no—
32C7×D65C3×D718yescomplemented
33C5×D91—78no—
34D5×D13⋊C3—491noHall
35C3×C5×C72—131noHall
36C72×C13C2×C3×D511yescharacteristic, complemented, Hall
37C2×C3×C7⋊D7—651noHall
38(C13⋊C3)⋊D7—78no—
39D7×C13⋊C3—358no—
40C7×D13⋊C3—58no—
41C5⋊(C7⋊D7)D13⋊C311yescharacteristic, complemented
42C72×D5—131no—
43C5×C7⋊D7—131no—
44C5×C7×C13C2×C3×D718yescomplemented
45C3×D5×D7—918no—
46C5⋊(D13⋊C3)C7⋊D711yescharacteristic, complemented
47D5×C13⋊C3—491no—
48C5×D13⋊C3—491no—
49D7×D13—358no—
50C2×C3×C72—651no—
51C3×C7⋊D7—131no—
52C3×C7⋊D7—651no—
53C7×C13⋊C3D5×D718yescomplemented
54D5×D13—491noHall
55C5×C72C2×D13⋊C311yescharacteristic, complemented, Hall
56C3×D35—918no—
57C3×C7×D5—138no—
58C3×C5×D7—918no—
59C2×C7⋊D7—651noHall
60C5×C13⋊C3C2×C7⋊D711yescharacteristic, complemented, Hall
61D91—78no—
62C7×D13—58no—
63C13×D7—358no—
64C2×D13⋊C3—2451noHall
65C3×C72—131noHall
66D5×D7—918no—
67D65C3×C7⋊D711yescharacteristic, complemented
68C5×D13—491no—
69D5×C13—491no—
70C3×C5×C7—138no—
71C2×C72—651no—
72C7⋊D7—51no—
73C7⋊D7—131no—
74C7×C13C3×D5×D718yescomplemented
75C2×C3×D7—4558no—
76C2×C13⋊C3—2451no—
77D13⋊C3—51no—
78D13⋊C3—491no—
79D35—78no—
80C5×D7—918no—
81C7×D5—138no—
82C5×C13C2×C3×C7⋊D711yescharacteristic, complemented, Hall
83C2×C3×D5—6371noHall
84C2×D13—2451noHall
85C72D5×D13⋊C311yescharacteristic, complemented, Sylow
86C2×C3×C7—658no—
87C3×D7—918no—
88C3×D7—4558no—
89C13⋊C3D5×C7⋊D711yescharacteristic, complemented, Hall
90C5×C7D7×D13⋊C318yescomplemented
91C2×C3×C5—6371no—
92C3×D5—131no—
93C3×D5—6371no—
94C2×D7—4558no—
95C2×C13—2451no—
96D13—51no—
97D13—491no—
98C3×C7—138no—
99C2×D5—6371noHall
100C3×C5—131noHall
101C2×C7—658no—
102D7—358no—
103D7—918no—
104C13C3×D5×C7⋊D711yescharacteristic, complemented, Sylow
105C22×C3—31851noHall
106C2×C5—6371no—
107D5—131no—
108D5—491no—
109C7(C5⋊(D13⋊C3))⋊D718yescomplemented
110C2×C3—651no—
111C2×C3—31851no—
112C2×C3—6371no—
113C5D13⋊C3×C7⋊D711yescharacteristic, complemented, Sylow
114C22—31851noSylow
115C3—131noSylow
116C2—651no—
117C2—6371no—
118C2—2451no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C13C22×C3
LCSG ▷ C5×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C13⋊C3×C5⋊(C7⋊D7)C2semidirect
2. C72×C5⋊(D13⋊C3)C2semidirect
3. C5×(C13⋊C3)⋊(C7⋊D7)C2semidirect
4. D65⋊(C7⋊D7)C3semidirect
5. C5×C72×C13⋊C3C22semidirect
7. C13×C5⋊(C7⋊D7)C2×C3semidirect
8. C72×D65C2×C3semidirect
9. C5×C7⋊D91C2×C3semidirect
12. (C13⋊C3)⋊(C7⋊D7)D5semidirect
14. C5×C72×C13C22×C3semidirect
17. C7×C5⋊(D13⋊C3)D7semidirect
20. C72×C13⋊C3C2×D5semidirect
25. C5×C7×C13⋊C3C2×D7semidirect
26. C7⋊D91C3×D5semidirect
32. C7×D65C3×D7semidirect
36. C72×C13C2×C3×D5semidirect
41. C5⋊(C7⋊D7)D13⋊C3semidirect
44. C5×C7×C13C2×C3×D7semidirect
46. C5⋊(D13⋊C3)C7⋊D7semidirect
53. C7×C13⋊C3D5×D7semidirect
55. C5×C72C2×D13⋊C3semidirect
60. C5×C13⋊C3C2×C7⋊D7semidirect
67. D65C3×C7⋊D7semidirect
74. C7×C13C3×D5×D7semidirect
82. C5×C13C2×C3×C7⋊D7semidirect
85. C72D5×D13⋊C3semidirect
89. C13⋊C3D5×C7⋊D7semidirect
90. C5×C7D7×D13⋊C3semidirect
104. C13C3×D5×C7⋊D7semidirect
109. C7(C5⋊(D13⋊C3))⋊D7semidirect
113. C5D13⋊C3×C7⋊D7semidirect

Maximal subgroups

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

subgroupindex
C13⋊C3×C5⋊(C7⋊D7)2
C72×C5⋊(D13⋊C3)2
C5×(C13⋊C3)⋊(C7⋊D7)2
D65⋊(C7⋊D7)3
D13⋊C3×C7⋊D75
(C5⋊(D13⋊C3))⋊D77
C3×D5×C7⋊D713