Finite Group Databasebeta

← C13×D15×C7⋊D7 #50304447

Subgroups — C13×D15×C7⋊D7 #50304447

Order 38220.

400 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 112 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×C13×D15C211yesmaximal, characteristic, complemented
3C13×C3⋊(C5⋊(C7⋊D7))C211yesmaximal, characteristic, complemented
4D5×C13×C7⋊D7—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6D3×C13×C7⋊D7—51nomaximal, Hall
7C13×C5⋊(C7⋊D7)—31no—
8C72×D5×C13—31no—
9C5×C13×C7⋊D7D311yescharacteristic, complemented
10C13×D7×D15—78nomaximal
11C13×C3⋊(C7⋊D7)—51no—
12D3×C72×C13—51no—
13C3×C13×C7⋊D7D511yescharacteristic, complemented
14C5×C72×C13C2×D311yescharacteristic, complemented, Hall
15D15×C7⋊D7C1311yesmaximal, characteristic, direct product factor, Hall
16C13×D105—78no—
17C7×C13×D15D718yescomplemented
18C3×C5×C13×D7—78no—
19C2×C13×C7⋊D7—151noHall
20C3×C72×C13C2×D511yescharacteristic, complemented, Hall
21D5×C13×D7—218no—
22C3⋊(C5⋊(C7⋊D7))C2×C1311yescharacteristic, complemented
23C72×D15C2×C1311yescharacteristic, complemented
24C3×C5×C7⋊D7C2×C1311yescharacteristic, complemented
25C3×C5×C7×C13C2×D718yescomplemented
26C2×C72×C13—151no—
27C13×C7⋊D7—151no—
28C13×C7⋊D7D1511yescharacteristic, direct product factor
29D3×C13×D7—358no—
30D5×C7⋊D7—31noHall
31C13×D35—218no—
32C7×D5×C13—38no—
33C5×C13×D7—78no—
34C2×C13×D15—491noHall
35C3×C5×C72C22×C1311yescharacteristic, complemented, Hall
36C72×C13C2×D1511yescharacteristic, complemented, Hall
37D3×C7⋊D7—51noHall
38C13×D21—358no—
39D3×C7×C13—58no—
40C3×C13×D7—78no—
41C5⋊(C7⋊D7)—31no—
42C72×D5—31no—
43C5×C7⋊D7D3×C1311yescharacteristic, complemented
44C5×C7×C13D3×D718yescomplemented
45D7×D15—78no—
46C2×C3×C5×C13—491no—
47C13×D15—491no—
48C13×D15C7⋊D711yescharacteristic, direct product factor
49C2×C13×D7—1058no—
50C3⋊(C7⋊D7)—51no—
51D3×C72—51no—
52C3×C7⋊D7D5×C1311yescharacteristic, complemented
53C3×C7×C13D5×D718yescomplemented
54C2×D5×C13—1471noHall
55C5×C72C2×D3×C1311yescharacteristic, complemented, Hall
56D105—78no—
57C7×D15C13×D718yescomplemented
58C3×C5×D7—78no—
59C2×C7⋊D7—151noHall
60C3×C5×C13C2×C7⋊D711yescharacteristic, complemented, Hall
61C2×C7×C13—158no—
62C13×D7—78no—
63C13×D7—1058no—
64C2×D3×C13—2451noHall
65C3×C72C2×D5×C1311yescharacteristic, complemented, Hall
66D5×D7—218no—
67C2×C5×C13—491no—
68D5×C13—31no—
69D5×C13—1471no—
70C3×C5×C7C2×C13×D718yescomplemented
71C2×C72—151no—
72C7⋊D7—151no—
73C7⋊D7C13×D1511yescharacteristic, direct product factor
74C7×C13D7×D1518yescomplemented
75D3×D7—358no—
76C2×C3×C13—491no—
77D3×C13—51no—
78D3×C13—2451no—
79D35—218no—
80C5×D7—78no—
81C7×D5—38no—
82C5×C13D3×C7⋊D711yescharacteristic, complemented, Hall
83C2×D15—491noHall
84C22×C13—7351noHall
85C72C2×C13×D1511yescharacteristic, complemented, Sylow
86D21—358no—
87C3×D7—78no—
88D3×C7—58no—
89C3×C13D5×C7⋊D711yescharacteristic, complemented, Hall
90C5×C7D3×C13×D718yescomplemented
91C2×C3×C5—491no—
92D15—491no—
93D15C13×C7⋊D711yescharacteristic, direct product factor
94C2×D7—1058no—
95C2×C13—151no—
96C2×C13—491no—
97C2×C13—7351no—
98C3×C7D5×C13×D718yescomplemented
99C2×D5—1471noHall
100C3×C5C2×C13×C7⋊D711yescharacteristic, complemented, Hall
101C2×C7—158no—
102D7—78no—
103D7—1058no—
104C13D15×C7⋊D711yescharacteristic, direct product factor, Sylow
105C2×D3—2451noHall
106C2×C5—491no—
107D5—31no—
108D5—1471no—
109C7C13×D7×D1518yescomplemented
110C2×C3—491no—
111D3—51no—
112D3—2451no—
113C5D3×C13×C7⋊D711yescharacteristic, complemented, Sylow
114C22—7351noSylow
115C3D5×C13×C7⋊D711yescharacteristic, complemented, Sylow
116C2—151no—
117C2—491no—
118C2—7351no—
subgroupG/H
center, hypercenterC13D15×C7⋊D7
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. C72×C13×D15C2semidirect
3. C13×C3⋊(C5⋊(C7⋊D7))C2semidirect
5. C3×C5×C72×C13C22semidirect
9. C5×C13×C7⋊D7D3semidirect
13. C3×C13×C7⋊D7D5semidirect
14. C5×C72×C13C2×D3semidirect
15. D15×C7⋊D7C13direct (N × H)
17. C7×C13×D15D7semidirect
20. C3×C72×C13C2×D5semidirect
22. C3⋊(C5⋊(C7⋊D7))C2×C13semidirect
23. C72×D15C2×C13semidirect
24. C3×C5×C7⋊D7C2×C13semidirect
25. C3×C5×C7×C13C2×D7semidirect
28. C13×C7⋊D7D15direct (N × H)
35. C3×C5×C72C22×C13semidirect
36. C72×C13C2×D15semidirect
43. C5×C7⋊D7D3×C13semidirect
44. C5×C7×C13D3×D7semidirect
48. C13×D15C7⋊D7direct (N × H)
52. C3×C7⋊D7D5×C13semidirect
53. C3×C7×C13D5×D7semidirect
55. C5×C72C2×D3×C13semidirect
57. C7×D15C13×D7semidirect
60. C3×C5×C13C2×C7⋊D7semidirect
65. C3×C72C2×D5×C13semidirect
70. C3×C5×C7C2×C13×D7semidirect
73. C7⋊D7C13×D15direct (N × H)
74. C7×C13D7×D15semidirect
82. C5×C13D3×C7⋊D7semidirect
85. C72C2×C13×D15semidirect
89. C3×C13D5×C7⋊D7semidirect
90. C5×C7D3×C13×D7semidirect
93. D15C13×C7⋊D7direct (N × H)
98. C3×C7D5×C13×D7semidirect
100. C3×C5C2×C13×C7⋊D7semidirect
104. C13D15×C7⋊D7direct (N × H)
109. C7C13×D7×D15semidirect
113. C5D3×C13×C7⋊D7semidirect
115. C3D5×C13×C7⋊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
C72×C13×D152
C13×C3⋊(C5⋊(C7⋊D7))2
D5×C13×C7⋊D73
D3×C13×C7⋊D75
C13×D7×D157
D15×C7⋊D713