Finite Group Databasebeta

← D5×(C13⋊C3)⋊(C7⋊D7) #50304214

Subgroups — D5×(C13⋊C3)⋊(C7⋊D7) #50304214

Order 38220.

400 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C5⋊((C13⋊C3)⋊(C7⋊D7))C211yesmaximal, characteristic, complemented
2C72×D5×C13⋊C3C211yesmaximal, characteristic, complemented
3C5×(C13⋊C3)⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
4D5×C7⋊D91C311yesmaximal, characteristic, complemented, Hall
5C5×C72×C13⋊C3C2211yescharacteristic, complemented, Hall
6C2×(C13⋊C3)⋊(C7⋊D7)—51nomaximal, Hall
7C5⋊(C7⋊D91)C2×C311yescharacteristic, complemented
8C72×D5×C13C2×C311yescharacteristic, complemented
9C5×C7⋊D91C2×C311yescharacteristic, complemented
10D5×(C13⋊C3)⋊D7—78nomaximal
11C2×C72×C13⋊C3—51no—
12(C13⋊C3)⋊(C7⋊D7)—51no—
13(C13⋊C3)⋊(C7⋊D7)D511yescharacteristic, direct product factor
14C5×C72×C13C22×C311yescharacteristic, complemented, Hall
15C3×D5×C7⋊D7—131nomaximal, Hall
16C5⋊((C13⋊C3)⋊D7)—78no—
17C7×D5×C13⋊C3D718yescomplemented
18C5×(C13⋊C3)⋊D7—78no—
19C2×C7⋊D91—51noHall
20C72×C13⋊C3C2×D511yescharacteristic, complemented, Hall
21D5×D91—78no—
22C3×C5⋊(C7⋊D7)—131no—
23C3×C72×D5—131no—
24C3×C5×C7⋊D7—131no—
25C5×C7×C13⋊C3C2×D718yescomplemented
26C2×C72×C13—51no—
27C7⋊D91—51no—
28C7⋊D91C3×D511yescharacteristic, complemented
29C2×(C13⋊C3)⋊D7—358no—
30D5×C7⋊D7—131noHall
31D455—78no—
32C7×D5×C13C3×D718yescomplemented
33C5×D91—78no—
34D5×D13⋊C3—491noHall
35C3×C5×C72—131noHall
36C72×C13C2×C3×D511yescharacteristic, complemented, Hall
37C2×C3×C7⋊D7—651noHall
38C2×C7×C13⋊C3—58no—
39(C13⋊C3)⋊D7—78no—
40(C13⋊C3)⋊D7—358no—
41C5⋊(C7⋊D7)—131no—
42C72×D5D13⋊C311yescharacteristic, complemented
43C5×C7⋊D7—131no—
44C5×C7×C13C2×C3×D718yescomplemented
45C3×D5×D7—918no—
46C5⋊(D13⋊C3)—491no—
47D5×C13⋊C3C7⋊D711yescharacteristic, complemented
48C5×D13⋊C3—491no—
49C2×D91—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
61C2×C7×C13—58no—
62D91—78no—
63D91—358no—
64C2×D13⋊C3—2451noHall
65C3×C72—131noHall
66D5×D7—918no—
67D65—491no—
68C5×D13—491no—
69D5×C13C3×C7⋊D711yescharacteristic, complemented
70C3×C5×C7—138no—
71C2×C72—51no—
72C7⋊D7—131no—
73C7⋊D7—651no—
74C7×C13C3×D5×D718yescomplemented
75C2×C3×D7—4558no—
76C2×C13⋊C3—51no—
77D13⋊C3—491no—
78D13⋊C3—2451no—
79D35—918no—
80C5×D7—918no—
81C7×D5(C13⋊C3)⋊D718yescomplemented
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×C7C2×(C13⋊C3)⋊D718yescomplemented
91C2×C3×C5—6371no—
92C3×D5—131no—
93C3×D5—6371no—
94C2×D7—4558no—
95C2×C13—51no—
96D13—491no—
97D13—2451no—
98C3×C7—138no—
99C2×D5—6371noHall
100C3×C5—131noHall
101C2×C7—58no—
102D7—918no—
103D7—4558no—
104C13C3×D5×C7⋊D711yescharacteristic, complemented, Sylow
105C22×C3—31851noHall
106C2×C5—6371no—
107D5—6371no—
108D5(C13⋊C3)⋊(C7⋊D7)11yescharacteristic, direct product factor
109C7D5×(C13⋊C3)⋊D718yescomplemented
110C2×C3—651no—
111C2×C3—31851no—
112C2×C3—6371no—
113C5C2×(C13⋊C3)⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
114C22—31851noSylow
115C3—131noSylow
116C2—51no—
117C2—31851no—
118C2—6371no—
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. C5⋊((C13⋊C3)⋊(C7⋊D7))C2semidirect
2. C72×D5×C13⋊C3C2semidirect
3. C5×(C13⋊C3)⋊(C7⋊D7)C2semidirect
4. D5×C7⋊D91C3semidirect
5. C5×C72×C13⋊C3C22semidirect
7. C5⋊(C7⋊D91)C2×C3semidirect
8. C72×D5×C13C2×C3semidirect
9. C5×C7⋊D91C2×C3semidirect
13. (C13⋊C3)⋊(C7⋊D7)D5direct (N × H)
14. C5×C72×C13C22×C3semidirect
17. C7×D5×C13⋊C3D7semidirect
20. C72×C13⋊C3C2×D5semidirect
25. C5×C7×C13⋊C3C2×D7semidirect
28. C7⋊D91C3×D5semidirect
32. C7×D5×C13C3×D7semidirect
36. C72×C13C2×C3×D5semidirect
42. C72×D5D13⋊C3semidirect
44. C5×C7×C13C2×C3×D7semidirect
47. D5×C13⋊C3C7⋊D7semidirect
53. C7×C13⋊C3D5×D7semidirect
55. C5×C72C2×D13⋊C3semidirect
60. C5×C13⋊C3C2×C7⋊D7semidirect
69. D5×C13C3×C7⋊D7semidirect
74. C7×C13C3×D5×D7semidirect
81. C7×D5(C13⋊C3)⋊D7semidirect
82. C5×C13C2×C3×C7⋊D7semidirect
85. C72D5×D13⋊C3semidirect
89. C13⋊C3D5×C7⋊D7semidirect
90. C5×C7C2×(C13⋊C3)⋊D7semidirect
104. C13C3×D5×C7⋊D7semidirect
108. D5(C13⋊C3)⋊(C7⋊D7)direct (N × H)
109. C7D5×(C13⋊C3)⋊D7semidirect
113. C5C2×(C13⋊C3)⋊(C7⋊D7)semidirect

Maximal subgroups

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

subgroupindex
C5⋊((C13⋊C3)⋊(C7⋊D7))2
C72×D5×C13⋊C32
C5×(C13⋊C3)⋊(C7⋊D7)2
D5×C7⋊D913
C2×(C13⋊C3)⋊(C7⋊D7)5
D5×(C13⋊C3)⋊D77
C3×D5×C7⋊D713