Finite Group Databasebeta

← C5×D3×C7⋊D91 #50304409

Subgroups — C5×D3×C7⋊D91 #50304409

Order 38220.

400 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 128 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×D3×C72×C13C211yesmaximal, characteristic, complemented
3C5×C3⋊(C7⋊D91)C211yesmaximal, characteristic, complemented
4C2×C5×C7⋊D91—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6D3×C7⋊D91C511yesmaximal, characteristic, direct product factor, Hall
7C5×C7⋊D91—31no—
8C5×C7⋊D91D311yescharacteristic, direct product factor
9C2×C5×C72×C13—31no—
10C5×D3×D91—78nomaximal
11C3⋊(C7⋊D91)C2×C511yescharacteristic, complemented
12D3×C72×C13C2×C511yescharacteristic, complemented
13C3×C7⋊D91C2×C511yescharacteristic, complemented
14C5×C72×C13C2×D311yescharacteristic, complemented, Hall
15C5×D3×C7⋊D7—131nomaximal, Hall
16C5×D273—78no—
17C5×D3×C7×C13D718yescomplemented
18C3×C5×D91—78no—
19C2×C7⋊D91—31noHall
20C3×C72×C13C22×C511yescharacteristic, complemented, Hall
21C2×C5×D91—218no—
22C5×C3⋊(C7⋊D7)—131no—
23C5×D3×C72D1311yescharacteristic, complemented
24C3×C5×C7⋊D7—131no—
25C3×C5×C7×C13C2×D718yescomplemented
26C2×C72×C13—31no—
27C7⋊D91—31no—
28C7⋊D91C5×D311yescharacteristic, direct product factor
29D3×D91—78no—
30C2×C5×C7⋊D7—391noHall
31C2×C5×C7×C13—38no—
32C5×D91—78no—
33C5×D91—218no—
34C5×D3×D13—491noHall
35C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
36C72×C13C2×C5×D311yescharacteristic, complemented, Hall
37D3×C7⋊D7—131noHall
38D273—78no—
39D3×C7×C13C5×D718yescomplemented
40C3×D91—78no—
41C2×C5×C72—31no—
42C5×C7⋊D7—131no—
43C5×C7⋊D7—391no—
44C5×C7×C13D3×D718yescomplemented
45C5×D3×D7—918no—
46C5×D39—491no—
47C5×D3×C13C7⋊D711yescharacteristic, complemented
48C3×C5×D13—491no—
49C2×D91—218no—
50C3⋊(C7⋊D7)—131no—
51D3×C72C5×D1311yescharacteristic, complemented
52C3×C7⋊D7—131no—
53C3×C7×C13C2×C5×D718yescomplemented
54C2×C5×D13—1471noHall
55C5×C72D3×D1311yescharacteristic, complemented, Hall
56C5×D21—918no—
57C5×D3×C7D9118yescomplemented
58C3×C5×D7—918no—
59C2×C7⋊D7—391noHall
60C3×C5×C13C2×C7⋊D711yescharacteristic, complemented, Hall
61C2×C7×C13—38no—
62D91—78no—
63D91—218no—
64D3×D13—491noHall
65C3×C72C2×C5×D1311yescharacteristic, complemented, Hall
66C2×C5×D7—2738no—
67C2×C5×C13—31no—
68C5×D13—491no—
69C5×D13—1471no—
70C3×C5×C7C2×D9118yescomplemented
71C2×C72—31no—
72C7⋊D7—131no—
73C7⋊D7—391no—
74C7×C13C5×D3×D718yescomplemented
75D3×D7—918no—
76D39—491no—
77C3×D13—491no—
78D3×C13C5×C7⋊D711yescharacteristic, complemented
79C2×C5×C7—38no—
80C5×D7—2738no—
81C5×D7—918no—
82C5×C13D3×C7⋊D711yescharacteristic, complemented, Hall
83C2×C5×D3—6371noHall
84C2×D13—1471noHall
85C72C5×D3×D1311yescharacteristic, complemented, Sylow
86D21—918no—
87C3×D7—918no—
88D3×C7C5×D9118yescomplemented
89C3×C13C2×C5×C7⋊D711yescharacteristic, complemented, Hall
90C5×C7D3×D9118yescomplemented
91C2×C3×C5—6371no—
92C5×D3—6371no—
93C5×D3C7⋊D9111yescharacteristic, direct product factor
94C2×D7—2738no—
95C2×C13—31no—
96D13—491no—
97D13—1471no—
98C3×C7C2×C5×D9118yescomplemented
99C22×C5—19111noHall
100C3×C5C2×C7⋊D9111yescharacteristic, complemented, Hall
101C2×C7—38no—
102D7—2738no—
103D7—918no—
104C13C5×D3×C7⋊D711yescharacteristic, complemented, Sylow
105C2×D3—6371noHall
106C2×C5—31no—
107C2×C5—19111no—
108C2×C5—6371no—
109C7C5×D3×D9118yescomplemented
110C2×C3—6371no—
111D3—6371no—
112D3C5×C7⋊D9111yescharacteristic, direct product factor
113C5D3×C7⋊D9111yescharacteristic, direct product factor, Sylow
114C22—19111noSylow
115C3C2×C5×C7⋊D9111yescharacteristic, complemented, Sylow
116C2—31no—
117C2—19111no—
118C2—6371no—
subgroupG/H
center, hypercenterC5D3×C7⋊D91
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×D3×C72×C13C2semidirect
3. C5×C3⋊(C7⋊D91)C2semidirect
5. C3×C5×C72×C13C22semidirect
6. D3×C7⋊D91C5direct (N × H)
8. C5×C7⋊D91D3direct (N × H)
11. C3⋊(C7⋊D91)C2×C5semidirect
12. D3×C72×C13C2×C5semidirect
13. C3×C7⋊D91C2×C5semidirect
14. C5×C72×C13C2×D3semidirect
17. C5×D3×C7×C13D7semidirect
20. C3×C72×C13C22×C5semidirect
23. C5×D3×C72D13semidirect
25. C3×C5×C7×C13C2×D7semidirect
28. C7⋊D91C5×D3direct (N × H)
35. C3×C5×C72C2×D13semidirect
36. C72×C13C2×C5×D3semidirect
39. D3×C7×C13C5×D7semidirect
44. C5×C7×C13D3×D7semidirect
47. C5×D3×C13C7⋊D7semidirect
51. D3×C72C5×D13semidirect
53. C3×C7×C13C2×C5×D7semidirect
55. C5×C72D3×D13semidirect
57. C5×D3×C7D91semidirect
60. C3×C5×C13C2×C7⋊D7semidirect
65. C3×C72C2×C5×D13semidirect
70. C3×C5×C7C2×D91semidirect
74. C7×C13C5×D3×D7semidirect
78. D3×C13C5×C7⋊D7semidirect
82. C5×C13D3×C7⋊D7semidirect
85. C72C5×D3×D13semidirect
88. D3×C7C5×D91semidirect
89. C3×C13C2×C5×C7⋊D7semidirect
90. C5×C7D3×D91semidirect
93. C5×D3C7⋊D91direct (N × H)
98. C3×C7C2×C5×D91semidirect
100. C3×C5C2×C7⋊D91semidirect
104. C13C5×D3×C7⋊D7semidirect
109. C7C5×D3×D91semidirect
112. D3C5×C7⋊D91direct (N × H)
113. C5D3×C7⋊D91direct (N × H)
115. C3C2×C5×C7⋊D91semidirect

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×D3×C72×C132
C5×C3⋊(C7⋊D91)2
C2×C5×C7⋊D913
D3×C7⋊D915
C5×D3×D917
C5×D3×C7⋊D713