Finite Group Databasebeta

← C2×C5⋊((C13⋊C9)⋊D7) #30655102

Subgroups — C2×C5⋊((C13⋊C9)⋊D7) #30655102

Order 16380.

120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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⋊C9)⋊D7)C211yesmaximal, characteristic, direct product factor
2C5⋊((C13⋊C9)⋊D7)C211yesmaximal, characteristic, direct product factor
3C2×C5×C7×C13⋊C9C211yesmaximal, characteristic, complemented
4C2×C3×D455C311yesmaximal, characteristic
5C5×C7×C13⋊C9C2211yescharacteristic, complemented, Hall
6C2×(C13⋊C9)⋊D7—51nomaximal, Hall
7C3×D455C2×C311yescharacteristic
8C3×D455C2×C311yescharacteristic
9C2×C3×C5×C7×C13C2×C311yescharacteristic
10C2×C5⋊(D13⋊C9)—71nomaximal, Hall
11C2×D455C911yescharacteristic, complemented, Hall
12C2×C7×C13⋊C9D511yescharacteristic, complemented
13(C13⋊C9)⋊D7—51no—
14(C13⋊C9)⋊D7—51no—
15C3×C5×C7×C13C22×C311yescharacteristic
16C2×C9×D35—131nomaximal, Hall
17C2×C5×C13⋊C9D711yescharacteristic, complemented
18C5⋊(D13⋊C9)—71no—
19C5⋊(D13⋊C9)—71no—
20C2×C3×D91—51no—
21C2×C5×C7×C13C2×C911yescharacteristic, complemented
22D455C2×C911yescharacteristic, complemented
23D455C2×C911yescharacteristic, complemented
24C7×C13⋊C9C2×D511yescharacteristic, complemented, Hall
25C2×C3×D65—71no—
26C2×C5×C7×C9—131no—
27C9×D35—131no—
28C9×D35—131no—
29C5×C13⋊C9C2×D711yescharacteristic, complemented, Hall
30C2×C3×C7×C13C3×D511yescharacteristic
31C3×D91—51no—
32C3×D91—51no—
33C2×D13⋊C9—351noHall
34C5×C7×C13C22×C911yescharacteristic, complemented, Hall
35C2×C3×D35—391no—
36C2×C3×C5×C13C3×D711yescharacteristic
37C3×D65—71no—
38C3×D65—71no—
39C2×D91—51noHall
40C5×C7×C9—131noHall
41C3×C7×C13C2×C3×D511yescharacteristic
42C2×D65—71noHall
43C2×C9×D7—651noHall
44C2×C13⋊C9D3511yescharacteristic, complemented
45D13⋊C9—351no—
46D13⋊C9—351no—
47C2×C3×C5×C7D13⋊C311yescharacteristic
48C3×D35—391no—
49C3×D35—391no—
50C3×C5×C13C2×C3×D711yescharacteristic
51C2×C7×C13C9×D511yescharacteristic, complemented
52D91—51no—
53D91—51no—
54C2×C9×D5—911noHall
55C2×C3×D13—351no—
56C2×D35—391noHall
57C2×C5×C13C9×D711yescharacteristic, complemented
58D65—71no—
59D65—71no—
60C2×C7×C9—131no—
61C9×D7—651no—
62C9×D7—651no—
63C13⋊C9C2×D3511yescharacteristic, complemented, Hall
64C3×C5×C7C2×D13⋊C311yescharacteristic
65C7×C13C2×C9×D511yescharacteristic, complemented, Hall
66C2×C5×C9—131no—
67C9×D5—911no—
68C9×D5—911no—
69C2×C3×D7—1951no—
70C2×C3×C13C3×D3511yescharacteristic
71C3×D13—351no—
72C3×D13—351no—
73C2×C5×C7D13⋊C911yescharacteristic, complemented
74D35—391no—
75D35—391no—
76C5×C13C2×C9×D711yescharacteristic, complemented, Hall
77C7×C9—131noHall
78C2×C3×D5—2731no—
79C2×D13—351noHall
80C5×C9—131noHall
81C2×C3×C7C5⋊(D13⋊C3)11yescharacteristic
82C3×D7—651no—
83C3×D7—1951no—
84C3×C13C2×C3×D3511yescharacteristic
85C22×C9—4551noHall
86C5×C7C2×D13⋊C911yescharacteristic, complemented, Hall
87C2×C3×C5(C13⋊C3)⋊D711yescharacteristic
88C3×D5—2731no—
89C3×D5—2731no—
90C2×D7—1951noHall
91C2×C13C9×D3511yescharacteristic, complemented
92D13—351no—
93D13—351no—
94C3×C7C2×C5⋊(D13⋊C3)11yescharacteristic
95C2×D5—2731noHall
96C2×C9—131no—
97C2×C9—4551no—
98C2×C9—4551no—
99C3×C5C2×(C13⋊C3)⋊D711yescharacteristic
100C2×C7C5⋊(D13⋊C9)11yescharacteristic, complemented
101D7—651no—
102D7—1951no—
103C13C2×C9×D3511yescharacteristic, complemented, Sylow
104C22×C3—13651no—
105C2×C5(C13⋊C9)⋊D711yescharacteristic, complemented
106D5—2731no—
107D5—2731no—
108C9—131noSylow
109C7C2×C5⋊(D13⋊C9)11yescharacteristic, complemented, Sylow
110C2×C3—13651no—
111C2×C3—13651no—
112C2×C3C5⋊((C13⋊C3)⋊D7)11yescharacteristic
113C5C2×(C13⋊C9)⋊D711yescharacteristic, complemented, Sylow
114C22—13651noSylow
115C3C2×C5⋊((C13⋊C3)⋊D7)11yescharacteristic
116C2—13651no—
117C2—13651no—
118C2C5⋊((C13⋊C9)⋊D7)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3C5⋊((C13⋊C3)⋊D7)
commutator, hypocenterC5×C7×C13C22×C9
FrattiniC3C2×C5⋊((C13⋊C3)⋊D7)
Fitting, socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×D455C3
cosocleC3×C5×C7×C13C22×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C5⋊((C13⋊C9)⋊D7)C2direct (N × H)
2. C5⋊((C13⋊C9)⋊D7)C2direct (N × H)
3. C2×C5×C7×C13⋊C9C2semidirect
5. C5×C7×C13⋊C9C22semidirect
11. C2×D455C9semidirect
12. C2×C7×C13⋊C9D5semidirect
17. C2×C5×C13⋊C9D7semidirect
21. C2×C5×C7×C13C2×C9semidirect
22. D455C2×C9semidirect
23. D455C2×C9semidirect
24. C7×C13⋊C9C2×D5semidirect
29. C5×C13⋊C9C2×D7semidirect
34. C5×C7×C13C22×C9semidirect
44. C2×C13⋊C9D35semidirect
51. C2×C7×C13C9×D5semidirect
57. C2×C5×C13C9×D7semidirect
63. C13⋊C9C2×D35semidirect
65. C7×C13C2×C9×D5semidirect
73. C2×C5×C7D13⋊C9semidirect
76. C5×C13C2×C9×D7semidirect
86. C5×C7C2×D13⋊C9semidirect
91. C2×C13C9×D35semidirect
100. C2×C7C5⋊(D13⋊C9)semidirect
103. C13C2×C9×D35semidirect
105. C2×C5(C13⋊C9)⋊D7semidirect
109. C7C2×C5⋊(D13⋊C9)semidirect
113. C5C2×(C13⋊C9)⋊D7semidirect
118. C2C5⋊((C13⋊C9)⋊D7)direct (N × H)

Maximal subgroups

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

subgroupindex
C5⋊((C13⋊C9)⋊D7)2
C2×C5×C7×C13⋊C92
C2×C3×D4553
C2×(C13⋊C9)⋊D75
C2×C5⋊(D13⋊C9)7
C2×C9×D3513