Finite Group Databasebeta

← D5×C11×D171 #49178397

Subgroups — D5×C11×D171 #49178397

Order 37620.

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C11×D855C211yesmaximal, characteristic, complemented
2C5×C11×D171C211yesmaximal, characteristic, complemented
3C9×D5×C11×C19C211yesmaximal, characteristic, complemented
4D5×C11×D57—31nomaximal
5C5×C9×C11×C19C2211yescharacteristic, complemented, Hall
6C2×C11×D171—51nomaximal, Hall
7C11×D285—31no—
8C5×C11×D57—31no—
9C3×D5×C11×C19D311yescharacteristic
10D5×C11×D19—91noHall
11C11×D171—51no—
12C11×D171D511yescharacteristic, direct product factor
13C2×C9×C11×C19—51no—
14D5×D171C1111yesmaximal, characteristic, direct product factor, Hall
15C3×C5×C11×C19C2×D311yescharacteristic
16C2×C11×D57—151no—
17C11×D95—91no—
18D5×C11×C19D911yescharacteristic, complemented
19C5×C11×D19—91no—
20D5×C11×D9—191nomaximal, Hall
21C9×C11×C19C2×D511yescharacteristic, complemented, Hall
22D855C2×C1111yescharacteristic, complemented
23C5×D171C2×C1111yescharacteristic, complemented
24C9×D5×C19C2×C1111yescharacteristic, complemented
25C2×C3×C11×C19—51no—
26C11×D57—31no—
27C11×D57—151no—
28D5×D57—31no—
29C5×C11×C19C2×D911yescharacteristic, complemented, Hall
30C11×D45—191no—
31C5×C11×D9—191no—
32C9×D5×C11D1911yescharacteristic, complemented
33C5×C9×C19C22×C1111yescharacteristic, complemented, Hall
34C2×C11×D19—451noHall
35C2×D171—51noHall
36D3×D5×C11—571no—
37C3×C11×C19D3×D511yescharacteristic
38D285—31no—
39C5×D57—31no—
40C3×D5×C19D3×C1111yescharacteristic
41C5×C9×C11C2×D1911yescharacteristic, complemented, Hall
42C2×C11×C19—51no—
43C11×D19—91no—
44C11×D19—451no—
45C2×C11×D9—951noHall
46D5×D19—91noHall
47C2×C9×C19—51no—
48D171—51no—
49D171D5×C1111yescharacteristic, direct product factor
50C11×D15—571no—
51C5×D3×C11—571no—
52C3×D5×C11D5711yescharacteristic
53C3×C5×C19C2×D3×C1111yescharacteristic
54C2×D57—151no—
55C2×D5×C11—1711noHall
56C11×C19D5×D911yescharacteristic, complemented, Hall
57C2×C9×C11—51no—
58C11×D9—191no—
59C11×D9—951no—
60D95—91no—
61C5×D19—91no—
62D5×C19C11×D911yescharacteristic, complemented
63D5×D9—191noHall
64C9×C19C2×D5×C1111yescharacteristic, complemented, Hall
65C3×C5×C11C2×D5711yescharacteristic
66C2×D3×C11—2851no—
67C2×C3×C19—51no—
68D57—31no—
69D57—151no—
70C2×C5×C11—1711no—
71D5×C11—1711no—
72D5×C11D17111yescharacteristic, direct product factor
73C9×C11D5×D1911yescharacteristic, complemented, Hall
74C5×C19C2×C11×D911yescharacteristic, complemented, Hall
75D45—191no—
76C9×D5C11×D1911yescharacteristic, complemented
77C5×D9—191no—
78C2×D19—451noHall
79C2×C3×C11—51no—
80D3×C11—2851no—
81D3×C11—571no—
82D3×D5—571no—
83C3×C19D3×D5×C1111yescharacteristic
84C5×C11C2×D17111yescharacteristic, complemented, Hall
85C5×C9C2×C11×D1911yescharacteristic, complemented, Hall
86C22×C11—8551noHall
87C2×C19—51no—
88D19—91no—
89D19—451no—
90C2×D9—951noHall
91C3×C11D5×D5711yescharacteristic
92D15—571no—
93C3×D5C11×D5711yescharacteristic
94C5×D3—571no—
95C2×C11—51no—
96C2×C11—8551no—
97C2×C11—1711no—
98C2×D5—1711noHall
99C19D5×C11×D911yescharacteristic, complemented, Sylow
100C2×C9—51no—
101D9—191no—
102D9—951no—
103C3×C5C2×C11×D5711yescharacteristic
104C2×D3—2851no—
105C11D5×D17111yescharacteristic, direct product factor, Sylow
106C2×C5—1711no—
107D5—1711no—
108D5C11×D17111yescharacteristic, direct product factor
109C9D5×C11×D1911yescharacteristic, complemented, Sylow
110C2×C3—51no—
111D3—2851no—
112D3—571no—
113C5C2×C11×D17111yescharacteristic, complemented, Sylow
114C22—8551noSylow
115C3D5×C11×D5711yescharacteristic
116C2—51no—
117C2—8551no—
118C2—1711no—
subgroupG/H
center, hypercenterC11D5×D171
commutator, cosocle, hypocenterC5×C9×C19C22×C11
FrattiniC3D5×C11×D57
FittingC5×C9×C11×C19C22
socleC3×C5×C11×C19C2×D3
LCSG ▷ C5×C9×C19
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×D855C2semidirect
2. C5×C11×D171C2semidirect
3. C9×D5×C11×C19C2semidirect
5. C5×C9×C11×C19C22semidirect
12. C11×D171D5direct (N × H)
14. D5×D171C11direct (N × H)
18. D5×C11×C19D9semidirect
21. C9×C11×C19C2×D5semidirect
22. D855C2×C11semidirect
23. C5×D171C2×C11semidirect
24. C9×D5×C19C2×C11semidirect
29. C5×C11×C19C2×D9semidirect
32. C9×D5×C11D19semidirect
33. C5×C9×C19C22×C11semidirect
41. C5×C9×C11C2×D19semidirect
49. D171D5×C11direct (N × H)
56. C11×C19D5×D9semidirect
62. D5×C19C11×D9semidirect
64. C9×C19C2×D5×C11semidirect
72. D5×C11D171direct (N × H)
73. C9×C11D5×D19semidirect
74. C5×C19C2×C11×D9semidirect
76. C9×D5C11×D19semidirect
84. C5×C11C2×D171semidirect
85. C5×C9C2×C11×D19semidirect
99. C19D5×C11×D9semidirect
105. C11D5×D171direct (N × H)
108. D5C11×D171direct (N × H)
109. C9D5×C11×D19semidirect
113. C5C2×C11×D171semidirect

Maximal subgroups

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

subgroupindex
C11×D8552
C5×C11×D1712
C9×D5×C11×C192
D5×C11×D573
C2×C11×D1715
D5×D17111
D5×C11×D919