Finite Group Databasebeta

← D49×D165 #44568400

Subgroups — D49×D165 #44568400

Order 32340.

120 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 37 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
1D8085C211yesmaximal, characteristic, complemented
2C49×D165C211yesmaximal, characteristic, complemented
3C3×C5×C11×D49C211yesmaximal, characteristic, complemented
4D49×D55—31nomaximal, Hall
5C3×C5×C11×C49C2211yescharacteristic, complemented, Hall
6D33×D49—51nomaximal, Hall
7D2695—31no—
8C49×D55—31no—
9C5×C11×D49D311yescharacteristic, complemented
10D7×D165—71nomaximal
11D1617—51no—
12C49×D33—51no—
13C3×C11×D49D511yescharacteristic, complemented
14D15×D49—111nomaximal, Hall
15C5×C11×C49C2×D311yescharacteristic, complemented, Hall
16D1155—71no—
17C7×D165D711yescharacteristic
18C3×C5×C11×D7—71no—
19D11×D49—151noHall
20C3×C11×C49C2×D511yescharacteristic, complemented, Hall
21D7×D55—211no—
22D735—111no—
23D15×C49—111no—
24C3×C5×D49D1111yescharacteristic, complemented
25C3×C5×C7×C11C2×D711yescharacteristic
26D539—151no—
27D11×C49—151no—
28C11×D49D1511yescharacteristic, complemented
29D5×D49—331noHall
30D7×D33—351no—
31D385—211no—
32C7×D55—31no—
33C5×C11×D7—71no—
34C3×C5×C49C2×D1111yescharacteristic, complemented, Hall
35C2×D165—491noHall
36D3×D49—551noHall
37C11×C49C2×D1511yescharacteristic, complemented, Hall
38D245—331no—
39C5×D49D3311yescharacteristic, complemented
40D5×C49—331no—
41D231—351no—
42C7×D33—51no—
43C3×C11×D7—71no—
44D7×D15—771no—
45C5×C7×C11D3×D711yescharacteristic
46C2×C3×C5×C11—491no—
47D165—491no—
48D165D4911yescharacteristic, direct product factor
49D7×D11—1051no—
50D147—551no—
51C3×D49D5511yescharacteristic, complemented
52D3×C49—551no—
53C5×C49C2×D3311yescharacteristic, complemented, Hall
54C3×C7×C11D5×D711yescharacteristic
55C2×D55—1471noHall
56D105—771no—
57C7×D15—111no—
58C3×C5×D7—71no—
59C2×D49—1651noHall
60C3×C5×C11C2×D4911yescharacteristic, complemented, Hall
61D77—1051no—
62C7×D11—151no—
63C11×D7—71no—
64C3×C49C2×D5511yescharacteristic, complemented, Hall
65D5×D7—2311no—
66C2×D33—2451noHall
67C2×C5×C11—491no—
68D55—31no—
69D55—1471no—
70C3×C5×C7D7×D1111yescharacteristic
71C2×C49—1651no—
72D49—1651no—
73D49D16511yescharacteristic, direct product factor
74D3×D7—3851no—
75C7×C11D7×D1511yescharacteristic
76D35—2311no—
77C5×D7—71no—
78C7×D5—331no—
79C2×C3×C11—491no—
80D33—51no—
81D33—2451no—
82C2×D15—5391noHall
83C5×C11D3×D4911yescharacteristic, complemented, Hall
84C49C2×D16511yescharacteristic, complemented, Sylow
85C2×D11—7351noHall
86D21—3851no—
87C3×D7—71no—
88D3×C7—551no—
89C5×C7D7×D3311yescharacteristic
90C3×C11D5×D4911yescharacteristic, complemented, Hall
91C2×C3×C5—491no—
92D15—111no—
93D15—5391no—
94C2×D7—11551no—
95C2×C11—491no—
96D11—151no—
97D11—7351no—
98C3×C7D7×D5511yescharacteristic
99C2×D5—16171noHall
100C3×C5D11×D4911yescharacteristic, complemented, Hall
101C2×C7—1651no—
102D7—71no—
103D7—11551no—
104C2×D3—26951noHall
105C11D15×D4911yescharacteristic, complemented, Sylow
106C2×C5—491no—
107D5—331no—
108D5—16171no—
109C7D7×D16511yescharacteristic
110C2×C3—491no—
111D3—551no—
112D3—26951no—
113C5D33×D4911yescharacteristic, complemented, Sylow
114C22—80851noSylow
115C3D49×D5511yescharacteristic, complemented, Sylow
116C2—491no—
117C2—80851no—
118C2—1651no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C5×C11×C49C22
FrattiniC7D7×D165
socleC3×C5×C7×C11C2×D7
LCSG ▷ C3×C5×C11×C49
UCSC1

Complements

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

NH ≅ G/Ntype
1. D8085C2semidirect
2. C49×D165C2semidirect
3. C3×C5×C11×D49C2semidirect
5. C3×C5×C11×C49C22semidirect
9. C5×C11×D49D3semidirect
13. C3×C11×D49D5semidirect
15. C5×C11×C49C2×D3semidirect
20. C3×C11×C49C2×D5semidirect
24. C3×C5×D49D11semidirect
28. C11×D49D15semidirect
34. C3×C5×C49C2×D11semidirect
37. C11×C49C2×D15semidirect
39. C5×D49D33semidirect
48. D165D49direct (N × H)
51. C3×D49D55semidirect
53. C5×C49C2×D33semidirect
60. C3×C5×C11C2×D49semidirect
64. C3×C49C2×D55semidirect
73. D49D165direct (N × H)
83. C5×C11D3×D49semidirect
84. C49C2×D165semidirect
90. C3×C11D5×D49semidirect
100. C3×C5D11×D49semidirect
105. C11D15×D49semidirect
113. C5D33×D49semidirect
115. C3D49×D55semidirect

Maximal subgroups

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

subgroupindex
D80852
C49×D1652
C3×C5×C11×D492
D49×D553
D33×D495
D7×D1657
D15×D4911