Finite Group Databasebeta

← D5×C3⋊(C7⋊D77) #44568914

Subgroups — D5×C3⋊(C7⋊D77) #44568914

Order 32340.

400 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 124 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×C72×D5×C11C211yesmaximal, characteristic, complemented
2C5×C3⋊(C7⋊D77)C211yesmaximal, characteristic, complemented
3C3⋊(C5⋊(C7⋊D77))C211yesmaximal, characteristic, complemented
4D5×C7⋊D77—31nomaximal, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6C2×C3⋊(C7⋊D77)—51nomaximal, Hall
7C5⋊(C7⋊D77)—31no—
8C72×D5×C11D311yescharacteristic, complemented
9C5×C7⋊D77—31no—
10D5×D231—78nomaximal
11C3⋊(C7⋊D77)—51no—
12C3⋊(C7⋊D77)D511yescharacteristic, direct product factor
13C2×C3×C72×C11—51no—
14D5×C3⋊(C7⋊D7)—111nomaximal, Hall
15C5×C72×C11C2×D311yescharacteristic, complemented, Hall
16D1155—78no—
17C5×D231—78no—
18C3×C7×D5×C11D718yescomplemented
19C2×C7⋊D77—151noHall
20C3×C72×C11C2×D511yescharacteristic, complemented, Hall
21D5×D77—218no—
22C3⋊(C5⋊(C7⋊D7))—111no—
23C5×C3⋊(C7⋊D7)—111no—
24C3×C72×D5D1111yescharacteristic, complemented
25C3×C5×C7×C11C2×D718yescomplemented
26C2×C72×C11—51no—
27C7⋊D77—31no—
28C7⋊D77—151no—
29D5×C7⋊D7—331noHall
30C2×D231—358no—
31D385—218no—
32C7×D5×C11D2118yescomplemented
33C5×D77—218no—
34C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
35D5×D33—491noHall
36C2×C3⋊(C7⋊D7)—551noHall
37C72×C11D3×D511yescharacteristic, complemented, Hall
38C5⋊(C7⋊D7)—331no—
39C72×D5D3311yescharacteristic, complemented
40C5×C7⋊D7—331no—
41C2×C3×C7×C11—58no—
42D231—78no—
43D231—358no—
44D5×D21—778no—
45C5×C7×C11C2×D2118yescomplemented
46D165—491no—
47C5×D33—491no—
48C3×D5×C11C7⋊D711yescharacteristic, complemented
49C2×D77—1058no—
50C2×C3×C72—51no—
51C3⋊(C7⋊D7)—111no—
52C3⋊(C7⋊D7)—551no—
53C5×C72C2×D3311yescharacteristic, complemented, Hall
54C3×C7×C11D5×D718yescomplemented
55D5×D11—1471noHall
56D105—778no—
57C5×D21—778no—
58C3×C7×D5D7718yescomplemented
59C2×C7⋊D7—1651noHall
60C3×C5×C11C2×C7⋊D711yescharacteristic, complemented, Hall
61C2×C7×C11—58no—
62D77—218no—
63D77—1058no—
64C3×C72D5×D1111yescharacteristic, complemented, Hall
65D5×D7—2318no—
66C2×D33—2451noHall
67D55—1471no—
68C5×D11—1471no—
69D5×C11C3⋊(C7⋊D7)11yescharacteristic, complemented
70C3×C5×C7C2×D7718yescomplemented
71C2×C72—51no—
72C7⋊D7—331no—
73C7⋊D7—1651no—
74C2×D21—3858no—
75C7×C11D5×D2118yescomplemented
76D35—2318no—
77C5×D7—2318no—
78C7×D5D23118yescomplemented
79C2×C3×C11—51no—
80D33—491no—
81D33—2451no—
82D3×D5—5391noHall
83C5×C11C2×C3⋊(C7⋊D7)11yescharacteristic, complemented, Hall
84C72D5×D3311yescharacteristic, complemented, Sylow
85C2×D11—7351noHall
86C2×C3×C7—58no—
87D21—778no—
88D21—3858no—
89C5×C7C2×D23118yescomplemented
90C3×C11D5×C7⋊D711yescharacteristic, complemented, Hall
91D15—5391no—
92C3×D5C7⋊D7711yescharacteristic, complemented
93C5×D3—5391no—
94C2×D7—11558no—
95C2×C11—51no—
96D11—1471no—
97D11—7351no—
98C3×C7D5×D7718yescomplemented
99C2×D5—16171noHall
100C3×C5C2×C7⋊D7711yescharacteristic, complemented, Hall
101C2×C7—58no—
102D7—11558no—
103D7—2318no—
104C2×D3—26951noHall
105C11D5×C3⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
106C2×C5—16171no—
107D5—16171no—
108D5C3⋊(C7⋊D77)11yescharacteristic, direct product factor
109C7D5×D23118yescomplemented
110C2×C3—51no—
111D3—5391no—
112D3—26951no—
113C5C2×C3⋊(C7⋊D77)11yescharacteristic, complemented, Sylow
114C22—80851noSylow
115C3D5×C7⋊D7711yescharacteristic, complemented, Sylow
116C2—51no—
117C2—16171no—
118C2—80851no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C11C22
LCSG ▷ C3×C5×C72×C11
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C72×D5×C11C2semidirect
2. C5×C3⋊(C7⋊D77)C2semidirect
3. C3⋊(C5⋊(C7⋊D77))C2semidirect
5. C3×C5×C72×C11C22semidirect
8. C72×D5×C11D3semidirect
12. C3⋊(C7⋊D77)D5direct (N × H)
15. C5×C72×C11C2×D3semidirect
18. C3×C7×D5×C11D7semidirect
20. C3×C72×C11C2×D5semidirect
24. C3×C72×D5D11semidirect
25. C3×C5×C7×C11C2×D7semidirect
32. C7×D5×C11D21semidirect
34. C3×C5×C72C2×D11semidirect
37. C72×C11D3×D5semidirect
39. C72×D5D33semidirect
45. C5×C7×C11C2×D21semidirect
48. C3×D5×C11C7⋊D7semidirect
53. C5×C72C2×D33semidirect
54. C3×C7×C11D5×D7semidirect
58. C3×C7×D5D77semidirect
60. C3×C5×C11C2×C7⋊D7semidirect
64. C3×C72D5×D11semidirect
69. D5×C11C3⋊(C7⋊D7)semidirect
70. C3×C5×C7C2×D77semidirect
75. C7×C11D5×D21semidirect
78. C7×D5D231semidirect
83. C5×C11C2×C3⋊(C7⋊D7)semidirect
84. C72D5×D33semidirect
89. C5×C7C2×D231semidirect
90. C3×C11D5×C7⋊D7semidirect
92. C3×D5C7⋊D77semidirect
98. C3×C7D5×D77semidirect
100. C3×C5C2×C7⋊D77semidirect
105. C11D5×C3⋊(C7⋊D7)semidirect
108. D5C3⋊(C7⋊D77)direct (N × H)
109. C7D5×D231semidirect
113. C5C2×C3⋊(C7⋊D77)semidirect
115. C3D5×C7⋊D77semidirect

Maximal subgroups

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

subgroupindex
C3×C72×D5×C112
C5×C3⋊(C7⋊D77)2
C3⋊(C5⋊(C7⋊D77))2
D5×C7⋊D773
C2×C3⋊(C7⋊D77)5
D5×D2317
D5×C3⋊(C7⋊D7)11