Finite Group Databasebeta

← C3×D5×C7⋊D77 #44568835

Subgroups — C3×D5×C7⋊D77 #44568835

Order 32340.

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⋊D77C211yesmaximal, characteristic, complemented
2C3×C72×D5×C11C211yesmaximal, characteristic, complemented
3C3×C5⋊(C7⋊D77)C211yesmaximal, characteristic, complemented
4D5×C7⋊D77C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6C2×C3×C7⋊D77—51nomaximal, Hall
7C5⋊(C7⋊D77)C2×C311yescharacteristic, complemented
8C72×D5×C11C2×C311yescharacteristic, complemented
9C5×C7⋊D77C2×C311yescharacteristic, complemented
10C3×D5×D77—78nomaximal
11C3×C7⋊D77—51no—
12C3×C7⋊D77D511yescharacteristic, direct product factor
13C2×C3×C72×C11—51no—
14C3×D5×C7⋊D7—111nomaximal, Hall
15C5×C72×C11C22×C311yescharacteristic, complemented, Hall
16C3×D385—78no—
17C3×C7×D5×C11D718yescomplemented
18C3×C5×D77—78no—
19C2×C7⋊D77—51noHall
20C3×C72×C11C2×D511yescharacteristic, complemented, Hall
21D5×D77—78no—
22C3×C5⋊(C7⋊D7)—111no—
23C3×C72×D5D1111yescharacteristic, complemented
24C3×C5×C7⋊D7—111no—
25C3×C5×C7×C11C2×D718yescomplemented
26C2×C72×C11—51no—
27C7⋊D77—51no—
28C7⋊D77C3×D511yescharacteristic, direct product factor
29D5×C7⋊D7—111noHall
30C2×C3×D77—358no—
31D385—78no—
32C7×D5×C11C3×D718yescomplemented
33C5×D77—78no—
34C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
35C3×D5×D11—491noHall
36C2×C3×C7⋊D7—551noHall
37C72×C11C2×C3×D511yescharacteristic, complemented, Hall
38C5⋊(C7⋊D7)—111no—
39C72×D5C3×D1111yescharacteristic, complemented
40C5×C7⋊D7—111no—
41C2×C3×C7×C11—58no—
42C3×D77—78no—
43C3×D77—358no—
44C3×D5×D7—778no—
45C5×C7×C11C2×C3×D718yescomplemented
46C3×D55—491no—
47C3×D5×C11C7⋊D711yescharacteristic, complemented
48C3×C5×D11—491no—
49C2×D77—358no—
50C2×C3×C72—51no—
51C3×C7⋊D7—111no—
52C3×C7⋊D7—551no—
53C5×C72C2×C3×D1111yescharacteristic, complemented, Hall
54C3×C7×C11D5×D718yescomplemented
55D5×D11—491noHall
56C3×D35—778no—
57C3×C7×D5D7718yescomplemented
58C3×C5×D7—778no—
59C2×C7⋊D7—551noHall
60C3×C5×C11C2×C7⋊D711yescharacteristic, complemented, Hall
61C2×C7×C11—58no—
62D77—78no—
63D77—358no—
64C3×C72D5×D1111yescharacteristic, complemented, Hall
65D5×D7—778no—
66C2×C3×D11—2451noHall
67D55—491no—
68C5×D11—491no—
69D5×C11C3×C7⋊D711yescharacteristic, complemented
70C3×C5×C7C2×D7718yescomplemented
71C2×C72—51no—
72C7⋊D7—111no—
73C7⋊D7—551no—
74C2×C3×D7—3858no—
75C7×C11C3×D5×D718yescomplemented
76D35—778no—
77C5×D7—778no—
78C7×D5C3×D7718yescomplemented
79C2×C3×C11—51no—
80C3×D11—491no—
81C3×D11—2451no—
82C2×C3×D5—5391noHall
83C5×C11C2×C3×C7⋊D711yescharacteristic, complemented, Hall
84C72C3×D5×D1111yescharacteristic, complemented, Sylow
85C2×D11—2451noHall
86C2×C3×C7—58no—
87C3×D7—778no—
88C3×D7—3858no—
89C5×C7C2×C3×D7718yescomplemented
90C3×C11D5×C7⋊D711yescharacteristic, complemented, Hall
91C2×C3×C5—5391no—
92C3×D5—5391no—
93C3×D5C7⋊D7711yescharacteristic, direct product factor
94C2×D7—3858no—
95C2×C11—51no—
96D11—491no—
97D11—2451no—
98C3×C7D5×D7718yescomplemented
99C2×D5—5391noHall
100C3×C5C2×C7⋊D7711yescharacteristic, complemented, Hall
101C2×C7—58no—
102D7—778no—
103D7—3858no—
104C22×C3—26951noHall
105C11C3×D5×C7⋊D711yescharacteristic, complemented, Sylow
106C2×C5—5391no—
107D5—5391no—
108D5C3×C7⋊D7711yescharacteristic, direct product factor
109C7C3×D5×D7718yescomplemented
110C2×C3—51no—
111C2×C3—5391no—
112C2×C3—26951no—
113C5C2×C3×C7⋊D7711yescharacteristic, complemented, Sylow
114C22—26951noSylow
115C3D5×C7⋊D7711yescharacteristic, direct product factor, Sylow
116C2—51no—
117C2—5391no—
118C2—26951no—
subgroupG/H
center, hypercenterC3D5×C7⋊D77
commutator, cosocle, hypocenterC5×C72×C11C22×C3
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C5×C72×C11
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7⋊D77C2semidirect
2. C3×C72×D5×C11C2semidirect
3. C3×C5⋊(C7⋊D77)C2semidirect
4. D5×C7⋊D77C3direct (N × H)
5. C3×C5×C72×C11C22semidirect
7. C5⋊(C7⋊D77)C2×C3semidirect
8. C72×D5×C11C2×C3semidirect
9. C5×C7⋊D77C2×C3semidirect
12. C3×C7⋊D77D5direct (N × H)
15. C5×C72×C11C22×C3semidirect
17. C3×C7×D5×C11D7semidirect
20. C3×C72×C11C2×D5semidirect
23. C3×C72×D5D11semidirect
25. C3×C5×C7×C11C2×D7semidirect
28. C7⋊D77C3×D5direct (N × H)
32. C7×D5×C11C3×D7semidirect
34. C3×C5×C72C2×D11semidirect
37. C72×C11C2×C3×D5semidirect
39. C72×D5C3×D11semidirect
45. C5×C7×C11C2×C3×D7semidirect
47. C3×D5×C11C7⋊D7semidirect
53. C5×C72C2×C3×D11semidirect
54. C3×C7×C11D5×D7semidirect
57. C3×C7×D5D77semidirect
60. C3×C5×C11C2×C7⋊D7semidirect
64. C3×C72D5×D11semidirect
69. D5×C11C3×C7⋊D7semidirect
70. C3×C5×C7C2×D77semidirect
75. C7×C11C3×D5×D7semidirect
78. C7×D5C3×D77semidirect
83. C5×C11C2×C3×C7⋊D7semidirect
84. C72C3×D5×D11semidirect
89. C5×C7C2×C3×D77semidirect
90. C3×C11D5×C7⋊D7semidirect
93. C3×D5C7⋊D77direct (N × H)
98. C3×C7D5×D77semidirect
100. C3×C5C2×C7⋊D77semidirect
105. C11C3×D5×C7⋊D7semidirect
108. D5C3×C7⋊D77direct (N × H)
109. C7C3×D5×D77semidirect
113. C5C2×C3×C7⋊D77semidirect
115. C3D5×C7⋊D77direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7⋊D772
C3×C72×D5×C112
C3×C5⋊(C7⋊D77)2
D5×C7⋊D773
C2×C3×C7⋊D775
C3×D5×D777
C3×D5×C7⋊D711