Finite Group Databasebeta

← C7×D5×D261 #49141290

Subgroups — C7×D5×D261 #49141290

Order 36540.

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
1C7×D1305C211yesmaximal, characteristic, complemented
2C5×C7×D261C211yesmaximal, characteristic, complemented
3C7×C9×D5×C29C211yesmaximal, characteristic, complemented
4C7×D5×D87—31nomaximal
5C5×C7×C9×C29C2211yescharacteristic, complemented, Hall
6C2×C7×D261—51nomaximal, Hall
7C7×D435—31no—
8C5×C7×D87—31no—
9C3×C7×D5×C29D311yescharacteristic
10D5×D261C711yesmaximal, characteristic, direct product factor, Hall
11C7×D5×D29—91noHall
12C7×D261—51no—
13C7×D261D511yescharacteristic, direct product factor
14C2×C7×C9×C29—51no—
15C3×C5×C7×C29C2×D311yescharacteristic
16D1305C2×C711yescharacteristic, complemented
17C5×D261C2×C711yescharacteristic, complemented
18C9×D5×C29C2×C711yescharacteristic, complemented
19C2×C7×D87—151no—
20C7×D145—91no—
21C7×D5×C29D911yescharacteristic, complemented
22C5×C7×D29—91no—
23C7×C9×C29C2×D511yescharacteristic, complemented, Hall
24D5×D87—31no—
25C5×C9×C29C22×C711yescharacteristic, complemented, Hall
26C7×D5×D9—291nomaximal, Hall
27C2×C3×C7×C29—51no—
28C7×D87—31no—
29C7×D87—151no—
30C2×D261—51noHall
31C5×C7×C29C2×D911yescharacteristic, complemented, Hall
32D435—31no—
33C5×D87—31no—
34C3×D5×C29D3×C711yescharacteristic
35C2×C7×D29—451noHall
36C7×D45—291no—
37C5×C7×D9—291no—
38C7×C9×D5D2911yescharacteristic, complemented
39C3×C7×C29D3×D511yescharacteristic
40D5×D29—91noHall
41C2×C9×C29—51no—
42D261—51no—
43D261C7×D511yescharacteristic, direct product factor
44C3×C5×C29C2×D3×C711yescharacteristic
45D3×C7×D5—871no—
46C2×C7×C29—51no—
47C7×D29—91no—
48C7×D29—451no—
49C2×D87—151no—
50C5×C7×C9C2×D2911yescharacteristic, complemented, Hall
51D145—91no—
52C5×D29—91no—
53D5×C29C7×D911yescharacteristic, complemented
54C9×C29C2×C7×D511yescharacteristic, complemented, Hall
55C2×C7×D9—1451noHall
56C7×D15—871no—
57C5×D3×C7—871no—
58C3×C7×D5D8711yescharacteristic
59C7×C29D5×D911yescharacteristic, complemented, Hall
60D5×D9—291noHall
61C2×C3×C29—51no—
62D87—31no—
63D87—151no—
64C5×C29C2×C7×D911yescharacteristic, complemented, Hall
65C2×C7×D5—2611noHall
66C2×C7×C9—51no—
67C7×D9—291no—
68C7×D9—1451no—
69C2×D29—451noHall
70C3×C5×C7C2×D8711yescharacteristic
71D45—291no—
72C9×D5C7×D2911yescharacteristic, complemented
73C5×D9—291no—
74C3×C29D3×C7×D511yescharacteristic
75C2×D3×C7—4351no—
76C2×C5×C7—2611no—
77C7×D5—2611no—
78C7×D5D26111yescharacteristic, direct product factor
79C7×C9D5×D2911yescharacteristic, complemented, Hall
80D3×D5—871no—
81C2×C29—51no—
82D29—91no—
83D29—451no—
84C5×C9C2×C7×D2911yescharacteristic, complemented, Hall
85C2×C3×C7—51no—
86D3×C7—871no—
87D3×C7—4351no—
88C2×D9—1451noHall
89C5×C7C2×D26111yescharacteristic, complemented, Hall
90D15—871no—
91C3×D5C7×D8711yescharacteristic
92C5×D3—871no—
93C29C7×D5×D911yescharacteristic, complemented, Sylow
94C22×C7—13051noHall
95C3×C7D5×D8711yescharacteristic
96C2×D5—2611noHall
97C2×C9—51no—
98D9—291no—
99D9—1451no—
100C3×C5C2×C7×D8711yescharacteristic
101C2×C7—51no—
102C2×C7—2611no—
103C2×C7—13051no—
104C2×D3—4351no—
105C2×C5—2611no—
106D5—2611no—
107D5C7×D26111yescharacteristic, direct product factor
108C9C7×D5×D2911yescharacteristic, complemented, Sylow
109C7D5×D26111yescharacteristic, direct product factor, Sylow
110C2×C3—51no—
111D3—871no—
112D3—4351no—
113C5C2×C7×D26111yescharacteristic, complemented, Sylow
114C22—13051noSylow
115C3C7×D5×D8711yescharacteristic
116C2—51no—
117C2—2611no—
118C2—13051no—
subgroupG/H
center, hypercenterC7D5×D261
commutator, cosocle, hypocenterC5×C9×C29C22×C7
FrattiniC3C7×D5×D87
FittingC5×C7×C9×C29C22
socleC3×C5×C7×C29C2×D3
LCSG ▷ C5×C9×C29
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C7×D1305C2semidirect
2. C5×C7×D261C2semidirect
3. C7×C9×D5×C29C2semidirect
5. C5×C7×C9×C29C22semidirect
10. D5×D261C7direct (N × H)
13. C7×D261D5direct (N × H)
16. D1305C2×C7semidirect
17. C5×D261C2×C7semidirect
18. C9×D5×C29C2×C7semidirect
21. C7×D5×C29D9semidirect
23. C7×C9×C29C2×D5semidirect
25. C5×C9×C29C22×C7semidirect
31. C5×C7×C29C2×D9semidirect
38. C7×C9×D5D29semidirect
43. D261C7×D5direct (N × H)
50. C5×C7×C9C2×D29semidirect
53. D5×C29C7×D9semidirect
54. C9×C29C2×C7×D5semidirect
59. C7×C29D5×D9semidirect
64. C5×C29C2×C7×D9semidirect
72. C9×D5C7×D29semidirect
78. C7×D5D261direct (N × H)
79. C7×C9D5×D29semidirect
84. C5×C9C2×C7×D29semidirect
89. C5×C7C2×D261semidirect
93. C29C7×D5×D9semidirect
107. D5C7×D261direct (N × H)
108. C9C7×D5×D29semidirect
109. C7D5×D261direct (N × H)
113. C5C2×C7×D261semidirect

Maximal subgroups

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

subgroupindex
C7×D13052
C5×C7×D2612
C7×C9×D5×C292
C7×D5×D873
C2×C7×D2615
D5×D2617
C7×D5×D929