Finite Group Databasebeta

← C3×C5×C7×C7⋊#261 #50304340

Subgroups — C3×C5×C7×C7⋊#261 #50304340

Order 38220.

144 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 56 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×C72×D13C211yesmaximal, characteristic
2C5×C7×C7⋊#261C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C72×C13C411yescharacteristic, complemented, Hall
4C3×C7×C7⋊#261C511yesmaximal, characteristic, direct product factor, Hall
5C5×C72×D13C2×C311yescharacteristic
6C3×C5×C7⋊#261C711yesmaximal, characteristic, direct product factor
7C3×C5×C7×#261—71nomaximal
8C3×C72×D13C2×C511yescharacteristic
9C5×C72×C13C3×C411yescharacteristic, complemented, Hall
10C3×C5×C7×Dic7—131nomaximal, Hall
11C3×C5×C7×D13—23no—
12C3×C5×C7×D13D711yescharacteristic
13C3×C5×C7×D13C2×C711yescharacteristic
14C7×C7⋊#261C3×C511yescharacteristic, direct product factor, Hall
15C3×C72×C13C4×C511yescharacteristic, complemented, Hall
16C5×C7⋊#261C3×C711yescharacteristic, direct product factor
17C5×C7×#261—71no—
18C2×C3×C5×C72—131no—
19C3×C5×C7×C13—23no—
20C3×C5×C7×C13Dic711yescharacteristic, complemented
21C3×C5×C7×C13C4×C711yescharacteristic, complemented
22C72×D13C2×C3×C511yescharacteristic
23C3×C7⋊#261C5×C711yescharacteristic, direct product factor
24C3×C7×#261—71no—
25C5×C7×Dic7—131noHall
26C5×C7×D13—23no—
27C5×C7×D13C3×D711yescharacteristic
28C5×C7×D13C2×C3×C711yescharacteristic
29C3×C5×#261—71noHall
30C3×C5×C72#26111yescharacteristic, complemented, Hall
31C72×C13C3×C4×C511yescharacteristic, complemented, Hall
32C3×C7×Dic7—131noHall
33C3×C7×D13—23no—
34C3×C7×D13C5×D711yescharacteristic
35C3×C7×D13C2×C5×C711yescharacteristic
36C2×C5×C72—131no—
37C5×C7×C13—23no—
38C5×C7×C13C3×Dic711yescharacteristic, complemented
39C5×C7×C13C3×C4×C711yescharacteristic, complemented
40C3×C4×C5×C7—911no—
41C3×C5×Dic7—131no—
42C3×C5×D13C7×D711yescharacteristic
43C7⋊#261C3×C5×C711yescharacteristic, direct product factor
44C7×#261—71no—
45C2×C3×C72—131no—
46C3×C7×C13—23no—
47C3×C7×C13C5×Dic711yescharacteristic, complemented
48C3×C7×C13C4×C5×C711yescharacteristic, complemented
49C5×#261—71noHall
50C5×C72C3×#26111yescharacteristic, complemented, Hall
51C2×C3×C5×C7—131no—
52C2×C3×C5×C7—131no—
53C2×C3×C5×C7—263no—
54C7×Dic7—131noHall
55C3×C5×C13C7×Dic711yescharacteristic, complemented, Hall
56C7×D13—23no—
57C7×D13C3×C5×D711yescharacteristic
58C7×D13C2×C3×C5×C711yescharacteristic
59C3×#261—71noHall
60C3×C72C5×#26111yescharacteristic, complemented, Hall
61C4×C5×C7—911no—
62C5×Dic7—131no—
63C5×D13C3×C7×D711yescharacteristic
64C3×C5×C7—23no—
65C3×C5×C7C7×#26111yescharacteristic, complemented
66C3×C5×C7C7⋊#26111yescharacteristic, direct product factor
67C2×C72—131no—
68C7×C13—23no—
69C7×C13C3×C5×Dic711yescharacteristic, complemented
70C7×C13C3×C4×C5×C711yescharacteristic, complemented
71C3×C4×C7—911no—
72C3×Dic7—131no—
73C3×D13C5×C7×D711yescharacteristic
74C2×C5×C7—131no—
75C2×C5×C7—131no—
76C2×C5×C7—263no—
77C5×C13C3×C7×Dic711yescharacteristic, complemented, Hall
78C3×C4×C5—911noHall
79#261—71noHall
80C72C3×C5×#26111yescharacteristic, complemented, Sylow
81C2×C3×C7—131no—
82C2×C3×C7—131no—
83C2×C3×C7—263no—
84C3×C13C5×C7×Dic711yescharacteristic, complemented, Hall
85C5×C7—23no—
86C5×C7C3×C7×#26111yescharacteristic, complemented
87C5×C7C3×C7⋊#26111yescharacteristic, direct product factor
88C2×C3×C5—131no—
89C4×C7—911no—
90Dic7—131no—
91D13C3×C5×C7×D711yescharacteristic
92C3×C7—23no—
93C3×C7C5×C7×#26111yescharacteristic, complemented
94C3×C7C5×C7⋊#26111yescharacteristic, direct product factor
95C4×C5—911noHall
96C3×C5C7×C7⋊#26111yescharacteristic, direct product factor, Hall
97C2×C7—131no—
98C2×C7—131no—
99C2×C7—263no—
100C13C3×C5×C7×Dic711yescharacteristic, complemented, Sylow
101C3×C4—911noHall
102C2×C5—131no—
103C7—23no—
104C7C3×C5×C7×#26111yescharacteristic, complemented
105C7C3×C5×C7⋊#26111yescharacteristic, direct product factor
106C2×C3—131no—
107C5C3×C7×C7⋊#26111yescharacteristic, direct product factor, Sylow
108C4—911noSylow
109C3C5×C7×C7⋊#26111yescharacteristic, direct product factor, Sylow
110C2—131no—
subgroupG/H
center, hypercenterC3×C5×C7C7⋊#261
commutator, hypocenterC7×C13C3×C4×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C5×C72×D13C2
cosocleC7×D13C2×C3×C5×C7
LCSG ▷ C7×C13
UCSC1 ◁ C3×C5×C7

Complements

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

NH ≅ G/Ntype
2. C5×C7×C7⋊#261C3direct (N × H)
3. C3×C5×C72×C13C4semidirect
4. C3×C7×C7⋊#261C5direct (N × H)
6. C3×C5×C7⋊#261C7direct (N × H)
9. C5×C72×C13C3×C4semidirect
14. C7×C7⋊#261C3×C5direct (N × H)
15. C3×C72×C13C4×C5semidirect
16. C5×C7⋊#261C3×C7direct (N × H)
20. C3×C5×C7×C13Dic7semidirect
21. C3×C5×C7×C13C4×C7semidirect
23. C3×C7⋊#261C5×C7direct (N × H)
30. C3×C5×C72#261semidirect
31. C72×C13C3×C4×C5semidirect
38. C5×C7×C13C3×Dic7semidirect
39. C5×C7×C13C3×C4×C7semidirect
43. C7⋊#261C3×C5×C7direct (N × H)
47. C3×C7×C13C5×Dic7semidirect
48. C3×C7×C13C4×C5×C7semidirect
50. C5×C72C3×#261semidirect
55. C3×C5×C13C7×Dic7semidirect
60. C3×C72C5×#261semidirect
65. C3×C5×C7C7×#261semidirect
66. C3×C5×C7C7⋊#261direct (N × H)
69. C7×C13C3×C5×Dic7semidirect
70. C7×C13C3×C4×C5×C7semidirect
77. C5×C13C3×C7×Dic7semidirect
80. C72C3×C5×#261semidirect
84. C3×C13C5×C7×Dic7semidirect
86. C5×C7C3×C7×#261semidirect
87. C5×C7C3×C7⋊#261direct (N × H)
93. C3×C7C5×C7×#261semidirect
94. C3×C7C5×C7⋊#261direct (N × H)
96. C3×C5C7×C7⋊#261direct (N × H)
100. C13C3×C5×C7×Dic7semidirect
104. C7C3×C5×C7×#261semidirect
105. C7C3×C5×C7⋊#261direct (N × H)
107. C5C3×C7×C7⋊#261direct (N × H)
109. C3C5×C7×C7⋊#261direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C72×D132
C5×C7×C7⋊#2613
C3×C7×C7⋊#2615
C3×C5×C7⋊#2617
C3×C5×C7×#2617
C3×C5×C7×Dic713