Finite Group Databasebeta

← C3×C5×C7×Dic91 #50303700

Subgroups — C3×C5×C7×Dic91 #50303700

Order 38220.

144 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C2×C3×C5×C72×C13C211yesmaximal, characteristic
2C5×C7×Dic91C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C72×C13C411yescharacteristic, complemented, Hall
4C3×C7×Dic91C511yesmaximal, characteristic, direct product factor, Hall
5C2×C5×C72×C13C2×C311yescharacteristic
6C3×C5×Dic91C711yesmaximal, characteristic, direct product factor
7C3×C5×C7×Dic13—71nomaximal
8C2×C3×C72×C13C2×C511yescharacteristic
9C5×C72×C13C3×C411yescharacteristic, complemented, Hall
10C3×C5×C7×Dic7—131nomaximal, Hall
11C2×C3×C5×C7×C13—23no—
12C2×C3×C5×C7×C13D711yescharacteristic
13C2×C3×C5×C7×C13C2×C711yescharacteristic
14C7×Dic91C3×C511yescharacteristic, direct product factor, Hall
15C3×C72×C13C4×C511yescharacteristic, complemented, Hall
16C5×Dic91C3×C711yescharacteristic, direct product factor
17C5×C7×Dic13—71no—
18C2×C3×C5×C72D1311yescharacteristic
19C3×C5×C7×C13—23no—
20C3×C5×C7×C13Dic711yescharacteristic, complemented
21C3×C5×C7×C13C4×C711yescharacteristic, complemented
22C2×C72×C13C2×C3×C511yescharacteristic
23C3×Dic91C5×C711yescharacteristic, direct product factor
24C3×C7×Dic13—71no—
25C5×C7×Dic7—131noHall
26C2×C5×C7×C13—23no—
27C2×C5×C7×C13C3×D711yescharacteristic
28C2×C5×C7×C13C2×C3×C711yescharacteristic
29C3×C5×Dic13—71noHall
30C3×C5×C72Dic1311yescharacteristic, complemented, Hall
31C72×C13C3×C4×C511yescharacteristic, complemented, Hall
32C3×C7×Dic7—131noHall
33C2×C3×C7×C13—23no—
34C2×C3×C7×C13C5×D711yescharacteristic
35C2×C3×C7×C13C2×C5×C711yescharacteristic
36C2×C5×C72C3×D1311yescharacteristic
37C5×C7×C13—23no—
38C5×C7×C13C3×Dic711yescharacteristic, complemented
39C5×C7×C13C3×C4×C711yescharacteristic, complemented
40C3×C4×C5×C7—911no—
41C3×C5×Dic7—131no—
42C2×C3×C5×C13C7×D711yescharacteristic
43Dic91C3×C5×C711yescharacteristic, direct product factor
44C7×Dic13—71no—
45C2×C3×C72C5×D1311yescharacteristic
46C3×C7×C13—23no—
47C3×C7×C13C5×Dic711yescharacteristic, complemented
48C3×C7×C13C4×C5×C711yescharacteristic, complemented
49C5×Dic13—71noHall
50C5×C72C3×Dic1311yescharacteristic, complemented, Hall
51C2×C3×C5×C7—23no—
52C2×C3×C5×C7C7×D1311yescharacteristic
53C2×C3×C5×C7D9111yescharacteristic
54C7×Dic7—131noHall
55C3×C5×C13C7×Dic711yescharacteristic, complemented, Hall
56C2×C7×C13—23no—
57C2×C7×C13C3×C5×D711yescharacteristic
58C2×C7×C13C2×C3×C5×C711yescharacteristic
59C3×Dic13—71noHall
60C3×C72C5×Dic1311yescharacteristic, complemented, Hall
61C4×C5×C7—911no—
62C5×Dic7—131no—
63C2×C5×C13C3×C7×D711yescharacteristic
64C3×C5×C7—23no—
65C3×C5×C7C7×Dic1311yescharacteristic, complemented
66C3×C5×C7Dic9111yescharacteristic, direct product factor
67C2×C72C3×C5×D1311yescharacteristic
68C7×C13—23no—
69C7×C13C3×C5×Dic711yescharacteristic, complemented
70C7×C13C3×C4×C5×C711yescharacteristic, complemented
71C3×C4×C7—911no—
72C3×Dic7—131no—
73C2×C3×C13C5×C7×D711yescharacteristic
74C2×C5×C7—23no—
75C2×C5×C7C3×C7×D1311yescharacteristic
76C2×C5×C7C3×D9111yescharacteristic
77C5×C13C3×C7×Dic711yescharacteristic, complemented, Hall
78C3×C4×C5—911noHall
79Dic13—71noHall
80C72C3×C5×Dic1311yescharacteristic, complemented, Sylow
81C2×C3×C7—23no—
82C2×C3×C7C5×C7×D1311yescharacteristic
83C2×C3×C7C5×D9111yescharacteristic
84C3×C13C5×C7×Dic711yescharacteristic, complemented, Hall
85C5×C7—23no—
86C5×C7C3×C7×Dic1311yescharacteristic, complemented
87C5×C7C3×Dic9111yescharacteristic, direct product factor
88C2×C3×C5C7×D9111yescharacteristic
89C4×C7—911no—
90Dic7—131no—
91C2×C13C3×C5×C7×D711yescharacteristic
92C3×C7—23no—
93C3×C7C5×C7×Dic1311yescharacteristic, complemented
94C3×C7C5×Dic9111yescharacteristic, direct product factor
95C4×C5—911noHall
96C3×C5C7×Dic9111yescharacteristic, direct product factor, Hall
97C2×C7—23no—
98C2×C7C3×C5×C7×D1311yescharacteristic
99C2×C7C3×C5×D9111yescharacteristic
100C13C3×C5×C7×Dic711yescharacteristic, complemented, Sylow
101C3×C4—911noHall
102C2×C5C3×C7×D9111yescharacteristic
103C7—23no—
104C7C3×C5×C7×Dic1311yescharacteristic, complemented
105C7C3×C5×Dic9111yescharacteristic, direct product factor
106C2×C3C5×C7×D9111yescharacteristic
107C5C3×C7×Dic9111yescharacteristic, direct product factor, Sylow
108C4—911noSylow
109C3C5×C7×Dic9111yescharacteristic, direct product factor, Sylow
110C2C3×C5×C7×D9111yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C5×C7D91
commutator, hypocenterC7×C13C3×C4×C5×C7
FrattiniC2C3×C5×C7×D91
Fitting, socle, prime radicalC2×C3×C5×C72×C13C2
cosocleC2×C7×C13C2×C3×C5×C7
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C5×C7

Complements

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

NH ≅ G/Ntype
2. C5×C7×Dic91C3direct (N × H)
3. C3×C5×C72×C13C4semidirect
4. C3×C7×Dic91C5direct (N × H)
6. C3×C5×Dic91C7direct (N × H)
9. C5×C72×C13C3×C4semidirect
14. C7×Dic91C3×C5direct (N × H)
15. C3×C72×C13C4×C5semidirect
16. C5×Dic91C3×C7direct (N × H)
20. C3×C5×C7×C13Dic7semidirect
21. C3×C5×C7×C13C4×C7semidirect
23. C3×Dic91C5×C7direct (N × H)
30. C3×C5×C72Dic13semidirect
31. C72×C13C3×C4×C5semidirect
38. C5×C7×C13C3×Dic7semidirect
39. C5×C7×C13C3×C4×C7semidirect
43. Dic91C3×C5×C7direct (N × H)
47. C3×C7×C13C5×Dic7semidirect
48. C3×C7×C13C4×C5×C7semidirect
50. C5×C72C3×Dic13semidirect
55. C3×C5×C13C7×Dic7semidirect
60. C3×C72C5×Dic13semidirect
65. C3×C5×C7C7×Dic13semidirect
66. C3×C5×C7Dic91direct (N × H)
69. C7×C13C3×C5×Dic7semidirect
70. C7×C13C3×C4×C5×C7semidirect
77. C5×C13C3×C7×Dic7semidirect
80. C72C3×C5×Dic13semidirect
84. C3×C13C5×C7×Dic7semidirect
86. C5×C7C3×C7×Dic13semidirect
87. C5×C7C3×Dic91direct (N × H)
93. C3×C7C5×C7×Dic13semidirect
94. C3×C7C5×Dic91direct (N × H)
96. C3×C5C7×Dic91direct (N × H)
100. C13C3×C5×C7×Dic7semidirect
104. C7C3×C5×C7×Dic13semidirect
105. C7C3×C5×Dic91direct (N × H)
107. C5C3×C7×Dic91direct (N × H)
109. C3C5×C7×Dic91direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C72×C132
C5×C7×Dic913
C3×C7×Dic915
C3×C5×Dic917
C3×C5×C7×Dic137
C3×C5×C7×Dic713