Finite Group Databasebeta

← C7×C13×Dic105 #50303683

Subgroups — C7×C13×Dic105 #50303683

Order 38220.

144 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 68 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
2C7×C13×Dic35—31nomaximal, Hall
3C3×C5×C72×C13C411yescharacteristic, complemented, Hall
4C7×C13×Dic21—51nomaximal, Hall
5C2×C5×C72×C13D311yescharacteristic
6C13×Dic105C711yesmaximal, characteristic, direct product factor
7C7×C13×Dic15—71nomaximal
8C2×C3×C72×C13D511yescharacteristic
9C5×C72×C13Dic311yescharacteristic, complemented, Hall
10C7×Dic105C1311yesmaximal, characteristic, direct product factor, Hall
11C2×C3×C5×C7×C13—23no—
12C2×C3×C5×C7×C13D711yescharacteristic
13C2×C3×C5×C7×C13C2×C711yescharacteristic
14C7×C13×Dic7—151noHall
15C3×C72×C13Dic511yescharacteristic, complemented, Hall
16C13×Dic35—31no—
17C7×C13×Dic5—211no—
18C2×C3×C5×C72C2×C1311yescharacteristic
19C3×C5×C7×C13—23no—
20C3×C5×C7×C13Dic711yescharacteristic, complemented
21C3×C5×C7×C13C4×C711yescharacteristic, complemented
22C2×C72×C13D1511yescharacteristic
23C13×Dic21—51no—
24C7×Dic3×C13—351no—
25C7×Dic35—31noHall
26C2×C5×C7×C13—23no—
27C2×C5×C7×C13D3×C711yescharacteristic
28C2×C5×C7×C13D2111yescharacteristic
29C13×Dic15—71noHall
30C3×C5×C72C4×C1311yescharacteristic, complemented, Hall
31C72×C13Dic1511yescharacteristic, complemented, Hall
32C7×Dic21—51noHall
33C2×C3×C7×C13—23no—
34C2×C3×C7×C13C7×D511yescharacteristic
35C2×C3×C7×C13D3511yescharacteristic
36C2×C5×C72D3×C1311yescharacteristic
37C5×C7×C13—23no—
38C5×C7×C13C7×Dic311yescharacteristic, complemented
39C5×C7×C13Dic2111yescharacteristic, complemented
40Dic105C7×C1311yescharacteristic, direct product factor
41C7×Dic15—71no—
42C2×C3×C5×C13C7×D711yescharacteristic
43C4×C7×C13—1051no—
44C13×Dic7—151no—
45C2×C3×C72D5×C1311yescharacteristic
46C3×C7×C13—23no—
47C3×C7×C13C7×Dic511yescharacteristic, complemented
48C3×C7×C13Dic3511yescharacteristic, complemented
49C13×Dic5—211noHall
50C5×C72Dic3×C1311yescharacteristic, complemented, Hall
51C2×C3×C5×C7—23no—
52C2×C3×C5×C7C13×D711yescharacteristic
53C2×C3×C5×C7C2×C7×C1311yescharacteristic
54C7×Dic7—151noHall
55C3×C5×C13C7×Dic711yescharacteristic, complemented, Hall
56C2×C7×C13—23no—
57C2×C7×C13C7×D1511yescharacteristic
58C2×C7×C13D10511yescharacteristic
59Dic3×C13—351noHall
60C3×C72C13×Dic511yescharacteristic, complemented, Hall
61Dic35—31no—
62C7×Dic5—211no—
63C2×C5×C13C7×D2111yescharacteristic
64C3×C5×C7—23no—
65C3×C5×C7C13×Dic711yescharacteristic, complemented
66C3×C5×C7C4×C7×C1311yescharacteristic, complemented
67C2×C72C13×D1511yescharacteristic
68C7×C13—23no—
69C7×C13C7×Dic1511yescharacteristic, complemented
70C7×C13Dic10511yescharacteristic, direct product factor
71Dic21—51no—
72C7×Dic3—351no—
73C2×C3×C13C7×D3511yescharacteristic
74C2×C5×C7—23no—
75C2×C5×C7D3×C7×C1311yescharacteristic
76C2×C5×C7C13×D2111yescharacteristic
77C5×C13C7×Dic2111yescharacteristic, complemented, Hall
78Dic15—71noHall
79C4×C13—1051noHall
80C72C13×Dic1511yescharacteristic, complemented, Sylow
81C2×C3×C7—23no—
82C2×C3×C7C7×D5×C1311yescharacteristic
83C2×C3×C7C13×D3511yescharacteristic
84C3×C13C7×Dic3511yescharacteristic, complemented, Hall
85C5×C7—23no—
86C5×C7C7×Dic3×C1311yescharacteristic, complemented
87C5×C7C13×Dic2111yescharacteristic, complemented
88C2×C3×C5C7×C13×D711yescharacteristic
89C4×C7—1051no—
90Dic7—151no—
91C2×C13C7×D10511yescharacteristic
92C3×C7—23no—
93C3×C7C7×C13×Dic511yescharacteristic, complemented
94C3×C7C13×Dic3511yescharacteristic, complemented
95Dic5—211noHall
96C3×C5C7×C13×Dic711yescharacteristic, complemented, Hall
97C2×C7—23no—
98C2×C7C7×C13×D1511yescharacteristic
99C2×C7C13×D10511yescharacteristic
100C13C7×Dic10511yescharacteristic, direct product factor, Sylow
101Dic3—351noHall
102C2×C5C7×C13×D2111yescharacteristic
103C7—23no—
104C7C7×C13×Dic1511yescharacteristic, complemented
105C7C13×Dic10511yescharacteristic, direct product factor
106C2×C3C7×C13×D3511yescharacteristic
107C5C7×C13×Dic2111yescharacteristic, complemented, Sylow
108C4—1051noSylow
109C3C7×C13×Dic3511yescharacteristic, complemented, Sylow
110C2C7×C13×D10511yescharacteristic
subgroupG/H
center, hypercenterC2×C7×C13D105
commutator, hypocenterC3×C5×C7C4×C7×C13
FrattiniC2C7×C13×D105
Fitting, socle, prime radicalC2×C3×C5×C72×C13C2
cosocleC2×C3×C5×C7C2×C7×C13
LCSG ▷ C3×C5×C7
UCSC1 ◁ C2×C7×C13

Complements

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

NH ≅ G/Ntype
3. C3×C5×C72×C13C4semidirect
6. C13×Dic105C7direct (N × H)
9. C5×C72×C13Dic3semidirect
10. C7×Dic105C13direct (N × H)
15. C3×C72×C13Dic5semidirect
20. C3×C5×C7×C13Dic7semidirect
21. C3×C5×C7×C13C4×C7semidirect
30. C3×C5×C72C4×C13semidirect
31. C72×C13Dic15semidirect
38. C5×C7×C13C7×Dic3semidirect
39. C5×C7×C13Dic21semidirect
40. Dic105C7×C13direct (N × H)
47. C3×C7×C13C7×Dic5semidirect
48. C3×C7×C13Dic35semidirect
50. C5×C72Dic3×C13semidirect
55. C3×C5×C13C7×Dic7semidirect
60. C3×C72C13×Dic5semidirect
65. C3×C5×C7C13×Dic7semidirect
66. C3×C5×C7C4×C7×C13semidirect
69. C7×C13C7×Dic15semidirect
70. C7×C13Dic105direct (N × H)
77. C5×C13C7×Dic21semidirect
80. C72C13×Dic15semidirect
84. C3×C13C7×Dic35semidirect
86. C5×C7C7×Dic3×C13semidirect
87. C5×C7C13×Dic21semidirect
93. C3×C7C7×C13×Dic5semidirect
94. C3×C7C13×Dic35semidirect
96. C3×C5C7×C13×Dic7semidirect
100. C13C7×Dic105direct (N × H)
104. C7C7×C13×Dic15semidirect
105. C7C13×Dic105direct (N × H)
107. C5C7×C13×Dic21semidirect
109. C3C7×C13×Dic35semidirect

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
C7×C13×Dic353
C7×C13×Dic215
C13×Dic1057
C7×C13×Dic157
C7×Dic10513