Finite Group Databasebeta

← D3×C72×D5×C13 #50304451

Subgroups — D3×C72×D5×C13 #50304451

Order 38220.

400 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 200 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×C72×D5×C13C211yesmaximal, characteristic, complemented
2C5×D3×C72×C13C211yesmaximal, characteristic, complemented
3C72×C13×D15C211yesmaximal, characteristic, complemented
4C2×C72×D5×C13—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6C2×D3×C72×C13—51nomaximal, Hall
7C72×D5×C13—31no—
8C72×D5×C13D311yescharacteristic, direct product factor
9C2×C5×C72×C13—31no—
10D3×C7×D5×C13C718yesmaximal, direct product factor
11D3×C72×C13—51no—
12D3×C72×C13D511yescharacteristic, direct product factor
13C2×C3×C72×C13—51no—
14C5×C72×C13C2×D311yescharacteristic, complemented, Hall
15D3×C72×D5C1311yesmaximal, characteristic, direct product factor, Hall
16C7×C13×D15C2×C718yescomplemented
17C5×D3×C7×C13C2×C718yescomplemented
18C3×C7×D5×C13C2×C718yescomplemented
19C22×C72×C13—151noHall
20C3×C72×C13C2×D511yescharacteristic, complemented, Hall
21C2×C7×D5×C13—38no—
22C72×D15C2×C1311yescharacteristic, complemented
23C5×D3×C72C2×C1311yescharacteristic, complemented
24C3×C72×D5C2×C1311yescharacteristic, complemented
25C3×C5×C7×C13C22×C718yescomplemented
26C2×C72×C13—31no—
27C2×C72×C13—51no—
28C2×C72×C13—151no—
29C2×D3×C7×C13—58no—
30C2×C72×D5—31noHall
31C2×C5×C7×C13—38no—
32C7×D5×C13—38no—
33C7×D5×C13D3×C718yesdirect product factor
34D3×D5×C13C7211yescharacteristic, direct product factor, Hall
35C3×C5×C72C22×C1311yescharacteristic, complemented, Hall
36C72×C13D3×D511yescharacteristic, direct product factor, Hall
37C2×D3×C72—51noHall
38C2×C3×C7×C13—58no—
39D3×C7×C13—58no—
40D3×C7×C13C7×D518yesdirect product factor
41C2×C5×C72—31no—
42C72×D5—31no—
43C72×D5D3×C1311yescharacteristic, direct product factor
44C5×C7×C13C2×D3×C718yescomplemented
45D3×C7×D5C7×C1318yesdirect product factor
46C13×D15C2×C7211yescharacteristic, complemented
47C5×D3×C13C2×C7211yescharacteristic, complemented
48C3×D5×C13C2×C7211yescharacteristic, complemented
49C22×C7×C13—158no—
50C2×C3×C72—51no—
51D3×C72—51no—
52D3×C72D5×C1311yescharacteristic, direct product factor
53C3×C7×C13C2×C7×D518yescomplemented
54C2×D5×C13—31noHall
55C5×C72C2×D3×C1311yescharacteristic, complemented, Hall
56C7×D15C2×C7×C1318yescomplemented
57C5×D3×C7C2×C7×C1318yescomplemented
58C3×C7×D5C2×C7×C1318yescomplemented
59C22×C72—151noHall
60C3×C5×C13C22×C7211yescharacteristic, complemented, Hall
61C2×C7×C13—38no—
62C2×C7×C13—58no—
63C2×C7×C13—158no—
64C2×D3×C13—51noHall
65C3×C72C2×D5×C1311yescharacteristic, complemented, Hall
66C2×C7×D5—38no—
67C2×C5×C13—31no—
68D5×C13—31no—
69D5×C13D3×C7211yescharacteristic, direct product factor
70C3×C5×C7C22×C7×C1318yescomplemented
71C2×C72—31no—
72C2×C72—51no—
73C2×C72—151no—
74C7×C13D3×C7×D518yesdirect product factor
75C2×D3×C7—58no—
76C2×C3×C13—51no—
77D3×C13—51no—
78D3×C13C72×D511yescharacteristic, direct product factor
79C2×C5×C7—38no—
80C7×D5—38no—
81C7×D5D3×C7×C1318yesdirect product factor
82C5×C13C2×D3×C7211yescharacteristic, complemented, Hall
83D3×D5C72×C1311yescharacteristic, direct product factor, Hall
84C22×C13—151noHall
85C72D3×D5×C1311yescharacteristic, direct product factor, Sylow
86C2×C3×C7—58no—
87D3×C7—58no—
88D3×C7C7×D5×C1318yesdirect product factor
89C3×C13C2×C72×D511yescharacteristic, complemented, Hall
90C5×C7C2×D3×C7×C1318yescomplemented
91D15C2×C72×C1311yescharacteristic, complemented
92C3×D5C2×C72×C1311yescharacteristic, complemented
93C5×D3C2×C72×C1311yescharacteristic, complemented
94C22×C7—158no—
95C2×C13—31no—
96C2×C13—51no—
97C2×C13—151no—
98C3×C7C2×C7×D5×C1318yescomplemented
99C2×D5—31noHall
100C3×C5C22×C72×C1311yescharacteristic, complemented, Hall
101C2×C7—38no—
102C2×C7—58no—
103C2×C7—158no—
104C13D3×C72×D511yescharacteristic, direct product factor, Sylow
105C2×D3—51noHall
106C2×C5—31no—
107D5—31no—
108D5D3×C72×C1311yescharacteristic, direct product factor
109C7D3×C7×D5×C1318yesdirect product factor
110C2×C3—51no—
111D3—51no—
112D3C72×D5×C1311yescharacteristic, direct product factor
113C5C2×D3×C72×C1311yescharacteristic, complemented, Sylow
114C22—151noSylow
115C3C2×C72×D5×C1311yescharacteristic, complemented, Sylow
116C2—31no—
117C2—51no—
118C2—151no—
subgroupG/H
center, hypercenterC72×C13D3×D5
commutator, cosocle, hypocenterC3×C5C22×C72×C13
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C3×C5
UCSC1 ◁ C72×C13

Complements

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

NH ≅ G/Ntype
1. C3×C72×D5×C13C2semidirect
2. C5×D3×C72×C13C2semidirect
3. C72×C13×D15C2semidirect
5. C3×C5×C72×C13C22semidirect
8. C72×D5×C13D3direct (N × H)
10. D3×C7×D5×C13C7direct (N × H)
12. D3×C72×C13D5direct (N × H)
14. C5×C72×C13C2×D3semidirect
15. D3×C72×D5C13direct (N × H)
16. C7×C13×D15C2×C7semidirect
17. C5×D3×C7×C13C2×C7semidirect
18. C3×C7×D5×C13C2×C7semidirect
20. C3×C72×C13C2×D5semidirect
22. C72×D15C2×C13semidirect
23. C5×D3×C72C2×C13semidirect
24. C3×C72×D5C2×C13semidirect
25. C3×C5×C7×C13C22×C7semidirect
33. C7×D5×C13D3×C7direct (N × H)
34. D3×D5×C13C72direct (N × H)
35. C3×C5×C72C22×C13semidirect
36. C72×C13D3×D5direct (N × H)
40. D3×C7×C13C7×D5direct (N × H)
43. C72×D5D3×C13direct (N × H)
44. C5×C7×C13C2×D3×C7semidirect
45. D3×C7×D5C7×C13direct (N × H)
46. C13×D15C2×C72semidirect
47. C5×D3×C13C2×C72semidirect
48. C3×D5×C13C2×C72semidirect
52. D3×C72D5×C13direct (N × H)
53. C3×C7×C13C2×C7×D5semidirect
55. C5×C72C2×D3×C13semidirect
56. C7×D15C2×C7×C13semidirect
57. C5×D3×C7C2×C7×C13semidirect
58. C3×C7×D5C2×C7×C13semidirect
60. C3×C5×C13C22×C72semidirect
65. C3×C72C2×D5×C13semidirect
69. D5×C13D3×C72direct (N × H)
70. C3×C5×C7C22×C7×C13semidirect
74. C7×C13D3×C7×D5direct (N × H)
78. D3×C13C72×D5direct (N × H)
81. C7×D5D3×C7×C13direct (N × H)
82. C5×C13C2×D3×C72semidirect
83. D3×D5C72×C13direct (N × H)
85. C72D3×D5×C13direct (N × H)
88. D3×C7C7×D5×C13direct (N × H)
89. C3×C13C2×C72×D5semidirect
90. C5×C7C2×D3×C7×C13semidirect
91. D15C2×C72×C13semidirect
92. C3×D5C2×C72×C13semidirect
93. C5×D3C2×C72×C13semidirect
98. C3×C7C2×C7×D5×C13semidirect
100. C3×C5C22×C72×C13semidirect
104. C13D3×C72×D5direct (N × H)
108. D5D3×C72×C13direct (N × H)
109. C7D3×C7×D5×C13direct (N × H)
112. D3C72×D5×C13direct (N × H)
113. C5C2×D3×C72×C13semidirect
115. C3C2×C72×D5×C13semidirect

Maximal subgroups

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

subgroupindex
C3×C72×D5×C132
C5×D3×C72×C132
C72×C13×D152
C2×C72×D5×C133
C2×D3×C72×C135
D3×C7×D5×C137
D3×C72×D513