Finite Group Databasebeta

← C3×C7×D52×C11 #37528614

Subgroups — C3×C7×D52×C11 #37528614

Order 23100.

192 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 80 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×C7×D5×C11C212yesmaximal, complemented
2C3×C7×C11×C5⋊D5C211yesmaximal, characteristic, complemented
3C7×D52×C11C311yesmaximal, characteristic, direct product factor, Hall
4C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
5C2×C3×C7×D5×C11—52nomaximal
6C7×C11×C5⋊D5C2×C311yescharacteristic, complemented
7C5×C7×D5×C11C2×C312yescomplemented
8C3×D52×C11C711yesmaximal, characteristic, direct product factor, Hall
9C3×C7×D5×C11—52no—
10C3×C7×D5×C11—102no—
11C3×C7×D5×C11D512yesdirect product factor
12C2×C3×C5×C7×C11—52no—
13C3×C7×D52C1111yesmaximal, characteristic, direct product factor, Hall
14C52×C7×C11C22×C311yescharacteristic, complemented, Hall
15C3×C11×C5⋊D5C2×C711yescharacteristic, complemented
16C3×C5×D5×C11C2×C712yescomplemented
17C2×C7×D5×C11—52no—
18C3×C5×C7×C11—22no—
19C3×C5×C7×C11C2×D512yescomplemented
20D52×C11C3×C711yescharacteristic, direct product factor, Hall
21C3×C7×C5⋊D5C2×C1111yescharacteristic, complemented
22C3×C5×C7×D5C2×C1112yescomplemented
23C22×C3×C7×C11—251noHall
24C3×C52×C11C22×C711yescharacteristic, complemented, Hall
25C2×C5×C7×C11—52no—
26C7×D5×C11—52no—
27C7×D5×C11—102no—
28C7×D5×C11C3×D512yesdirect product factor
29C7×D52C3×C1111yescharacteristic, direct product factor, Hall
30C2×C3×D5×C11—52no—
31C11×C5⋊D5C2×C3×C711yescharacteristic, complemented
32C5×D5×C11C2×C3×C712yescomplemented
33C3×C52×C7C22×C1111yescharacteristic, complemented, Hall
34C2×C3×C7×C11—52no—
35C2×C3×C7×C11—251no—
36C2×C3×C7×D5—52no—
37C5×C7×C11—22no—
38C5×C7×C11C2×C3×D512yescomplemented
39C7×C5⋊D5C2×C3×C1111yescharacteristic, complemented
40C5×C7×D5C2×C3×C1112yescomplemented
41C2×C3×C5×C11—52no—
42C3×D5×C11—52no—
43C3×D5×C11—102no—
44C3×D5×C11C7×D512yesdirect product factor
45C22×C7×C11—251noHall
46C3×D52C7×C1111yescharacteristic, direct product factor, Hall
47C52×C11C22×C3×C711yescharacteristic, complemented, Hall
48C3×C7×C11D5211yescharacteristic, direct product factor, Hall
49C2×D5×C11—52no—
50C2×C3×C5×C7—52no—
51C3×C7×D5—52no—
52C3×C7×D5—102no—
53C3×C7×D5D5×C1112yesdirect product factor
54C52×C7C22×C3×C1111yescharacteristic, complemented, Hall
55C3×C5×C11—22no—
56C3×C5×C11C2×C7×D512yescomplemented
57C2×C7×C11—52no—
58C2×C7×C11—251no—
59C3×C5⋊D5C2×C7×C1111yescharacteristic, complemented
60C3×C5×D5C2×C7×C1112yescomplemented
61C2×C7×D5—52no—
62C22×C3×C11—251noHall
63C2×C5×C11—52no—
64D5×C11—52no—
65D5×C11—102no—
66D5×C11C3×C7×D512yesdirect product factor
67C3×C5×C7—22no—
68C3×C5×C7C2×D5×C1112yescomplemented
69D52C3×C7×C1111yescharacteristic, direct product factor, Hall
70C22×C3×C7—251noHall
71C7×C11C3×D5211yescharacteristic, direct product factor, Hall
72C3×C52C22×C7×C1111yescharacteristic, complemented, Hall
73C2×C5×C7—52no—
74C7×D5—52no—
75C7×D5—102no—
76C7×D5C3×D5×C1112yesdirect product factor
77C2×C3×C11—52no—
78C2×C3×C11—251no—
79C2×C3×D5—52no—
80C5×C11—22no—
81C5×C11C2×C3×C7×D512yescomplemented
82C5⋊D5C2×C3×C7×C1111yescharacteristic, complemented
83C5×D5C2×C3×C7×C1112yescomplemented
84C22×C11—251noHall
85C2×C3×C7—52no—
86C2×C3×C7—251no—
87C5×C7—22no—
88C5×C7C2×C3×D5×C1112yescomplemented
89C3×C11C7×D5211yescharacteristic, direct product factor, Hall
90C2×C3×C5—52no—
91C3×D5—52no—
92C3×D5—102no—
93C3×D5C7×D5×C1112yesdirect product factor
94C22×C7—251noHall
95C52C22×C3×C7×C1111yescharacteristic, complemented, Sylow
96C2×C11—52no—
97C2×C11—251no—
98C3×C7D52×C1111yescharacteristic, direct product factor, Hall
99C2×D5—52no—
100C3×C5—22no—
101C3×C5C2×C7×D5×C1112yescomplemented
102C2×C7—52no—
103C2×C7—251no—
104C22×C3—251noHall
105C11C3×C7×D5211yescharacteristic, direct product factor, Sylow
106C2×C5—52no—
107D5—52no—
108D5—102no—
109D5C3×C7×D5×C1112yesdirect product factor
110C7C3×D52×C1111yescharacteristic, direct product factor, Sylow
111C2×C3—52no—
112C2×C3—251no—
113C5—22no—
114C5C2×C3×C7×D5×C1112yescomplemented
115C22—251noSylow
116C3C7×D52×C1111yescharacteristic, direct product factor, Sylow
117C2—52no—
118C2—251no—
subgroupG/H
center, hypercenterC3×C7×C11D52
commutator, cosocle, hypocenterC52C22×C3×C7×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C52
UCSC1 ◁ C3×C7×C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D5×C11C2semidirect
2. C3×C7×C11×C5⋊D5C2semidirect
3. C7×D52×C11C3direct (N × H)
4. C3×C52×C7×C11C22semidirect
6. C7×C11×C5⋊D5C2×C3semidirect
7. C5×C7×D5×C11C2×C3semidirect
8. C3×D52×C11C7direct (N × H)
11. C3×C7×D5×C11D5direct (N × H)
13. C3×C7×D52C11direct (N × H)
14. C52×C7×C11C22×C3semidirect
15. C3×C11×C5⋊D5C2×C7semidirect
16. C3×C5×D5×C11C2×C7semidirect
19. C3×C5×C7×C11C2×D5semidirect
20. D52×C11C3×C7direct (N × H)
21. C3×C7×C5⋊D5C2×C11semidirect
22. C3×C5×C7×D5C2×C11semidirect
24. C3×C52×C11C22×C7semidirect
28. C7×D5×C11C3×D5direct (N × H)
29. C7×D52C3×C11direct (N × H)
31. C11×C5⋊D5C2×C3×C7semidirect
32. C5×D5×C11C2×C3×C7semidirect
33. C3×C52×C7C22×C11semidirect
38. C5×C7×C11C2×C3×D5semidirect
39. C7×C5⋊D5C2×C3×C11semidirect
40. C5×C7×D5C2×C3×C11semidirect
44. C3×D5×C11C7×D5direct (N × H)
46. C3×D52C7×C11direct (N × H)
47. C52×C11C22×C3×C7semidirect
48. C3×C7×C11D52direct (N × H)
53. C3×C7×D5D5×C11direct (N × H)
54. C52×C7C22×C3×C11semidirect
56. C3×C5×C11C2×C7×D5semidirect
59. C3×C5⋊D5C2×C7×C11semidirect
60. C3×C5×D5C2×C7×C11semidirect
66. D5×C11C3×C7×D5direct (N × H)
68. C3×C5×C7C2×D5×C11semidirect
69. D52C3×C7×C11direct (N × H)
71. C7×C11C3×D52direct (N × H)
72. C3×C52C22×C7×C11semidirect
76. C7×D5C3×D5×C11direct (N × H)
81. C5×C11C2×C3×C7×D5semidirect
82. C5⋊D5C2×C3×C7×C11semidirect
83. C5×D5C2×C3×C7×C11semidirect
88. C5×C7C2×C3×D5×C11semidirect
89. C3×C11C7×D52direct (N × H)
93. C3×D5C7×D5×C11direct (N × H)
95. C52C22×C3×C7×C11semidirect
98. C3×C7D52×C11direct (N × H)
101. C3×C5C2×C7×D5×C11semidirect
105. C11C3×C7×D52direct (N × H)
109. D5C3×C7×D5×C11direct (N × H)
110. C7C3×D52×C11direct (N × H)
114. C5C2×C3×C7×D5×C11semidirect
116. C3C7×D52×C11direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7×D5×C112
C3×C7×C11×C5⋊D52
C7×D52×C113
C2×C3×C7×D5×C115
C3×D52×C117
C3×C7×D5211