Finite Group Databasebeta

← C2×C3×C7×C5⋊D55 #37528745

Subgroups — C2×C3×C7×C5⋊D55 #37528745

Order 23100.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×C5⋊D55C212yesmaximal, direct product factor
2C2×C3×C52×C7×C11C211yesmaximal, characteristic, complemented
3C2×C7×C5⋊D55C311yesmaximal, characteristic, direct product factor, Hall
4C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
5C2×C3×C7×D55—56nomaximal
6C7×C5⋊D55C2×C312yesdirect product factor
7C2×C52×C7×C11C2×C311yescharacteristic, complemented
8C2×C3×C5⋊D55C711yesmaximal, characteristic, direct product factor, Hall
9C3×C7×D55—512no—
10C2×C3×C5×C7×C11D516yescomplemented
11C2×C3×C7×C5⋊D5—111nomaximal, Hall
12C52×C7×C11C22×C311yescharacteristic, complemented, Hall
13C2×C3×C52×C11C2×C711yescharacteristic, complemented
14C3×C5⋊D55C2×C712yesdirect product factor
15C2×C7×D55—56no—
16C3×C5×C7×C11C2×D516yescomplemented
17C2×C5⋊D55C3×C711yescharacteristic, direct product factor, Hall
18C2×C3×C52×C7D1111yescharacteristic, complemented
19C3×C7×C5⋊D5—112no—
20C2×C3×C7×D11—251noHall
21C3×C52×C11C22×C711yescharacteristic, complemented, Hall
22C2×C5×C7×C11C3×D516yescomplemented
23C7×D55—512no—
24C2×C7×C5⋊D5—111noHall
25C2×C3×D55—56no—
26C2×C52×C11C2×C3×C711yescharacteristic, complemented
27C5⋊D55C2×C3×C712yesdirect product factor
28C3×C52×C7C2×D1111yescharacteristic, complemented, Hall
29C2×C3×C7×C11C5⋊D511yescharacteristic, complemented
30C3×C7×D11—252no—
31C2×C3×C7×D5—556no—
32C5×C7×C11C2×C3×D516yescomplemented
33C2×C52×C7C3×D1111yescharacteristic, complemented
34C7×C5⋊D5—112no—
35C2×C3×C5×C11C7×D516yescomplemented
36C3×D55—512no—
37C2×C7×D11—251noHall
38C2×C3×C5⋊D5—111noHall
39C52×C11C22×C3×C711yescharacteristic, complemented, Hall
40C3×C7×C11C2×C5⋊D511yescharacteristic, complemented, Hall
41C2×D55—56no—
42C2×C3×C5×C7D5516yescomplemented
43C3×C7×D5—5512no—
44C52×C7C2×C3×D1111yescharacteristic, complemented, Hall
45C3×C5×C11C2×C7×D516yescomplemented
46C2×C7×C11C3×C5⋊D511yescharacteristic, complemented
47C7×D11—252no—
48C2×C3×C52C7×D1111yescharacteristic, complemented
49C3×C5⋊D5—112no—
50C2×C7×D5—556no—
51C2×C3×D11—251noHall
52C2×C5×C11C3×C7×D516yescomplemented
53D55—512no—
54C3×C5×C7C2×D5516yescomplemented
55C2×C5⋊D5—111noHall
56C22×C3×C7—2751noHall
57C7×C11C2×C3×C5⋊D511yescharacteristic, complemented, Hall
58C3×C52C2×C7×D1111yescharacteristic, complemented, Hall
59C2×C5×C7C3×D5516yescomplemented
60C7×D5—5512no—
61C2×C3×C11C7×C5⋊D511yescharacteristic, complemented
62C3×D11—252no—
63C2×C3×D5—556no—
64C5×C11C2×C3×C7×D516yescomplemented
65C2×C52C3×C7×D1111yescharacteristic, complemented
66C5⋊D5—112no—
67C2×D11—251noHall
68C2×C3×C7—2752no—
69C2×C3×C7C5⋊D5511yescharacteristic, direct product factor
70C5×C7C2×C3×D5516yescomplemented
71C3×C11C2×C7×C5⋊D511yescharacteristic, complemented, Hall
72C2×C3×C5C7×D5516yescomplemented
73C3×D5—5512no—
74C22×C7—2751noHall
75C52C2×C3×C7×D1111yescharacteristic, complemented, Sylow
76C2×C11C3×C7×C5⋊D511yescharacteristic, complemented
77D11—252no—
78C3×C7C2×C5⋊D5511yescharacteristic, direct product factor, Hall
79C2×D5—556no—
80C3×C5C2×C7×D5516yescomplemented
81C2×C7—2752no—
82C2×C7C3×C5⋊D5511yescharacteristic, direct product factor
83C22×C3—2751noHall
84C11C2×C3×C7×C5⋊D511yescharacteristic, complemented, Sylow
85C2×C5C3×C7×D5516yescomplemented
86D5—5512no—
87C7C2×C3×C5⋊D5511yescharacteristic, direct product factor, Sylow
88C2×C3—2752no—
89C2×C3C7×C5⋊D5511yescharacteristic, direct product factor
90C5C2×C3×C7×D5516yescomplemented
91C22—2751noSylow
92C3C2×C7×C5⋊D5511yescharacteristic, direct product factor, Sylow
93C2—2752no—
94C2C3×C7×C5⋊D5511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C7C5⋊D55
commutator, cosocle, hypocenterC52×C11C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C52×C7×C11C2
LCSG ▷ C52×C11
UCSC1 ◁ C2×C3×C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×C5⋊D55C2direct (N × H)
2. C2×C3×C52×C7×C11C2semidirect
3. C2×C7×C5⋊D55C3direct (N × H)
4. C3×C52×C7×C11C22semidirect
6. C7×C5⋊D55C2×C3direct (N × H)
7. C2×C52×C7×C11C2×C3semidirect
8. C2×C3×C5⋊D55C7direct (N × H)
10. C2×C3×C5×C7×C11D5semidirect
12. C52×C7×C11C22×C3semidirect
13. C2×C3×C52×C11C2×C7semidirect
14. C3×C5⋊D55C2×C7direct (N × H)
16. C3×C5×C7×C11C2×D5semidirect
17. C2×C5⋊D55C3×C7direct (N × H)
18. C2×C3×C52×C7D11semidirect
21. C3×C52×C11C22×C7semidirect
22. C2×C5×C7×C11C3×D5semidirect
26. C2×C52×C11C2×C3×C7semidirect
27. C5⋊D55C2×C3×C7direct (N × H)
28. C3×C52×C7C2×D11semidirect
29. C2×C3×C7×C11C5⋊D5semidirect
32. C5×C7×C11C2×C3×D5semidirect
33. C2×C52×C7C3×D11semidirect
35. C2×C3×C5×C11C7×D5semidirect
39. C52×C11C22×C3×C7semidirect
40. C3×C7×C11C2×C5⋊D5semidirect
42. C2×C3×C5×C7D55semidirect
44. C52×C7C2×C3×D11semidirect
45. C3×C5×C11C2×C7×D5semidirect
46. C2×C7×C11C3×C5⋊D5semidirect
48. C2×C3×C52C7×D11semidirect
52. C2×C5×C11C3×C7×D5semidirect
54. C3×C5×C7C2×D55semidirect
57. C7×C11C2×C3×C5⋊D5semidirect
58. C3×C52C2×C7×D11semidirect
59. C2×C5×C7C3×D55semidirect
61. C2×C3×C11C7×C5⋊D5semidirect
64. C5×C11C2×C3×C7×D5semidirect
65. C2×C52C3×C7×D11semidirect
69. C2×C3×C7C5⋊D55direct (N × H)
70. C5×C7C2×C3×D55semidirect
71. C3×C11C2×C7×C5⋊D5semidirect
72. C2×C3×C5C7×D55semidirect
75. C52C2×C3×C7×D11semidirect
76. C2×C11C3×C7×C5⋊D5semidirect
78. C3×C7C2×C5⋊D55direct (N × H)
80. C3×C5C2×C7×D55semidirect
82. C2×C7C3×C5⋊D55direct (N × H)
84. C11C2×C3×C7×C5⋊D5semidirect
85. C2×C5C3×C7×D55semidirect
87. C7C2×C3×C5⋊D55direct (N × H)
89. C2×C3C7×C5⋊D55direct (N × H)
90. C5C2×C3×C7×D55semidirect
92. C3C2×C7×C5⋊D55direct (N × H)
94. C2C3×C7×C5⋊D55direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C7×C5⋊D552
C2×C3×C52×C7×C112
C2×C7×C5⋊D553
C2×C3×C7×D555
C2×C3×C5⋊D557
C2×C3×C7×C5⋊D511