Finite Group Databasebeta

← C5×C11×C3⋊D105 #46831680

Subgroups — C5×C11×C3⋊D105 #46831680

Order 34650.

240 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C32×C52×C7×C11C211yesmaximal, characteristic, complemented, Hall
2C5×C11×D105—34nomaximal
3C11×C3⋊D105C511yesmaximal, characteristic, direct product factor
4C5×C11×C3⋊D21—51nomaximal
5C3×C52×C7×C11D314yescomplemented
6C5×C11×C3⋊D15—71nomaximal, Hall
7C5×C11×D35—91noHall
8C32×C5×C7×C11—22no—
9C32×C5×C7×C11D511yescharacteristic, complemented
10C32×C5×C7×C11C2×C511yescharacteristic, complemented
11C5×C3⋊D105C1111yesmaximal, characteristic, direct product factor, Hall
12C32×C52×C11D711yescharacteristic, complemented, Hall
13C11×D105—34no—
14C5×C11×D21—154no—
15C52×C7×C11C3⋊D311yescharacteristic, complemented, Hall
16C5×C11×D15—214no—
17C32×C52×C7C2×C1111yescharacteristic, complemented, Hall
18C11×C3⋊D21—51noHall
19C3×C5×C7×C11—28no—
20C3×C5×C7×C11C5×D314yescomplemented
21C3×C5×C7×C11D1514yescomplemented
22C5×D105—34no—
23C11×C3⋊D15—71no—
24C5×C11×C3⋊D3—351no—
25C3×C52×C11D2114yescomplemented
26C11×D35—91no—
27C5×C11×D7—451no—
28C32×C7×C11C5×D511yescharacteristic, complemented, Hall
29C3⋊D105C5×C1111yescharacteristic, direct product factor
30C5×C3⋊D21—51no—
31C5×D5×C11—631noHall
32C3×C52×C7D3×C1114yescomplemented
33C32×C5×C11—22no—
34C32×C5×C11C5×D711yescharacteristic, complemented
35C32×C5×C11D3511yescharacteristic, complemented
36C11×D21—154no—
37C5×C3⋊D15—71noHall
38C5×C7×C11—22no—
39C5×C7×C11C5×C3⋊D311yescharacteristic, complemented
40C5×C7×C11C3⋊D1511yescharacteristic, complemented
41C5×D35—91noHall
42C11×D15—214no—
43C5×D3×C11—1054no—
44C32×C5×C7—22no—
45C32×C5×C7D5×C1111yescharacteristic, complemented
46C32×C5×C7C2×C5×C1111yescharacteristic, complemented
47C52×C11C3⋊D2111yescharacteristic, complemented, Hall
48C3×C7×C11C5×D1514yescomplemented
49C32×C52C11×D711yescharacteristic, complemented, Hall
50D105—34no—
51C5×D21—154no—
52C11×C3⋊D3—351noHall
53C52×C7C11×C3⋊D311yescharacteristic, complemented, Hall
54C3×C5×C11—28no—
55C3×C5×C11C5×D2114yescomplemented
56C3×C5×C11D10514yescomplemented
57C11×D7—451noHall
58C5×D15—214no—
59C3⋊D21—51noHall
60C2×C5×C11—3151no—
61D5×C11—631no—
62C3×C5×C7—28no—
63C3×C5×C7C5×D3×C1114yescomplemented
64C3×C5×C7C11×D1514yescomplemented
65C32×C11C5×D3511yescharacteristic, complemented, Hall
66C3⋊D15—71no—
67C5×C3⋊D3—351no—
68C7×C11C5×C3⋊D1511yescharacteristic, complemented, Hall
69C3×C52C11×D2114yescomplemented
70D35—91no—
71C5×D7—451no—
72D3×C11—1054no—
73C32×C7C5×D5×C1111yescharacteristic, complemented, Hall
74C5×C11—22no—
75C5×C11C5×C3⋊D2111yescharacteristic, complemented
76C5×C11C3⋊D10511yescharacteristic, direct product factor
77C5×D5—631noHall
78C32×C5—22no—
79C32×C5C5×C11×D711yescharacteristic, complemented
80C32×C5C11×D3511yescharacteristic, complemented
81D21—154no—
82C5×C7—22no—
83C5×C7C5×C11×C3⋊D311yescharacteristic, complemented
84C5×C7C11×C3⋊D1511yescharacteristic, complemented
85C3×C11C5×D10514yescomplemented
86D15—214no—
87C5×D3—1054no—
88C52C11×C3⋊D2111yescharacteristic, complemented, Sylow
89C2×C11—3151noHall
90C3×C7C5×C11×D1514yescomplemented
91C3⋊D3—351noHall
92C3×C5—28no—
93C3×C5C5×C11×D2114yescomplemented
94C3×C5C11×D10514yescomplemented
95D7—451noHall
96C11C5×C3⋊D10511yescharacteristic, direct product factor, Sylow
97C2×C5—3151no—
98D5—631no—
99C32C5×C11×D3511yescharacteristic, complemented, Sylow
100C7C5×C11×C3⋊D1511yescharacteristic, complemented, Sylow
101D3—1054no—
102C5—22no—
103C5C5×C11×C3⋊D2111yescharacteristic, complemented
104C5C11×C3⋊D10511yescharacteristic, direct product factor
105C3C5×C11×D10514yescomplemented
106C2—3151noSylow
subgroupG/H
center, hypercenterC5×C11C3⋊D105
commutator, cosocle, hypocenterC32×C5×C7C2×C5×C11
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C32×C5×C7
UCSC1 ◁ C5×C11

Complements

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

NH ≅ G/Ntype
1. C32×C52×C7×C11C2semidirect
3. C11×C3⋊D105C5direct (N × H)
5. C3×C52×C7×C11D3semidirect
9. C32×C5×C7×C11D5semidirect
10. C32×C5×C7×C11C2×C5semidirect
11. C5×C3⋊D105C11direct (N × H)
12. C32×C52×C11D7semidirect
15. C52×C7×C11C3⋊D3semidirect
17. C32×C52×C7C2×C11semidirect
20. C3×C5×C7×C11C5×D3semidirect
21. C3×C5×C7×C11D15semidirect
25. C3×C52×C11D21semidirect
28. C32×C7×C11C5×D5semidirect
29. C3⋊D105C5×C11direct (N × H)
32. C3×C52×C7D3×C11semidirect
34. C32×C5×C11C5×D7semidirect
35. C32×C5×C11D35semidirect
39. C5×C7×C11C5×C3⋊D3semidirect
40. C5×C7×C11C3⋊D15semidirect
45. C32×C5×C7D5×C11semidirect
46. C32×C5×C7C2×C5×C11semidirect
47. C52×C11C3⋊D21semidirect
48. C3×C7×C11C5×D15semidirect
49. C32×C52C11×D7semidirect
53. C52×C7C11×C3⋊D3semidirect
55. C3×C5×C11C5×D21semidirect
56. C3×C5×C11D105semidirect
63. C3×C5×C7C5×D3×C11semidirect
64. C3×C5×C7C11×D15semidirect
65. C32×C11C5×D35semidirect
68. C7×C11C5×C3⋊D15semidirect
69. C3×C52C11×D21semidirect
73. C32×C7C5×D5×C11semidirect
75. C5×C11C5×C3⋊D21semidirect
76. C5×C11C3⋊D105direct (N × H)
79. C32×C5C5×C11×D7semidirect
80. C32×C5C11×D35semidirect
83. C5×C7C5×C11×C3⋊D3semidirect
84. C5×C7C11×C3⋊D15semidirect
85. C3×C11C5×D105semidirect
88. C52C11×C3⋊D21semidirect
90. C3×C7C5×C11×D15semidirect
93. C3×C5C5×C11×D21semidirect
94. C3×C5C11×D105semidirect
96. C11C5×C3⋊D105direct (N × H)
99. C32C5×C11×D35semidirect
100. C7C5×C11×C3⋊D15semidirect
103. C5C5×C11×C3⋊D21semidirect
104. C5C11×C3⋊D105direct (N × H)
105. C3C5×C11×D105semidirect

Maximal subgroups

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

subgroupindex
C32×C52×C7×C112
C5×C11×D1053
C11×C3⋊D1055
C5×C11×C3⋊D215
C5×C11×C3⋊D157
C5×C3⋊D10511