Finite Group Databasebeta

← C2×C3×C5×(C11⋊C5)⋊D11 #49137628

Subgroups — C2×C3×C5×(C11⋊C5)⋊D11 #49137628

Order 36300.

360 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 128 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×C11×C11⋊C5C211yesmaximal, characteristic, complemented
2C3×C5×(C11⋊C5)⋊D11C212yesmaximal, direct product factor
3C2×C5×(C11⋊C5)⋊D11C311yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C11×C11⋊C5C2211yescharacteristic, complemented, Hall
5C2×C3×C5×C11⋊D11C511yesmaximal, characteristic, complemented
6C2×C3×(C11⋊C5)⋊D11C515yesmaximal, direct product factor
7C2×C5×C11×C11⋊C5C2×C311yescharacteristic, complemented
8C5×(C11⋊C5)⋊D11C2×C312yesdirect product factor
9C3×C5×C11⋊D11C2×C512yescomplemented
10C2×C3×C11×C11⋊C5C2×C515yescomplemented
11C3×(C11⋊C5)⋊D11C2×C5110yesdirect product factor
12C2×C3×C5×C112C2×C511yescharacteristic, complemented
13C2×C3×C52×D11—111nomaximal
14C2×C3×C5×AGL(1,𝔽11)—111nomaximal
15C5×C11×C11⋊C5C22×C311yescharacteristic, complemented, Hall
16C2×C5×C11⋊D11C3×C511yescharacteristic, complemented
17C2×(C11⋊C5)⋊D11C3×C515yesdirect product factor
18C3×C5×C112C22×C511yescharacteristic, complemented
19C3×C11×C11⋊C5C22×C515yescomplemented
20C2×C3×C52×C11—111no—
21C3×C52×D11—112no—
22C2×C3×C5×C11⋊C5D1111yescharacteristic, complemented
23C3×C5×AGL(1,𝔽11)—112no—
24C2×C3×C11⋊D11C5211yescharacteristic, complemented, Hall
25C2×C5×C112C2×C3×C511yescharacteristic, complemented
26C5×C11⋊D11C2×C3×C512yescomplemented
27C2×C11×C11⋊C5C2×C3×C515yescomplemented
28(C11⋊C5)⋊D11C2×C3×C5110yesdirect product factor
29C2×C52×D11—111no—
30C2×C5×AGL(1,𝔽11)—111no—
31C3×C52×C11—111no—
32C3×C5×C11⋊C5C2×D1111yescharacteristic, complemented
33C2×C3×C112C2×C5211yescharacteristic, complemented
34C3×C11⋊D11C2×C5212yescomplemented
35C2×C3×C5×D11—111no—
36C2×C3×C5×D11—115no—
37C2×C3×C5×D11—552no—
38C2×C3×C5×D11—551no—
39C2×C3×AGL(1,𝔽11)—115no—
40C5×C112C22×C3×C511yescharacteristic, complemented
41C11×C11⋊C5C22×C3×C515yescomplemented
42C2×C52×C11—111no—
43C52×D11—112no—
44C2×C5×C11⋊C5C3×D1111yescharacteristic, complemented
45C5×AGL(1,𝔽11)—112no—
46C2×C11⋊D11C3×C5211yescharacteristic, complemented, Hall
47C3×C112C22×C5211yescharacteristic, complemented, Hall
48C2×C3×C5×C11—52no—
49C2×C3×C5×C11—115no—
50C2×C3×C5×C11AGL(1,𝔽11)11yescharacteristic, complemented
51C2×C3×C5×C11C5×D1111yescharacteristic, complemented
52C3×C5×D11—112no—
53C3×C5×D11—1110no—
54C3×C5×D11—554no—
55C3×C5×D11—552no—
56C2×C3×C11⋊C5C5×D1115yescomplemented
57C3×AGL(1,𝔽11)—1110no—
58C22×C3×C52—1211noHall
59C52×C11—111no—
60C5×C11⋊C5C2×C3×D1111yescharacteristic, complemented
61C2×C112C2×C3×C5211yescharacteristic, complemented
62C11⋊D11C2×C3×C5212yescomplemented
63C2×C5×D11—111no—
64C2×C5×D11—115no—
65C2×C5×D11—552no—
66C2×C5×D11—551no—
67C2×AGL(1,𝔽11)—115no—
68C3×C5×C11—52no—
69C3×C5×C11—115no—
70C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
71C3×C5×C11C2×C5×D1111yescharacteristic, complemented
72C3×C11⋊C5C2×C5×D1115yescomplemented
73C2×C3×C52—111no—
74C2×C3×C52—1212no—
75C2×C3×D11—111no—
76C2×C3×D11—552no—
77C2×C3×D11—551no—
78C112C22×C3×C5211yescharacteristic, complemented, Sylow
79C2×C5×C11—52no—
80C2×C5×C11—115no—
81C2×C5×C11C3×AGL(1,𝔽11)11yescharacteristic, complemented
82C2×C5×C11C3×C5×D1111yescharacteristic, complemented
83C5×D11—112no—
84C5×D11—1110no—
85C5×D11—554no—
86C5×D11—552no—
87C2×C11⋊C5C3×C5×D1115yescomplemented
88AGL(1,𝔽11)—1110no—
89C22×C52—1211noHall
90C3×C52—111noHall
91C2×C3×C11—52no—
92C2×C3×C11C5×AGL(1,𝔽11)11yescharacteristic, complemented
93C2×C3×C11C52×D1111yescharacteristic, complemented
94C3×D11—112no—
95C3×D11—554no—
96C3×D11—552no—
97C22×C3×C5—6051no—
98C22×C3×C5—1215no—
99C5×C11—52no—
100C5×C11—115no—
101C5×C11C2×C3×AGL(1,𝔽11)11yescharacteristic, complemented
102C5×C11C2×C3×C5×D1111yescharacteristic, complemented
103C11⋊C5C2×C3×C5×D1115yescomplemented
104C2×C52—111no—
105C2×C52—1212no—
106C2×D11—111no—
107C2×D11—552no—
108C2×D11—551no—
109C3×C11—52no—
110C3×C11C2×C5×AGL(1,𝔽11)11yescharacteristic, complemented
111C3×C11C2×C52×D1111yescharacteristic, complemented
112C2×C3×C5—115no—
113C2×C3×C5—6052no—
114C2×C3×C5—12110no—
115C2×C3×C5(C11⋊C5)⋊D1111yescharacteristic, direct product factor
116C52—111noSylow
117C2×C11—52no—
118C2×C11C3×C5×AGL(1,𝔽11)11yescharacteristic, complemented
119C2×C11C3×C52×D1111yescharacteristic, complemented
120D11—112no—
121D11—554no—
122D11—552no—
123C22×C5—6051no—
124C22×C5—1215no—
125C3×C5—115no—
126C3×C5C2×(C11⋊C5)⋊D1111yescharacteristic, direct product factor
127C22×C3—6051noHall
128C11—52no—
129C11C2×C3×C5×AGL(1,𝔽11)11yescharacteristic, complemented
130C11C2×C3×C52×D1111yescharacteristic, complemented
131C2×C5—115no—
132C2×C5—6052no—
133C2×C5—12110no—
134C2×C5C3×(C11⋊C5)⋊D1111yescharacteristic, direct product factor
135C2×C3—6052no—
136C2×C3C5×(C11⋊C5)⋊D1111yescharacteristic, direct product factor
137C5—115no—
138C5C2×C3×(C11⋊C5)⋊D1111yescharacteristic, direct product factor
139C22—6051noSylow
140C3C2×C5×(C11⋊C5)⋊D1111yescharacteristic, direct product factor, Sylow
141C2—6052no—
142C2C3×C5×(C11⋊C5)⋊D1111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5(C11⋊C5)⋊D11
commutator, cosocle, hypocenterC112C22×C3×C52
FrattiniC1G
Fitting, socleC2×C3×C5×C112C2×C5
LCSG ▷ C112
UCSC1 ◁ C2×C3×C5

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C11×C11⋊C5C2semidirect
2. C3×C5×(C11⋊C5)⋊D11C2direct (N × H)
3. C2×C5×(C11⋊C5)⋊D11C3direct (N × H)
4. C3×C5×C11×C11⋊C5C22semidirect
5. C2×C3×C5×C11⋊D11C5semidirect
6. C2×C3×(C11⋊C5)⋊D11C5direct (N × H)
7. C2×C5×C11×C11⋊C5C2×C3semidirect
8. C5×(C11⋊C5)⋊D11C2×C3direct (N × H)
9. C3×C5×C11⋊D11C2×C5semidirect
10. C2×C3×C11×C11⋊C5C2×C5semidirect
11. C3×(C11⋊C5)⋊D11C2×C5direct (N × H)
12. C2×C3×C5×C112C2×C5semidirect
15. C5×C11×C11⋊C5C22×C3semidirect
16. C2×C5×C11⋊D11C3×C5semidirect
17. C2×(C11⋊C5)⋊D11C3×C5direct (N × H)
18. C3×C5×C112C22×C5semidirect
19. C3×C11×C11⋊C5C22×C5semidirect
22. C2×C3×C5×C11⋊C5D11semidirect
24. C2×C3×C11⋊D11C52semidirect
25. C2×C5×C112C2×C3×C5semidirect
26. C5×C11⋊D11C2×C3×C5semidirect
27. C2×C11×C11⋊C5C2×C3×C5semidirect
28. (C11⋊C5)⋊D11C2×C3×C5direct (N × H)
32. C3×C5×C11⋊C5C2×D11semidirect
33. C2×C3×C112C2×C52semidirect
34. C3×C11⋊D11C2×C52semidirect
40. C5×C112C22×C3×C5semidirect
41. C11×C11⋊C5C22×C3×C5semidirect
44. C2×C5×C11⋊C5C3×D11semidirect
46. C2×C11⋊D11C3×C52semidirect
47. C3×C112C22×C52semidirect
50. C2×C3×C5×C11AGL(1,𝔽11)semidirect
51. C2×C3×C5×C11C5×D11semidirect
56. C2×C3×C11⋊C5C5×D11semidirect
60. C5×C11⋊C5C2×C3×D11semidirect
61. C2×C112C2×C3×C52semidirect
62. C11⋊D11C2×C3×C52semidirect
70. C3×C5×C11C2×AGL(1,𝔽11)semidirect
71. C3×C5×C11C2×C5×D11semidirect
72. C3×C11⋊C5C2×C5×D11semidirect
78. C112C22×C3×C52semidirect
81. C2×C5×C11C3×AGL(1,𝔽11)semidirect
82. C2×C5×C11C3×C5×D11semidirect
87. C2×C11⋊C5C3×C5×D11semidirect
92. C2×C3×C11C5×AGL(1,𝔽11)semidirect
93. C2×C3×C11C52×D11semidirect
101. C5×C11C2×C3×AGL(1,𝔽11)semidirect
102. C5×C11C2×C3×C5×D11semidirect
103. C11⋊C5C2×C3×C5×D11semidirect
110. C3×C11C2×C5×AGL(1,𝔽11)semidirect
111. C3×C11C2×C52×D11semidirect
115. C2×C3×C5(C11⋊C5)⋊D11direct (N × H)
118. C2×C11C3×C5×AGL(1,𝔽11)semidirect
119. C2×C11C3×C52×D11semidirect
126. C3×C5C2×(C11⋊C5)⋊D11direct (N × H)
129. C11C2×C3×C5×AGL(1,𝔽11)semidirect
130. C11C2×C3×C52×D11semidirect
134. C2×C5C3×(C11⋊C5)⋊D11direct (N × H)
136. C2×C3C5×(C11⋊C5)⋊D11direct (N × H)
138. C5C2×C3×(C11⋊C5)⋊D11direct (N × H)
140. C3C2×C5×(C11⋊C5)⋊D11direct (N × H)
142. C2C3×C5×(C11⋊C5)⋊D11direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C11×C11⋊C52
C3×C5×(C11⋊C5)⋊D112
C2×C5×(C11⋊C5)⋊D113
C2×C3×C5×C11⋊D115
C2×C3×(C11⋊C5)⋊D115
C2×C3×C52×D1111
C2×C3×C5×AGL(1,𝔽11)11