Finite Group Databasebeta

← C3×C5×#11925896⋊C2 #49137371

Subgroups — C3×C5×#11925896⋊C2 #49137371

Order 36300.

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

normal subgroups only

This group has 328 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
1C3×C5×#11925896C211yesmaximal, characteristic, complemented
2C3×C5×#11925896C211yesmaximal, characteristic, complemented
3C3×C5×#11925893C211yesmaximal, characteristic, complemented
4C5×#11925896⋊C2C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×#10597245C2211yescharacteristic, complemented, Hall
6C3×C5×D112C511yesmaximal, characteristic, complemented
7C3×#11925896⋊C2C515yesmaximal, direct product factor
8C5×#11925896C2×C311yescharacteristic, complemented
9C5×#11925896C2×C311yescharacteristic, complemented
10C5×#11925893C2×C311yescharacteristic, complemented
11C3×C5×C11⋊D11C2×C511yescharacteristic, complemented
12C3×C5×C11×D11C2×C511yescharacteristic, complemented
13C3×C5×C11×D11C2×C511yescharacteristic, complemented
14C3×#11925896C2×C515yescomplemented
15C3×#11925896C2×C515yescomplemented
16C3×#11925893C2×C515yescomplemented
17C2×C3×C5×AGL(1,𝔽11)—111nomaximal
18C2×C3×C5×AGL(1,𝔽11)—111nomaximal
19C5×#10597245C22×C311yescharacteristic, complemented, Hall
20C5×D112C3×C511yescharacteristic, complemented
21#11925896⋊C2C3×C515yesdirect product factor
22C3×C5×C112C22×C511yescharacteristic, complemented
23C3×#10597245C22×C515yescomplemented
24C2×C3×C5×C11⋊C5—111no—
25C2×C3×C5×C11⋊C5—111no—
26C3×C5×AGL(1,𝔽11)—111no—
27C3×C5×AGL(1,𝔽11)—111no—
28C3×C5×AGL(1,𝔽11)—111no—
29C3×C5×AGL(1,𝔽11)—111no—
30C3×D112C5211yescharacteristic, complemented, Hall
31C5×C11⋊D11C2×C3×C511yescharacteristic, complemented
32C5×C11×D11C2×C3×C511yescharacteristic, complemented
33C5×C11×D11C2×C3×C511yescharacteristic, complemented
34#11925896C2×C3×C515yescomplemented
35#11925896C2×C3×C515yescomplemented
36#11925893C2×C3×C515yescomplemented
37C2×C5×AGL(1,𝔽11)—111no—
38C2×C5×AGL(1,𝔽11)—111no—
39C3×C5×C11⋊C5—111no—
40C3×C5×C11⋊C5—111no—
41C3×C11⋊D11C2×C5211yescharacteristic, complemented
42C3×C11×D11C2×C5211yescharacteristic, complemented
43C3×C11×D11C2×C5211yescharacteristic, complemented
44C2×C3×C5×D11—551no—
45C2×C3×C5×D11—551no—
46C2×C3×AGL(1,𝔽11)—115no—
47C2×C3×AGL(1,𝔽11)—115no—
48C5×C112C22×C3×C511yescharacteristic, complemented
49#10597245C22×C3×C515yescomplemented
50C2×C5×C11⋊C5—111no—
51C2×C5×C11⋊C5—111no—
52C5×AGL(1,𝔽11)—111no—
53C5×AGL(1,𝔽11)—111no—
54C5×AGL(1,𝔽11)—111no—
55C5×AGL(1,𝔽11)—111no—
56D112C3×C5211yescharacteristic, complemented, Hall
57C3×C112C22×C5211yescharacteristic, complemented, Hall
58C2×C3×C5×C11—551no—
59C2×C3×C5×C11—551no—
60C3×C5×D11—551no—
61C3×C5×D11—551no—
62C3×C5×D11—1101no—
63C3×C5×D11AGL(1,𝔽11)11yescharacteristic, complemented
64C3×C5×D11AGL(1,𝔽11)11yescharacteristic, complemented
65C2×C3×C11⋊C5—115no—
66C2×C3×C11⋊C5—115no—
67C3×AGL(1,𝔽11)—115no—
68C3×AGL(1,𝔽11)—115no—
69C3×AGL(1,𝔽11)—115no—
70C3×AGL(1,𝔽11)—115no—
71C22×C3×C52—1211noHall
72C5×C11⋊C5—111no—
73C5×C11⋊C5—111no—
74C11⋊D11C2×C3×C5211yescharacteristic, complemented
75C11×D11C2×C3×C5211yescharacteristic, complemented
76C11×D11C2×C3×C5211yescharacteristic, complemented
77C2×C5×D11—551no—
78C2×C5×D11—551no—
79C2×AGL(1,𝔽11)—115no—
80C2×AGL(1,𝔽11)—115no—
81C3×C5×C11—101no—
82C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
83C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
84C3×C11⋊C5—115no—
85C3×C11⋊C5—115no—
86C2×C3×C52—1211no—
87C2×C3×C52—1211no—
88C2×C3×C52—1211no—
89C2×C3×D11—551no—
90C2×C3×D11—551no—
91C112C22×C3×C5211yescharacteristic, complemented, Sylow
92C2×C5×C11—551no—
93C2×C5×C11—551no—
94C5×D11—551no—
95C5×D11—551no—
96C5×D11—1101no—
97C5×D11C3×AGL(1,𝔽11)11yescharacteristic, complemented
98C5×D11C3×AGL(1,𝔽11)11yescharacteristic, complemented
99C2×C11⋊C5—115no—
100C2×C11⋊C5—115no—
101AGL(1,𝔽11)—115no—
102AGL(1,𝔽11)—115no—
103AGL(1,𝔽11)—115no—
104AGL(1,𝔽11)—115no—
105C22×C52—1211noHall
106C3×C52—1211noHall
107C2×C3×C11—551no—
108C2×C3×C11—551no—
109C3×D11—551no—
110C3×D11—551no—
111C3×D11—1101no—
112C3×D11C5×AGL(1,𝔽11)11yescharacteristic, complemented
113C3×D11C5×AGL(1,𝔽11)11yescharacteristic, complemented
114C22×C3×C5—6051no—
115C22×C3×C5—1215no—
116C5×C11—101no—
117C5×C11C2×C3×AGL(1,𝔽11)11yescharacteristic, complemented
118C5×C11C2×C3×AGL(1,𝔽11)11yescharacteristic, complemented
119C11⋊C5—115no—
120C11⋊C5—115no—
121C2×C52—1211no—
122C2×C52—1211no—
123C2×C52—1211no—
124C2×D11—551no—
125C2×D11—551no—
126C3×C11—101no—
127C3×C11C2×C5×AGL(1,𝔽11)11yescharacteristic, complemented
128C3×C11C2×C5×AGL(1,𝔽11)11yescharacteristic, complemented
129C2×C3×C5—111no—
130C2×C3×C5—551no—
131C2×C3×C5—6051no—
132C2×C3×C5—1215no—
133C2×C3×C5—1215no—
134C2×C3×C5—1215no—
135C52—1211noSylow
136C2×C11—551no—
137C2×C11—551no—
138D11—551no—
139D11—551no—
140D11—1101no—
141D11C3×C5×AGL(1,𝔽11)11yescharacteristic, complemented
142D11C3×C5×AGL(1,𝔽11)11yescharacteristic, complemented
143C22×C5—6051no—
144C22×C5—1215no—
145C3×C5—1215no—
146C3×C5#11925896⋊C211yescharacteristic, direct product factor
147C22×C3—6051noHall
148C11—101no—
149C11C2×C3×C5×AGL(1,𝔽11)11yescharacteristic, complemented
150C11C2×C3×C5×AGL(1,𝔽11)11yescharacteristic, complemented
151C2×C5—551no—
152C2×C5—551no—
153C2×C5—6051no—
154C2×C5—1215no—
155C2×C5—1215no—
156C2×C5—1215no—
157C2×C3—111no—
158C2×C3—551no—
159C2×C3—6051no—
160C5—1215no—
161C5C3×#11925896⋊C211yescharacteristic, direct product factor
162C22—6051noSylow
163C3C5×#11925896⋊C211yescharacteristic, direct product factor, Sylow
164C2—551no—
165C2—551no—
166C2—6051no—
subgroupG/H
center, hypercenterC3×C5#11925896⋊C2
commutator, cosocle, hypocenterC112C22×C3×C52
FrattiniC1G
Fitting, socleC3×C5×C112C22×C5
LCSG ▷ C112
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×#11925896C2semidirect
2. C3×C5×#11925896C2semidirect
3. C3×C5×#11925893C2semidirect
4. C5×#11925896⋊C2C3direct (N × H)
5. C3×C5×#10597245C22semidirect
6. C3×C5×D112C5semidirect
7. C3×#11925896⋊C2C5direct (N × H)
8. C5×#11925896C2×C3semidirect
9. C5×#11925896C2×C3semidirect
10. C5×#11925893C2×C3semidirect
11. C3×C5×C11⋊D11C2×C5semidirect
12. C3×C5×C11×D11C2×C5semidirect
13. C3×C5×C11×D11C2×C5semidirect
14. C3×#11925896C2×C5semidirect
15. C3×#11925896C2×C5semidirect
16. C3×#11925893C2×C5semidirect
19. C5×#10597245C22×C3semidirect
20. C5×D112C3×C5semidirect
21. #11925896⋊C2C3×C5direct (N × H)
22. C3×C5×C112C22×C5semidirect
23. C3×#10597245C22×C5semidirect
30. C3×D112C52semidirect
31. C5×C11⋊D11C2×C3×C5semidirect
32. C5×C11×D11C2×C3×C5semidirect
33. C5×C11×D11C2×C3×C5semidirect
34. #11925896C2×C3×C5semidirect
35. #11925896C2×C3×C5semidirect
36. #11925893C2×C3×C5semidirect
41. C3×C11⋊D11C2×C52semidirect
42. C3×C11×D11C2×C52semidirect
43. C3×C11×D11C2×C52semidirect
48. C5×C112C22×C3×C5semidirect
49. #10597245C22×C3×C5semidirect
56. D112C3×C52semidirect
57. C3×C112C22×C52semidirect
63. C3×C5×D11AGL(1,𝔽11)semidirect
64. C3×C5×D11AGL(1,𝔽11)semidirect
74. C11⋊D11C2×C3×C52semidirect
75. C11×D11C2×C3×C52semidirect
76. C11×D11C2×C3×C52semidirect
82. C3×C5×C11C2×AGL(1,𝔽11)semidirect
83. C3×C5×C11C2×AGL(1,𝔽11)semidirect
91. C112C22×C3×C52semidirect
97. C5×D11C3×AGL(1,𝔽11)semidirect
98. C5×D11C3×AGL(1,𝔽11)semidirect
112. C3×D11C5×AGL(1,𝔽11)semidirect
113. C3×D11C5×AGL(1,𝔽11)semidirect
117. C5×C11C2×C3×AGL(1,𝔽11)semidirect
118. C5×C11C2×C3×AGL(1,𝔽11)semidirect
127. C3×C11C2×C5×AGL(1,𝔽11)semidirect
128. C3×C11C2×C5×AGL(1,𝔽11)semidirect
141. D11C3×C5×AGL(1,𝔽11)semidirect
142. D11C3×C5×AGL(1,𝔽11)semidirect
146. C3×C5#11925896⋊C2direct (N × H)
149. C11C2×C3×C5×AGL(1,𝔽11)semidirect
150. C11C2×C3×C5×AGL(1,𝔽11)semidirect
161. C5C3×#11925896⋊C2direct (N × H)
163. C3C5×#11925896⋊C2direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#119258962
C3×C5×#119258932
C5×#11925896⋊C23
C3×C5×D1125
C3×#11925896⋊C25
C2×C3×C5×AGL(1,𝔽11)11