Finite Group Databasebeta

← C3×C5×#11925892⋊C2 #49137369

Subgroups — C3×C5×#11925892⋊C2 #49137369

Order 36300.

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

normal subgroups only

This group has 480 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×#11925895C212yesmaximal, complemented
2C3×C5×#11925892C211yesmaximal, characteristic, complemented
3C5×#11925892⋊C2C311yesmaximal, characteristic, direct product factor, Hall
4C3×C5×#10597243C2211yescharacteristic, complemented, Hall
5C3×C5×D112C511yesmaximal, characteristic, complemented
6C3×#11925892⋊C2C515yesmaximal, direct product factor
7C5×#11925895C2×C312yescomplemented
8C5×#11925892C2×C311yescharacteristic, complemented
9C3×C5×C11⋊D11C2×C511yescharacteristic, complemented
10C3×C5×C11×D11C2×C512yescomplemented
11C3×#11925895C2×C5110yescomplemented
12C3×#11925892C2×C515yescomplemented
13C2×C3×C5×AGL(1,𝔽11)—112nomaximal
14C5×#10597243C22×C311yescharacteristic, complemented, Hall
15C5×D112C3×C511yescharacteristic, complemented
16#11925892⋊C2C3×C515yesdirect product factor
17C3×C5×C112C22×C511yescharacteristic, complemented
18C3×#10597243C22×C515yescomplemented
19C2×C3×C5×C11⋊C5—112no—
20C3×C5×AGL(1,𝔽11)—112no—
21C3×C5×AGL(1,𝔽11)—112no—
22C3×C5×AGL(1,𝔽11)—221no—
23C3×C5×AGL(1,𝔽11)—224no—
24C3×D112C5211yescharacteristic, complemented, Hall
25C5×C11⋊D11C2×C3×C511yescharacteristic, complemented
26C5×C11×D11C2×C3×C512yescomplemented
27#11925895C2×C3×C5110yescomplemented
28#11925892C2×C3×C515yescomplemented
29C2×C5×AGL(1,𝔽11)—112no—
30C3×C5×C11⋊C5—112no—
31C3×C5×C11⋊C5—221no—
32C3×C5×C11⋊C5—224no—
33C3×C11⋊D11C2×C5211yescharacteristic, complemented
34C3×C11×D11C2×C5212yescomplemented
35C2×C3×C5×D11—552no—
36C2×C3×AGL(1,𝔽11)—1110no—
37C5×C112C22×C3×C511yescharacteristic, complemented
38#10597243C22×C3×C515yescomplemented
39C2×C5×C11⋊C5—112no—
40C5×AGL(1,𝔽11)—112no—
41C5×AGL(1,𝔽11)—112no—
42C5×AGL(1,𝔽11)—221no—
43C5×AGL(1,𝔽11)—224no—
44D112C3×C5211yescharacteristic, complemented, Hall
45C3×C112C22×C5211yescharacteristic, complemented, Hall
46C2×C3×C5×C11—552no—
47C3×C5×D11—552no—
48C3×C5×D11—1101no—
49C3×C5×D11—1104no—
50C3×C5×D11AGL(1,𝔽11)12yescomplemented
51C2×C3×C11⋊C5—1110no—
52C3×AGL(1,𝔽11)—1110no—
53C3×AGL(1,𝔽11)—1110no—
54C3×AGL(1,𝔽11)—225no—
55C3×AGL(1,𝔽11)—2220no—
56C22×C3×C52—1211noHall
57C5×C11⋊C5—112no—
58C5×C11⋊C5—221no—
59C5×C11⋊C5—224no—
60C11⋊D11C2×C3×C5211yescharacteristic, complemented
61C11×D11C2×C3×C5212yescomplemented
62C2×C5×D11—552no—
63C2×AGL(1,𝔽11)—1110no—
64C3×C5×C11—21no—
65C3×C5×C11—24no—
66C3×C5×C11C2×AGL(1,𝔽11)12yescomplemented
67C3×C11⋊C5—1110no—
68C3×C11⋊C5—225no—
69C3×C11⋊C5—2220no—
70C2×C3×C52—1212no—
71C2×C3×C52—1211no—
72C2×C3×D11—552no—
73C112C22×C3×C5211yescharacteristic, complemented, Sylow
74C2×C5×C11—552no—
75C5×D11—221no—
76C5×D11—552no—
77C5×D11—1104no—
78C5×D11C3×AGL(1,𝔽11)12yescomplemented
79C2×C11⋊C5—1110no—
80AGL(1,𝔽11)—1110no—
81AGL(1,𝔽11)—1110no—
82AGL(1,𝔽11)—225no—
83AGL(1,𝔽11)—2220no—
84C22×C52—1211noHall
85C3×C52—1211noHall
86C2×C3×C11—552no—
87C3×D11—552no—
88C3×D11—1101no—
89C3×D11—1104no—
90C3×D11C5×AGL(1,𝔽11)12yescomplemented
91C22×C3×C5—6051no—
92C22×C3×C5—1215no—
93C5×C11—21no—
94C5×C11—24no—
95C5×C11C2×C3×AGL(1,𝔽11)12yescomplemented
96C11⋊C5—1110no—
97C11⋊C5—225no—
98C11⋊C5—2220no—
99C2×C52—1212no—
100C2×C52—1211no—
101C2×D11—552no—
102C3×C11—21no—
103C3×C11—24no—
104C3×C11C2×C5×AGL(1,𝔽11)12yescomplemented
105C2×C3×C5—112no—
106C2×C3×C5—6051no—
107C2×C3×C5—12110no—
108C2×C3×C5—1215no—
109C52—1211noSylow
110C2×C11—552no—
111D11—221no—
112D11—552no—
113D11—1104no—
114D11C3×C5×AGL(1,𝔽11)12yescomplemented
115C22×C5—6051no—
116C22×C5—1215no—
117C3×C5—1215no—
118C3×C5#11925892⋊C211yescharacteristic, direct product factor
119C22×C3—6051noHall
120C11—21no—
121C11—24no—
122C11C2×C3×C5×AGL(1,𝔽11)12yescomplemented
123C2×C5—552no—
124C2×C5—12110no—
125C2×C5—1215no—
126C2×C5—1211no—
127C2×C3—112no—
128C2×C3—6051no—
129C5—1215no—
130C5C3×#11925892⋊C211yescharacteristic, direct product factor
131C22—6051noSylow
132C3C5×#11925892⋊C211yescharacteristic, direct product factor, Sylow
133C2—552no—
134C2—1211no—
subgroupG/H
center, hypercenterC3×C5#11925892⋊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×#11925895C2semidirect
2. C3×C5×#11925892C2semidirect
3. C5×#11925892⋊C2C3direct (N × H)
4. C3×C5×#10597243C22semidirect
5. C3×C5×D112C5semidirect
6. C3×#11925892⋊C2C5direct (N × H)
7. C5×#11925895C2×C3semidirect
8. C5×#11925892C2×C3semidirect
9. C3×C5×C11⋊D11C2×C5semidirect
10. C3×C5×C11×D11C2×C5semidirect
11. C3×#11925895C2×C5semidirect
12. C3×#11925892C2×C5semidirect
14. C5×#10597243C22×C3semidirect
15. C5×D112C3×C5semidirect
16. #11925892⋊C2C3×C5direct (N × H)
17. C3×C5×C112C22×C5semidirect
18. C3×#10597243C22×C5semidirect
24. C3×D112C52semidirect
25. C5×C11⋊D11C2×C3×C5semidirect
26. C5×C11×D11C2×C3×C5semidirect
27. #11925895C2×C3×C5semidirect
28. #11925892C2×C3×C5semidirect
33. C3×C11⋊D11C2×C52semidirect
34. C3×C11×D11C2×C52semidirect
37. C5×C112C22×C3×C5semidirect
38. #10597243C22×C3×C5semidirect
44. D112C3×C52semidirect
45. C3×C112C22×C52semidirect
50. C3×C5×D11AGL(1,𝔽11)semidirect
60. C11⋊D11C2×C3×C52semidirect
61. C11×D11C2×C3×C52semidirect
66. C3×C5×C11C2×AGL(1,𝔽11)semidirect
73. C112C22×C3×C52semidirect
78. C5×D11C3×AGL(1,𝔽11)semidirect
90. C3×D11C5×AGL(1,𝔽11)semidirect
95. C5×C11C2×C3×AGL(1,𝔽11)semidirect
104. C3×C11C2×C5×AGL(1,𝔽11)semidirect
114. D11C3×C5×AGL(1,𝔽11)semidirect
118. C3×C5#11925892⋊C2direct (N × H)
122. C11C2×C3×C5×AGL(1,𝔽11)semidirect
130. C5C3×#11925892⋊C2direct (N × H)
132. C3C5×#11925892⋊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×#119258952
C3×C5×#119258922
C5×#11925892⋊C23
C3×C5×D1125
C3×#11925892⋊C25
C2×C3×C5×AGL(1,𝔽11)11