Finite Group Databasebeta

← C5×D3×#11925898 #49137427

Subgroups — C5×D3×#11925898 #49137427

Order 36300.

328 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C5×D3×#10597244C211yesmaximal, characteristic, complemented
2C5×C3⋊#11925898C211yesmaximal, characteristic, complemented
3C3×C5×#11925898C211yesmaximal, characteristic, complemented
4C2×C5×#11925898—31nomaximal, Hall
5C3×C5×#10597244C2211yescharacteristic, complemented, Hall
6C5×D3×C11×D11C511yesmaximal, characteristic, complemented
7D3×#11925898C515yesmaximal, direct product factor
8C2×C5×#10597244—31no—
9C5×#11925898—31no—
10C5×#11925898D311yescharacteristic, direct product factor
11C5×C11×D33C2×C511yescharacteristic, complemented
12C5×D3×C112C2×C511yescharacteristic, complemented
13C3×C5×C11×D11C2×C511yescharacteristic, complemented
14D3×#10597244C2×C515yescomplemented
15C3⋊#11925898C2×C515yescomplemented
16C3×#11925898C2×C515yescomplemented
17C2×C5×D3×C11⋊C5—111nomaximal
18C5×D3×AGL(1,𝔽11)—111nomaximal
19C5×#10597244C2×D311yescharacteristic, complemented, Hall
20C2×C5×C11×D11—31no—
21C2×#11925898—35no—
22C3×C5×C112C22×C511yescharacteristic, complemented
23C3×#10597244C22×C515yescomplemented
24C2×C3×C5×C11⋊C5—111no—
25C5×C3⋊AGL(1,𝔽11)—111no—
26C5×D3×C11⋊C5—111no—
27C5×D3×C11⋊C5—111no—
28C5×D3×C11⋊C5—111no—
29C3×C5×AGL(1,𝔽11)—111no—
30D3×C11×D11C5211yescharacteristic, complemented, Hall
31C2×C5×C112—31no—
32C5×C11×D11—31no—
33C5×C11×D11C5×D311yescharacteristic, complemented
34C2×#10597244—35no—
35#11925898—35no—
36#11925898C5×D315yesdirect product factor
37C22×C5×C11⋊C5—331no—
38C2×C5×AGL(1,𝔽11)—331no—
39C3×C5×C11⋊C5—111no—
40C3×C5×C11⋊C5—111no—
41C11×D33C2×C5211yescharacteristic, complemented
42D3×C112C2×C5211yescharacteristic, complemented
43C3×C11×D11C2×C5211yescharacteristic, complemented
44C2×C5×D3×C11—551no—
45C5×D3×D11C11⋊C511yescharacteristic, complemented
46C2×D3×C11⋊C5—115no—
47D3×AGL(1,𝔽11)—115no—
48C5×C112C2×C5×D311yescharacteristic, complemented
49#10597244C2×C5×D315yescomplemented
50C2×C5×C11⋊C5—111no—
51C2×C5×C11⋊C5—331no—
52C2×C5×C11⋊C5—331no—
53C2×C5×C11⋊C5—331no—
54C5×AGL(1,𝔽11)—111no—
55C5×AGL(1,𝔽11)—331no—
56C2×C11×D11—31noHall
57C3×C112C22×C5211yescharacteristic, complemented, Hall
58C2×C3×C5×C11—551no—
59C5×D33C2×C11⋊C511yescharacteristic, complemented
60C5×D3×C11—101no—
61C5×D3×C11—551no—
62C5×D3×C11AGL(1,𝔽11)11yescharacteristic, complemented
63C5×D3×C11C2×C11⋊C511yescharacteristic, complemented
64C3×C5×D11C2×C11⋊C511yescharacteristic, complemented
65C2×C3×C11⋊C5—115no—
66C3⋊AGL(1,𝔽11)—115no—
67D3×C11⋊C5—115no—
68D3×C11⋊C5—115no—
69D3×C11⋊C5—115no—
70C3×AGL(1,𝔽11)—115no—
71C2×C52×D3—1211noHall
72C5×C11⋊C5—111no—
73C5×C11⋊C5—111no—
74C2×C112—31no—
75C11×D11—31no—
76C11×D11C52×D311yescharacteristic, complemented
77C22×C5×C11—1651no—
78C2×C5×D11—31no—
79C22×C11⋊C5—335no—
80C2×AGL(1,𝔽11)—335no—
81C3×C5×C11—101no—
82C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
83C3×C5×C11C22×C11⋊C511yescharacteristic, complemented
84C3×C11⋊C5—115no—
85C3×C11⋊C5—115no—
86C2×C3×C52—1211no—
87C52×D3—1211no—
88C52×D3—1211no—
89C2×D3×C11—551no—
90D3×D11C5×C11⋊C511yescharacteristic, complemented
91C112C2×C52×D311yescharacteristic, complemented, Sylow
92C2×C5×C11—31no—
93C2×C5×C11—31no—
94C2×C5×C11—301no—
95C2×C5×C11—331no—
96C2×C5×C11—551no—
97C5×D11—31no—
98C5×D11D3×C11⋊C511yescharacteristic, complemented
99C2×C11⋊C5—115no—
100C2×C11⋊C5—335no—
101C2×C11⋊C5—335no—
102C2×C11⋊C5—335no—
103AGL(1,𝔽11)—115no—
104AGL(1,𝔽11)—335no—
105C22×C52—3631noHall
106C3×C52—1211noHall
107C2×C3×C11—551no—
108D33C2×C5×C11⋊C511yescharacteristic, complemented
109C3×D11C2×C5×C11⋊C511yescharacteristic, complemented
110D3×C11—101no—
111D3×C11—551no—
112D3×C11C5×AGL(1,𝔽11)11yescharacteristic, complemented
113D3×C11C2×C5×C11⋊C511yescharacteristic, complemented
114C2×C5×D3—111no—
115C2×C5×D3—1215no—
116C5×C11—101no—
117C5×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
118C5×C11C2×D3×C11⋊C511yescharacteristic, complemented
119C11⋊C5—115no—
120C11⋊C5—115no—
121C2×C52—3631no—
122C2×C52—3631no—
123C2×C52—1211no—
124C22×C11—1651no—
125C2×D11—31no—
126C3×C11—101no—
127C3×C11C2×C5×AGL(1,𝔽11)11yescharacteristic, complemented
128C3×C11C22×C5×C11⋊C511yescharacteristic, complemented
129C2×C3×C5—551no—
130C2×C3×C5—1215no—
131C5×D3—551no—
132C5×D3—1215no—
133C5×D3—1215no—
134C5×D3#1192589811yescharacteristic, direct product factor
135C52—1211noSylow
136C2×C11—31no—
137C2×C11—31no—
138C2×C11—301no—
139C2×C11—331no—
140C2×C11—551no—
141D11—31no—
142D11C5×D3×C11⋊C511yescharacteristic, complemented
143C22×C5—3635no—
144C22×C5—1651no—
145C3×C5—1215no—
146C3×C5C2×#1192589811yescharacteristic, complemented
147C2×D3—111noHall
148C11—101no—
149C11C5×D3×AGL(1,𝔽11)11yescharacteristic, complemented
150C11C2×C5×D3×C11⋊C511yescharacteristic, complemented
151C2×C5—31no—
152C2×C5—551no—
153C2×C5—3635no—
154C2×C5—3635no—
155C2×C5—1215no—
156C2×C5—1651no—
157C2×C3—551no—
158D3—551no—
159D3C5×#1192589811yescharacteristic, direct product factor
160C5—1215no—
161C5D3×#1192589811yescharacteristic, direct product factor
162C22—1651noSylow
163C3C2×C5×#1192589811yescharacteristic, complemented, Sylow
164C2—31no—
165C2—551no—
166C2—1651no—
subgroupG/H
center, hypercenterC5D3×#11925898
commutator, cosocle, hypocenterC3×C112C22×C52
FrattiniC1G
Fitting, socleC3×C5×C112C22×C5
LCSG ▷ C3×C112
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×D3×#10597244C2semidirect
2. C5×C3⋊#11925898C2semidirect
3. C3×C5×#11925898C2semidirect
5. C3×C5×#10597244C22semidirect
6. C5×D3×C11×D11C5semidirect
7. D3×#11925898C5direct (N × H)
10. C5×#11925898D3direct (N × H)
11. C5×C11×D33C2×C5semidirect
12. C5×D3×C112C2×C5semidirect
13. C3×C5×C11×D11C2×C5semidirect
14. D3×#10597244C2×C5semidirect
15. C3⋊#11925898C2×C5semidirect
16. C3×#11925898C2×C5semidirect
19. C5×#10597244C2×D3semidirect
22. C3×C5×C112C22×C5semidirect
23. C3×#10597244C22×C5semidirect
30. D3×C11×D11C52semidirect
33. C5×C11×D11C5×D3semidirect
36. #11925898C5×D3direct (N × H)
41. C11×D33C2×C52semidirect
42. D3×C112C2×C52semidirect
43. C3×C11×D11C2×C52semidirect
45. C5×D3×D11C11⋊C5semidirect
48. C5×C112C2×C5×D3semidirect
49. #10597244C2×C5×D3semidirect
57. C3×C112C22×C52semidirect
59. C5×D33C2×C11⋊C5semidirect
62. C5×D3×C11AGL(1,𝔽11)semidirect
63. C5×D3×C11C2×C11⋊C5semidirect
64. C3×C5×D11C2×C11⋊C5semidirect
76. C11×D11C52×D3semidirect
82. C3×C5×C11C2×AGL(1,𝔽11)semidirect
83. C3×C5×C11C22×C11⋊C5semidirect
90. D3×D11C5×C11⋊C5semidirect
91. C112C2×C52×D3semidirect
98. C5×D11D3×C11⋊C5semidirect
108. D33C2×C5×C11⋊C5semidirect
109. C3×D11C2×C5×C11⋊C5semidirect
112. D3×C11C5×AGL(1,𝔽11)semidirect
113. D3×C11C2×C5×C11⋊C5semidirect
117. C5×C11D3×AGL(1,𝔽11)semidirect
118. C5×C11C2×D3×C11⋊C5semidirect
127. C3×C11C2×C5×AGL(1,𝔽11)semidirect
128. C3×C11C22×C5×C11⋊C5semidirect
134. C5×D3#11925898direct (N × H)
142. D11C5×D3×C11⋊C5semidirect
146. C3×C5C2×#11925898semidirect
149. C11C5×D3×AGL(1,𝔽11)semidirect
150. C11C2×C5×D3×C11⋊C5semidirect
159. D3C5×#11925898direct (N × H)
161. C5D3×#11925898direct (N × H)
163. C3C2×C5×#11925898semidirect

Maximal subgroups

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

subgroupindex
C5×D3×#105972442
C5×C3⋊#119258982
C3×C5×#119258982
C2×C5×#119258983
C5×D3×C11×D115
D3×#119258985
C2×C5×D3×C11⋊C511
C5×D3×AGL(1,𝔽11)11