Finite Group Databasebeta

← C2×C3⋊#20258405 #49137142

Subgroups — C2×C3⋊#20258405 #49137142

Order 36300.

180 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 51 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×#15690027C211yesmaximal, characteristic, complemented
2C3⋊#20258405C211yesmaximal, characteristic, direct product factor
3C3⋊#20258405C211yesmaximal, characteristic, direct product factor
4C2×#20258405—31nomaximal, Hall
5C3×#15690027C2211yescharacteristic, complemented, Hall
6C2×C5×C11×D33C511yesmaximal, characteristic
7C2×#15690027D311yescharacteristic, complemented
8#20258405—31no—
9#20258405—31no—
10C5×C11×D33C2×C511yescharacteristic
11C5×C11×D33C2×C511yescharacteristic
12C2×C3×C5×C112C2×C511yescharacteristic
13C2×C3⋊(D11⋊C25)—111nomaximal
14C2×D3×C11⋊C25—111nomaximal
15#15690027C2×D311yescharacteristic, complemented, Hall
16C2×C5×C11×D11—31no—
17C3×C5×C112C22×C511yescharacteristic
18C2×C3×C11⋊C25—111no—
19C2×C3×C11⋊C25—111no—
20C2×C3×C11⋊C25—225no—
21C3⋊(D11⋊C25)—111no—
22C3⋊(D11⋊C25)—111no—
23D3×C11⋊C25—111no—
24D3×C11⋊C25—111no—
25C2×C11×D33C2511yescharacteristic, complemented, Hall
26C2×C5×C112C5×D311yescharacteristic
27C5×C11×D11—31no—
28C5×C11×D11—31no—
29C22×C11⋊C25—331no—
30C2×D11⋊C25—331no—
31C3×C11⋊C25—111no—
32C3×C11⋊C25—111no—
33C3×C11⋊C25—225no—
34C2×C3×C112C2×C2511yescharacteristic, complemented
35C11×D33C2×C2511yescharacteristic, complemented
36C11×D33C2×C2511yescharacteristic, complemented
37C2×C5×D33C11⋊C511yescharacteristic
38C2×C5×D3×C11—551no—
39C5×C112C2×C5×D311yescharacteristic
40C2×C11⋊C25—111no—
41C2×C11⋊C25—111no—
42C2×C11⋊C25—225no—
43C2×C11⋊C25—331no—
44C2×C11⋊C25—331no—
45D11⋊C25—331no—
46D11⋊C25—331no—
47C2×C11×D11—31noHall
48C3×C112C22×C2511yescharacteristic, complemented, Hall
49C2×C3×C5×C11—25no—
50C2×C3×C5×C11AGL(1,𝔽11)11yescharacteristic
51C2×C3×C5×C11C2×C11⋊C511yescharacteristic
52C5×D33C2×C11⋊C511yescharacteristic
53C5×D33C2×C11⋊C511yescharacteristic
54C5×D3×C11—551no—
55C5×D3×C11—551no—
56C2×D3×C25—1211noHall
57C11⋊C25—111no—
58C11⋊C25—111no—
59C11⋊C25—225no—
60C2×C112D3×C2511yescharacteristic, complemented
61C11×D11—31no—
62C11×D11—31no—
63C22×C5×C11—1651no—
64C2×C5×D11—31no—
65C3×C5×C11—25no—
66C3×C5×C11C2×AGL(1,𝔽11)11yescharacteristic
67C3×C5×C11C22×C11⋊C511yescharacteristic
68C2×C3×C25—1211no—
69D3×C25—1211no—
70D3×C25—1211no—
71C2×D33C11⋊C2511yescharacteristic, complemented
72C2×D3×C11—551no—
73C112C2×D3×C2511yescharacteristic, complemented, Sylow
74C2×C5×C11—25no—
75C2×C5×C11—1651no—
76C2×C5×C11—1651no—
77C2×C5×C11D3×C11⋊C511yescharacteristic
78C2×C5×C11C3⋊AGL(1,𝔽11)11yescharacteristic
79C5×D11—31no—
80C5×D11—31no—
81C22×C25—3631noHall
82C3×C25—1211noHall
83C2×C3×C11—25no—
84C2×C3×C11D11⋊C2511yescharacteristic, complemented
85C2×C3×C11C2×C11⋊C2511yescharacteristic, complemented
86D33C2×C11⋊C2511yescharacteristic, complemented
87D33C2×C11⋊C2511yescharacteristic, complemented
88D3×C11—551no—
89D3×C11—551no—
90C2×C5×D3—111no—
91C5×C11—25no—
92C5×C11C2×D3×C11⋊C511yescharacteristic
93C5×C11C2×C3⋊AGL(1,𝔽11)11yescharacteristic
94C2×C25—3631no—
95C2×C25—3631no—
96C2×C25—1211no—
97C22×C11—1651no—
98C2×D11—31no—
99C3×C11—25no—
100C3×C11C2×D11⋊C2511yescharacteristic, complemented
101C3×C11C22×C11⋊C2511yescharacteristic, complemented
102C2×C3×C5#1192589511yescharacteristic
103C5×D3—111no—
104C5×D3—551no—
105C25—1211noSylow
106C2×C11—25no—
107C2×C11—1651no—
108C2×C11—1651no—
109C2×C11D3×C11⋊C2511yescharacteristic, complemented
110C2×C11C3⋊(D11⋊C25)11yescharacteristic, complemented
111D11—31no—
112D11—31no—
113C22×C5—1651no—
114C3×C5C2×#1192589511yescharacteristic
115C2×D3—111noHall
116C11—25no—
117C11C2×D3×C11⋊C2511yescharacteristic, complemented
118C11C2×C3⋊(D11⋊C25)11yescharacteristic, complemented
119C2×C5—331no—
120C2×C5—1651no—
121C2×C5C3⋊#1192589511yescharacteristic
122C2×C3#2025840511yescharacteristic, complemented
123D3—111no—
124D3—551no—
125C5C2×C3⋊#1192589511yescharacteristic
126C22—1651noSylow
127C3C2×#2025840511yescharacteristic, complemented, Sylow
128C2—331no—
129C2—1651no—
130C2C3⋊#2025840511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5C3⋊#11925895
commutator, hypocenterC3×C112C22×C25
FrattiniC5C2×C3⋊#11925895
Fitting, socleC2×C3×C5×C112C2×C5
prime radicalC2×C5×C11×D33C5
cosocleC3×C5×C112C22×C5
LCSG ▷ C3×C112
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
1. C2×C3×#15690027C2semidirect
2. C3⋊#20258405C2direct (N × H)
3. C3⋊#20258405C2direct (N × H)
5. C3×#15690027C22semidirect
7. C2×#15690027D3semidirect
15. #15690027C2×D3semidirect
25. C2×C11×D33C25semidirect
34. C2×C3×C112C2×C25semidirect
35. C11×D33C2×C25semidirect
36. C11×D33C2×C25semidirect
48. C3×C112C22×C25semidirect
60. C2×C112D3×C25semidirect
71. C2×D33C11⋊C25semidirect
73. C112C2×D3×C25semidirect
84. C2×C3×C11D11⋊C25semidirect
85. C2×C3×C11C2×C11⋊C25semidirect
86. D33C2×C11⋊C25semidirect
87. D33C2×C11⋊C25semidirect
100. C3×C11C2×D11⋊C25semidirect
101. C3×C11C22×C11⋊C25semidirect
109. C2×C11D3×C11⋊C25semidirect
110. C2×C11C3⋊(D11⋊C25)semidirect
117. C11C2×D3×C11⋊C25semidirect
118. C11C2×C3⋊(D11⋊C25)semidirect
122. C2×C3#20258405semidirect
127. C3C2×#20258405semidirect
130. C2C3⋊#20258405direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#156900272
C3⋊#202584052
C2×#202584053
C2×C5×C11×D335
C2×C3⋊(D11⋊C25)11
C2×D3×C11⋊C2511