Finite Group Databasebeta

← C2×C5×C3⋊#10587722 #30655586

Subgroups — C2×C5×C3⋊#10587722 #30655586

Order 16380.

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 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×#63270C211yesmaximal, characteristic, complemented
2C5×C3⋊#10587722C212yesmaximal, direct product factor
3C2×C5×D273C311yesmaximal, characteristic, complemented
4C2×C5×#10587722—31nomaximal
5C3×C5×#63270C2211yescharacteristic, complemented, Hall
6C2×C3⋊#10587722C511yesmaximal, characteristic, direct product factor, Hall
7C5×#10587722—32no—
8C5×D273C2×C312yescomplemented
9C2×C5×#63270—21no—
10C2×C5×#63270D311yescharacteristic, complemented
11C2×C3×C5×C7×C13C2×C311yescharacteristic, complemented
12C2×C5×C3⋊(D13⋊C3)—71nomaximal, Hall
13C2×C5×D91—31noHall
14C2×C3×#63270C2×C511yescharacteristic, complemented
15C3⋊#10587722C2×C512yesdirect product factor
16C3×C5×C7×C13C22×C311yescharacteristic, complemented
17C5×#63270—21no—
18C5×#63270C2×D311yescharacteristic, complemented
19C2×C5×C3⋊AGL(1,𝔽7)—131nomaximal, Hall
20C2×C3×C5×C13⋊C3—71no—
21C5×C3⋊(D13⋊C3)—72no—
22C2×D273C3×C511yescharacteristic, complemented
23C2×#10587722—31no—
24C2×C5×C7×C13C3×D311yescharacteristic, complemented
25C5×D91—32no—
26C3×#63270C22×C511yescharacteristic, complemented, Hall
27C2×C5×D39—71no—
28C2×C5×D13⋊C3—211no—
29C2×C3×C5×ΓL(1,𝔽8)—131no—
30C5×C3⋊AGL(1,𝔽7)—132no—
31C3×C5×C13⋊C3—71noHall
32C2×C3×C7×C13C2×C3×C511yescharacteristic, complemented
33D273C2×C3×C512yescomplemented
34C2×#63270—21no—
35C2×#63270C5×D311yescharacteristic, complemented
36#10587722—32no—
37C2×C3⋊(D13⋊C3)—71noHall
38C5×C7×C13C2×C3×D311yescharacteristic, complemented, Hall
39C2×C5×D21—131no—
40C2×C5×AGL(1,𝔽7)—391no—
41C2×C3×C5×C13AGL(1,𝔽7)11yescharacteristic, complemented
42C5×D39—72no—
43C2×C5×C13⋊C3—71no—
44C2×C5×C13⋊C3—141no—
45C5×D13⋊C3—212no—
46C2×D91—31noHall
47C3×C5×ΓL(1,𝔽8)—131noHall
48C3×C7×C13C22×C3×C511yescharacteristic, complemented
49#63270—21no—
50#63270C2×C5×D311yescharacteristic, complemented
51C2×C5×D13—211noHall
52C2×C3⋊AGL(1,𝔽7)—131noHall
53C2×C3×C13⋊C3—71no—
54C3⋊(D13⋊C3)—72no—
55C2×C3×C5×C7D13⋊C311yescharacteristic, complemented
56C5×D21—132no—
57C2×C5×ΓL(1,𝔽8)—131no—
58C2×C5×ΓL(1,𝔽8)—261no—
59C5×AGL(1,𝔽7)—392no—
60C3×C5×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
61C5×C13⋊C3—71no—
62C5×C13⋊C3—141no—
63C2×C7×C13C3×C5×D311yescharacteristic, complemented
64D91—32no—
65C2×C3×C5×D3—911noHall
66C2×D39—71no—
67C2×D13⋊C3—211no—
68C2×C5×D7—391noHall
69C2×C5×C13C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
70C5×D13—212no—
71C2×C3×ΓL(1,𝔽8)—131no—
72C3⋊AGL(1,𝔽7)—132no—
73C3×C13⋊C3—71noHall
74C3×C5×C7C2×D13⋊C311yescharacteristic, complemented
75C5×ΓL(1,𝔽8)—131no—
76C5×ΓL(1,𝔽8)—261no—
77C7×C13C2×C3×C5×D311yescharacteristic, complemented, Hall
78C2×C32×C5—911no—
79C3×C5×D3—912no—
80C2×D21—131no—
81C2×AGL(1,𝔽7)—391no—
82C2×C3×C13C5×AGL(1,𝔽7)11yescharacteristic, complemented
83D39—72no—
84C2×C13⋊C3—71no—
85C2×C13⋊C3—141no—
86D13⋊C3—212no—
87C2×C5×C7C3⋊(D13⋊C3)11yescharacteristic, complemented
88C5×D7—392no—
89C5×C13C2×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Hall
90C3×ΓL(1,𝔽8)—131noHall
91C22×C3×C5—2731no—
92C2×C5×D3—911no—
93C2×D13—211noHall
94C32×C5—911noHall
95C2×C3×C7C5×D13⋊C311yescharacteristic, complemented
96D21—132no—
97C2×ΓL(1,𝔽8)—131no—
98C2×ΓL(1,𝔽8)—261no—
99AGL(1,𝔽7)—392no—
100C3×C13C2×C5×AGL(1,𝔽7)11yescharacteristic, complemented
101C13⋊C3—71no—
102C13⋊C3—141no—
103C2×C3×D3—911noHall
104C5×C7C2×C3⋊(D13⋊C3)11yescharacteristic, complemented, Hall
105C2×C3×C5—2732no—
106C2×C3×C5—911no—
107C2×C3×C5—1821no—
108C2×C3×C5#1058772211yescharacteristic, complemented
109C5×D3—912no—
110C2×D7—391noHall
111C2×C13C5×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
112D13—212no—
113C3×C7C2×C5×D13⋊C311yescharacteristic, complemented
114ΓL(1,𝔽8)—131no—
115ΓL(1,𝔽8)—261no—
116C22×C5—2731noHall
117C2×C32—911no—
118C3×D3—912no—
119C3×C5—911no—
120C3×C5—1821no—
121C3×C5C2×#1058772211yescharacteristic, complemented
122C2×C7C5×C3⋊(D13⋊C3)11yescharacteristic, complemented
123D7—392no—
124C13C2×C5×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
125C22×C3—2731no—
126C2×D3—911no—
127C2×C5—2732no—
128C2×C5C3⋊#1058772211yescharacteristic, direct product factor
129C32—911noSylow
130C7C2×C5×C3⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
131C2×C3—2732no—
132C2×C3—911no—
133C2×C3—1821no—
134C2×C3C5×#1058772211yescharacteristic, complemented
135D3—912no—
136C5C2×C3⋊#1058772211yescharacteristic, direct product factor, Sylow
137C22—2731noSylow
138C3—911no—
139C3—1821no—
140C3C2×C5×#1058772211yescharacteristic, complemented
141C2—2732no—
142C2C5×C3⋊#1058772211yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5C3⋊#10587722
commutator, cosocle, hypocenterC3×C7×C13C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C13C2×C3
LCSG ▷ C3×C7×C13
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#63270C2semidirect
2. C5×C3⋊#10587722C2direct (N × H)
3. C2×C5×D273C3semidirect
5. C3×C5×#63270C22semidirect
6. C2×C3⋊#10587722C5direct (N × H)
8. C5×D273C2×C3semidirect
10. C2×C5×#63270D3semidirect
11. C2×C3×C5×C7×C13C2×C3semidirect
14. C2×C3×#63270C2×C5semidirect
15. C3⋊#10587722C2×C5direct (N × H)
16. C3×C5×C7×C13C22×C3semidirect
18. C5×#63270C2×D3semidirect
22. C2×D273C3×C5semidirect
24. C2×C5×C7×C13C3×D3semidirect
26. C3×#63270C22×C5semidirect
32. C2×C3×C7×C13C2×C3×C5semidirect
33. D273C2×C3×C5semidirect
35. C2×#63270C5×D3semidirect
38. C5×C7×C13C2×C3×D3semidirect
41. C2×C3×C5×C13AGL(1,𝔽7)semidirect
48. C3×C7×C13C22×C3×C5semidirect
50. #63270C2×C5×D3semidirect
55. C2×C3×C5×C7D13⋊C3semidirect
60. C3×C5×C13C2×AGL(1,𝔽7)semidirect
63. C2×C7×C13C3×C5×D3semidirect
69. C2×C5×C13C3⋊AGL(1,𝔽7)semidirect
74. C3×C5×C7C2×D13⋊C3semidirect
77. C7×C13C2×C3×C5×D3semidirect
82. C2×C3×C13C5×AGL(1,𝔽7)semidirect
87. C2×C5×C7C3⋊(D13⋊C3)semidirect
89. C5×C13C2×C3⋊AGL(1,𝔽7)semidirect
95. C2×C3×C7C5×D13⋊C3semidirect
100. C3×C13C2×C5×AGL(1,𝔽7)semidirect
104. C5×C7C2×C3⋊(D13⋊C3)semidirect
108. C2×C3×C5#10587722semidirect
111. C2×C13C5×C3⋊AGL(1,𝔽7)semidirect
113. C3×C7C2×C5×D13⋊C3semidirect
121. C3×C5C2×#10587722semidirect
122. C2×C7C5×C3⋊(D13⋊C3)semidirect
124. C13C2×C5×C3⋊AGL(1,𝔽7)semidirect
128. C2×C5C3⋊#10587722direct (N × H)
130. C7C2×C5×C3⋊(D13⋊C3)semidirect
134. C2×C3C5×#10587722semidirect
136. C5C2×C3⋊#10587722direct (N × H)
140. C3C2×C5×#10587722semidirect
142. C2C5×C3⋊#10587722direct (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×#632702
C5×C3⋊#105877222
C2×C5×D2733
C2×C5×#105877223
C2×C3⋊#105877225
C2×C5×C3⋊(D13⋊C3)7
C2×C5×C3⋊AGL(1,𝔽7)13