Finite Group Databasebeta

← C5×#64120 #13088094

Subgroups — C5×#64120 #13088094

Order 1440.

408 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 110 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×#3830C211yesmaximal, characteristic, complemented
2C5×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×C5×D8C211yesmaximal, characteristic, complemented
4C5×#3754C211yesmaximal, characteristic, complemented
5C5×#3753C211yesmaximal, characteristic, complemented
6C5×#3744C211yesmaximal, characteristic, complemented
7C5×#3743C211yesmaximal, characteristic, complemented
8C5×#911—34nomaximal
9C22×C5×C3⋊D3—21no—
10C32×C5×D4C2211yescharacteristic
11C32×C5×D4C2211yescharacteristic, complemented
12C5×#638—21no—
13C5×#638—21no—
14C2×C5×C3⋊Dic3—21no—
15C5×C4⋊(C3⋊D3)C2211yescharacteristic
16C4×C5×C3⋊D3C2211yescharacteristic
17C5×#634C2211yescharacteristic, complemented
18C32×C5×C8C2211yescharacteristic, complemented
19C5×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
20#64120C511yesmaximal, characteristic, direct product factor, Hall
21C5×#237—34no—
22C5×D3×D4—34no—
23C3×C5×D8D314yescomplemented
24C5×#214—34no—
25C5×#213—34no—
26C5×#204—34no—
27C5×ΓL(1,𝔽25)—34no—
28C22×C32×C5—21no—
29C22×C32×C5—21no—
30C2×C5×C3⋊D3—21no—
31C2×C5×C3⋊D3—42no—
32C2×C5×C3⋊D3D411yescharacteristic
33C32×C4×C5C2311yescharacteristic
34C5×C3⋊Dic3—21no—
35C5×C3⋊Dic3D411yescharacteristic
36C5×AGL(1,ℤ/8)—91noHall
37#3830C2×C511yescharacteristic, complemented
38D4×C3⋊D3C2×C511yescharacteristic, complemented
39C32×D8C2×C511yescharacteristic, complemented
40#3754C2×C511yescharacteristic, complemented
41#3753C2×C511yescharacteristic, complemented
42#3744C2×C511yescharacteristic, complemented
43#3743C2×C511yescharacteristic, complemented
44C22×C5×D3—64no—
45C3×C5×D4C2×D314yes—
46C3×C5×D4C2×D314yescomplemented
47C5×#67—64no—
48C5×#67—64no—
49C2×C5×Dic3—64no—
50C5×D12—34no—
51C4×C5×D3—34no—
52C5×Dic6—34no—
53C3×C5×C8C2×D314yescomplemented
54C5×C3⋊C8—34no—
55#911—34no—
56C2×C32×C5—41no—
57C2×C32×C5—41no—
58C2×C32×C5C2×D411yescharacteristic
59C5×C3⋊D3—21no—
60C5×C3⋊D3—41no—
61C5×#41—91no—
62C2×C5×D4—91no—
63C5×SD16—91no—
64C5×SD16—91no—
65C5×D8—91no—
66C5×D8C3⋊D311yescharacteristic, complemented
67C5×M16—91no—
68C22×C3⋊D3—21no—
69C32×D4C22×C511yescharacteristic
70C32×D4C22×C511yescharacteristic, complemented
71#638—21no—
72#638—21no—
73C2×C3⋊Dic3—21no—
74C4⋊(C3⋊D3)C22×C511yescharacteristic
75C4×C3⋊D3C22×C511yescharacteristic
76#634C22×C511yescharacteristic, complemented
77C32×C8C22×C511yescharacteristic, complemented
78C3⋊(C3⋊C8)C22×C511yescharacteristic, complemented
79C22×C3×C5—24no—
80C22×C3×C5—24no—
81C2×C5×D3—34no—
82C2×C5×D3—64no—
83C2×C5×D3—128no—
84C3×C4×C5C22×D314yes—
85C5×Dic3—34no—
86C5×Dic3—64no—
87#237—34no—
88D3×D4—34no—
89C3×D8C5×D314yescomplemented
90#214—34no—
91#213—34no—
92#204—34no—
93ΓL(1,𝔽25)—34no—
94C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
95C23×C5—181no—
96C5×Q8—91no—
97C5×D4—91no—
98C5×D4—181no—
99C5×D4—181no—
100C5×D4C2×C3⋊D311yescharacteristic
101C5×D4C2×C3⋊D311yescharacteristic, complemented
102C2×C4×C5—91no—
103C2×C4×C5—181no—
104C5×C8—91no—
105C5×C8C2×C3⋊D311yescharacteristic, complemented
106C22×C32—21no—
107C22×C32—21no—
108C2×C3⋊D3—21no—
109C2×C3⋊D3—42no—
110C2×C3⋊D3C5×D411yescharacteristic
111C32×C4C23×C511yescharacteristic
112C3⋊Dic3—21no—
113C3⋊Dic3C5×D411yescharacteristic
114AGL(1,ℤ/8)—91noSylow
115C2×C3×C5—44no—
116C2×C3×C5—44no—
117C2×C3×C5D3×D414yes—
118C5×D3—64no—
119C5×D3—124no—
120C22×D3—64no—
121C3×D4C2×C5×D314yes—
122C3×D4C2×C5×D314yescomplemented
123#67—64no—
124#67—64no—
125C2×Dic3—64no—
126D12—34no—
127C4×D3—34no—
128Dic6—34no—
129C3×C8C2×C5×D314yescomplemented
130C3⋊C8—34no—
131C22×C5—21no—
132C22×C5—21no—
133C22×C5—91no—
134C22×C5—181no—
135C22×C5—362no—
136C4×C5—91no—
137C4×C5—181no—
138C4×C5C22×C3⋊D311yescharacteristic
139C2×C32—41no—
140C2×C32—41no—
141C2×C32C2×C5×D411yescharacteristic
142C3⋊D3—21no—
143C3⋊D3—41no—
144#41—91no—
145C2×D4—91no—
146SD16—91no—
147SD16—91no—
148D8—91no—
149D8C5×C3⋊D311yescharacteristic, complemented
150M16—91no—
151C3×C5#91114yescomplemented
152C22×C3—24no—
153C22×C3—24no—
154C2×D3—34no—
155C2×D3—64no—
156C2×D3—128no—
157C3×C4C22×C5×D314yes—
158Dic3—34no—
159Dic3—64no—
160C2×C5—41no—
161C2×C5—41no—
162C2×C5—181no—
163C2×C5—361no—
164C2×C5D4×C3⋊D311yescharacteristic
165C32C5×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
166C23—181no—
167Q8—91no—
168D4—91no—
169D4—181no—
170D4—181no—
171D4C2×C5×C3⋊D311yescharacteristic
172D4C2×C5×C3⋊D311yescharacteristic, complemented
173C2×C4—91no—
174C2×C4—181no—
175C8—91no—
176C8C2×C5×C3⋊D311yescharacteristic, complemented
177C2×C3—44no—
178C2×C3—44no—
179C2×C3C5×D3×D414yes—
180D3—64no—
181D3—124no—
182C5#6412011yescharacteristic, direct product factor, Sylow
183C22—21no—
184C22—21no—
185C22—91no—
186C22—181no—
187C22—362no—
188C4—91no—
189C4—181no—
190C4C22×C5×C3⋊D311yescharacteristic
191C3C5×#91114yescomplemented
192C2—41no—
193C2—41no—
194C2—181no—
195C2—361no—
196C2C5×D4×C3⋊D311yescharacteristic
subgroupG/H
centerC2×C5D4×C3⋊D3
commutator, cosocleC32×C4C23×C5
FrattiniC4C22×C5×C3⋊D3
FittingC32×C5×D8C2
socleC2×C32×C5C2×D4
hypercenterC5×D8C3⋊D3
hypocenterC32C5×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×D8

Complements

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

NH ≅ G/Ntype
1. C5×#3830C2semidirect
2. C5×D4×C3⋊D3C2semidirect
3. C32×C5×D8C2semidirect
4. C5×#3754C2semidirect
5. C5×#3753C2semidirect
6. C5×#3744C2semidirect
7. C5×#3743C2semidirect
11. C32×C5×D4C22semidirect
17. C5×#634C22semidirect
18. C32×C5×C8C22semidirect
19. C5×C3⋊(C3⋊C8)C22semidirect
20. #64120C5direct (N × H)
23. C3×C5×D8D3semidirect
37. #3830C2×C5semidirect
38. D4×C3⋊D3C2×C5semidirect
39. C32×D8C2×C5semidirect
40. #3754C2×C5semidirect
41. #3753C2×C5semidirect
42. #3744C2×C5semidirect
43. #3743C2×C5semidirect
46. C3×C5×D4C2×D3semidirect
53. C3×C5×C8C2×D3semidirect
66. C5×D8C3⋊D3semidirect
70. C32×D4C22×C5semidirect
76. #634C22×C5semidirect
77. C32×C8C22×C5semidirect
78. C3⋊(C3⋊C8)C22×C5semidirect
89. C3×D8C5×D3semidirect
94. C32×C5AGL(1,ℤ/8)semidirect
101. C5×D4C2×C3⋊D3semidirect
105. C5×C8C2×C3⋊D3semidirect
122. C3×D4C2×C5×D3semidirect
129. C3×C8C2×C5×D3semidirect
149. D8C5×C3⋊D3semidirect
151. C3×C5#911semidirect
165. C32C5×AGL(1,ℤ/8)semidirect
172. D4C2×C5×C3⋊D3semidirect
176. C8C2×C5×C3⋊D3semidirect
182. C5#64120direct (N × H)
191. C3C5×#911semidirect

Maximal subgroups

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

subgroupindex
C5×#38302
C5×D4×C3⋊D32
C32×C5×D82
C5×#37542
C5×#37532
C5×#37442
C5×#37432
C5×#9113
#641205