Finite Group Databasebeta

← C2×C5×#3830 #13089493

Subgroups — C2×C5×#3830 #13089493

Order 1440.

984 conjugacy classes of subgroups; only the 330 normal subgroups are shown.

normal subgroups only

This group has 984 conjugacy classes of subgroups — too many to draw. Only its 330 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×C32×C5×D4C211yesmaximal, characteristic, complemented
2C2×C5×#638C212yesmaximal, complemented
3C22×C5×C3⋊Dic3C212yesmaximal, complemented
4C5×#3830C218yesmaximal, direct product factor
5C2×C4×C5×C3⋊D3C211yesmaximal, characteristic, complemented
6C2×C5×#634C211yesmaximal, characteristic, complemented
7C2×C5×#237—34nomaximal
8C23×C32×C5C2212yes—
9C22×C5×C3⋊D3C2211yescharacteristic
10C32×C5×D4C2214yescomplemented
11C2×C32×C4×C5C2211yescharacteristic
12C5×#638C2218yescomplemented
13C2×C5×C3⋊Dic3C2212yes—
14C2×C5×C3⋊Dic3C2211yescharacteristic
15C2×C5×C3⋊Dic3C2218yescomplemented
16C4×C5×C3⋊D3C2214yescomplemented
17C5×#634C2214yescomplemented
18C2×#3830C511yesmaximal, characteristic, direct product factor, Hall
19C2×C3×C5×D4D314yescomplemented
20C2×C5×#67—38no—
21C22×C5×Dic3—38no—
22C5×#237—332no—
23C2×C4×C5×D3—34no—
24C2×C5×Dic6—34no—
25C22×C32×C5—24no—
26C22×C32×C5C2314yes—
27C22×C32×C5C2311yescharacteristic
28C2×C5×C3⋊D3—22no—
29C2×C5×C3⋊D3C2312yes—
30C32×C4×C5C2312yes—
31C5×C3⋊Dic3C2314yes—
32C5×C3⋊Dic3C2312yes—
33C2×C5×#41—91noHall
34C2×C32×D4C2×C511yescharacteristic, complemented
35C2×#638C2×C512yescomplemented
36C22×C3⋊Dic3C2×C512yescomplemented
37#3830C2×C518yesdirect product factor
38C2×C4×C3⋊D3C2×C511yescharacteristic, complemented
39C2×#634C2×C511yescharacteristic, complemented
40C23×C3×C5C2×D318yes—
41C22×C5×D3—34no—
42C3×C5×D4C2×D3116yescomplemented
43C2×C3×C4×C5C2×D314yes—
44C5×#67—332no—
45C2×C5×Dic3—38no—
46C2×C5×Dic3—34no—
47C2×C5×Dic3—332no—
48C4×C5×D3—316no—
49C5×Dic6—316no—
50C2×#237—34no—
51C2×C32×C5—24no—
52C2×C32×C5#4112yescomplemented
53C2×C32×C5C2411yescharacteristic
54C5×C3⋊D3—22no—
55C5×#41—98no—
56C2×C5×Q8—91no—
57C2×C5×D4—92no—
58C2×C5×D4C3⋊D311yescharacteristic, complemented
59C22×C4×C5—92no—
60C22×C4×C5—91no—
61C23×C32C22×C512yes—
62C22×C3⋊D3C22×C511yescharacteristic
63C32×D4C22×C514yescomplemented
64C2×C32×C4C22×C511yescharacteristic
65#638C22×C518yescomplemented
66C2×C3⋊Dic3C22×C512yes—
67C2×C3⋊Dic3C22×C511yescharacteristic
68C2×C3⋊Dic3C22×C518yescomplemented
69C4×C3⋊D3C22×C514yescomplemented
70#634C22×C514yescomplemented
71C22×C3×C5—216no—
72C22×C3×C5C22×D3116yes—
73C22×C3×C5C22×D314yes—
74C2×C5×D3—38no—
75C2×C5×D3—68no—
76C3×C4×C5C22×D318yes—
77C5×Dic3—316no—
78C5×Dic3—38no—
79C2×C3×D4C5×D314yescomplemented
80C2×#67—38no—
81C22×Dic3—38no—
82#237—332no—
83C2×C4×D3—34no—
84C2×Dic6—34no—
85C32×C5C2×#4111yescharacteristic, complemented, Hall
86C23×C5—91no—
87C23×C5C2×C3⋊D312yes—
88C5×Q8—94no—
89C5×D4—98no—
90C5×D4C2×C3⋊D314yescomplemented
91C2×C4×C5—98no—
92C2×C4×C5—91no—
93C2×C4×C5—92no—
94C2×C4×C5—94no—
95C2×C4×C5C2×C3⋊D311yescharacteristic
96C22×C32—24no—
97C22×C32C23×C514yes—
98C22×C32C23×C511yescharacteristic
99C2×C3⋊D3—22no—
100C2×C3⋊D3C23×C512yes—
101C32×C4C23×C512yes—
102C3⋊Dic3C23×C514yes—
103C3⋊Dic3C23×C512yes—
104C2×#41—91noSylow
105C2×C3×C5—216no—
106C2×C3×C5#23718yescomplemented
107C2×C3×C5C23×D314yes—
108C5×D3—68no—
109C23×C3C2×C5×D318yes—
110C22×D3—34no—
111C3×D4C2×C5×D3116yescomplemented
112C2×C3×C4C2×C5×D314yes—
113#67—332no—
114C2×Dic3—38no—
115C2×Dic3—34no—
116C2×Dic3—332no—
117C4×D3—316no—
118Dic6—316no—
119C22×C5—24no—
120C22×C5—92no—
121C22×C5—182no—
122C22×C5C22×C3⋊D314yes—
123C22×C5C22×C3⋊D311yescharacteristic
124C4×C5—92no—
125C4×C5—94no—
126C4×C5C22×C3⋊D312yes—
127C2×C32—24no—
128C2×C32C5×#4112yescomplemented
129C2×C32C24×C511yescharacteristic
130C3⋊D3—22no—
131#41—98no—
132C2×Q8—91no—
133C2×D4—92no—
134C2×D4C5×C3⋊D311yescharacteristic, complemented
135C22×C4—92no—
136C22×C4—91no—
137C3×C5C2×#23714yescomplemented
138C22×C3—216no—
139C22×C3C22×C5×D3116yes—
140C22×C3C22×C5×D314yes—
141C2×D3—38no—
142C2×D3—68no—
143C3×C4C22×C5×D318yes—
144Dic3—316no—
145Dic3—38no—
146C2×C5—24no—
147C2×C5—182no—
148C2×C5#383012yesdirect product factor
149C2×C5C23×C3⋊D311yescharacteristic
150C32C2×C5×#4111yescharacteristic, complemented, Sylow
151C23—91no—
152C23C2×C5×C3⋊D312yes—
153Q8—94no—
154D4—98no—
155D4C2×C5×C3⋊D314yescomplemented
156C2×C4—91no—
157C2×C4—92no—
158C2×C4—98no—
159C2×C4—94no—
160C2×C4C2×C5×C3⋊D311yescharacteristic
161C2×C3—216no—
162C2×C3C5×#23718yescomplemented
163C2×C3C23×C5×D314yes—
164D3—68no—
165C5C2×#383011yescharacteristic, direct product factor, Sylow
166C22—24no—
167C22—92no—
168C22—182no—
169C22C22×C5×C3⋊D314yes—
170C22C22×C5×C3⋊D311yescharacteristic
171C4—92no—
172C4—94no—
173C4C22×C5×C3⋊D312yes—
174C3C2×C5×#23714yescomplemented
175C2—24no—
176C2—182no—
177C2C5×#383012yesdirect product factor
178C2C23×C5×C3⋊D311yescharacteristic
subgroupG/H
centerC22×C5C22×C3⋊D3
commutator, cosocleC2×C32C24×C5
FrattiniC2C23×C5×C3⋊D3
FittingC2×C32×C5×D4C2
socleC22×C32×C5C23
hypercenterC2×C5×D4C3⋊D3
hypocenterC32C2×C5×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C5 ◁ C2×C5×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×D4C2semidirect
2. C2×C5×#638C2semidirect
3. C22×C5×C3⋊Dic3C2semidirect
4. C5×#3830C2direct (N × H)
5. C2×C4×C5×C3⋊D3C2semidirect
6. C2×C5×#634C2semidirect
10. C32×C5×D4C22semidirect
12. C5×#638C22semidirect
15. C2×C5×C3⋊Dic3C22semidirect
16. C4×C5×C3⋊D3C22semidirect
17. C5×#634C22semidirect
18. C2×#3830C5direct (N × H)
19. C2×C3×C5×D4D3semidirect
34. C2×C32×D4C2×C5semidirect
35. C2×#638C2×C5semidirect
36. C22×C3⋊Dic3C2×C5semidirect
37. #3830C2×C5direct (N × H)
38. C2×C4×C3⋊D3C2×C5semidirect
39. C2×#634C2×C5semidirect
42. C3×C5×D4C2×D3semidirect
52. C2×C32×C5#41semidirect
58. C2×C5×D4C3⋊D3semidirect
63. C32×D4C22×C5semidirect
65. #638C22×C5semidirect
68. C2×C3⋊Dic3C22×C5semidirect
69. C4×C3⋊D3C22×C5semidirect
70. #634C22×C5semidirect
79. C2×C3×D4C5×D3semidirect
85. C32×C5C2×#41semidirect
90. C5×D4C2×C3⋊D3semidirect
106. C2×C3×C5#237semidirect
111. C3×D4C2×C5×D3semidirect
128. C2×C32C5×#41semidirect
134. C2×D4C5×C3⋊D3semidirect
137. C3×C5C2×#237semidirect
148. C2×C5#3830direct (N × H)
150. C32C2×C5×#41semidirect
155. D4C2×C5×C3⋊D3semidirect
162. C2×C3C5×#237semidirect
165. C5C2×#3830direct (N × H)
174. C3C2×C5×#237semidirect
177. C2C5×#3830direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C5×D42
C2×C5×#6382
C22×C5×C3⋊Dic32
C5×#38302
C2×C4×C5×C3⋊D32
C2×C5×#6342
C2×C5×#2373
C2×#38305