Finite Group Databasebeta

← C5×C22⋊C4×C3⋊D3 #13088064

Subgroups — C5×C22⋊C4×C3⋊D3 #13088064

Order 1440.

792 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 186 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
1C23×C5×C3⋊D3C211yesmaximal, characteristic
2C2×C4×C5×C3⋊D3C212yesmaximal, complemented
3C32×C5×C22⋊C4C211yesmaximal, characteristic, complemented
4C5×#3757C211yesmaximal, characteristic, complemented
5C5×#3752C212yesmaximal, complemented
6C5×D3×C22⋊C4—34nomaximal
7C23×C32×C5C2211yescharacteristic
8C22×C5×C3⋊D3—24no—
9C22×C5×C3⋊D3C414yescomplemented
10C22×C5×C3⋊D3C2211yescharacteristic
11C22×C5×C3⋊D3C2211yescharacteristic
12C2×C32×C4×C5C2212yescomplemented
13C2×C5×C3⋊Dic3C2212yescomplemented
14C4×C5×C3⋊D3—24no—
15C22⋊C4×C3⋊D3C511yesmaximal, characteristic, direct product factor, Hall
16C23×C5×D3—34no—
17C2×C4×C5×D3—38no—
18C3×C5×C22⋊C4D314yescomplemented
19C5×#217—34no—
20C5×(C2×D3)⋊C4—38no—
21C22×C32×C5—22no—
22C22×C32×C5C2×C412yescomplemented
23C22×C32×C5C2311yescharacteristic
24C2×C5×C3⋊D3—22no—
25C2×C5×C3⋊D3—28no—
26C2×C5×C3⋊D3C2×C412yes—
27C2×C5×C3⋊D3C2×C412yescomplemented
28C2×C5×C3⋊D3D414yes—
29C32×C4×C5—22no—
30C5×C3⋊Dic3—22no—
31C2×C5×C22⋊C4—91noHall
32C23×C3⋊D3C2×C511yescharacteristic
33C2×C4×C3⋊D3C2×C512yescomplemented
34C32×C22⋊C4C2×C511yescharacteristic, complemented
35#3757C2×C511yescharacteristic, complemented
36#3752C2×C512yescomplemented
37C23×C3×C5C2×D314yes—
38C22×C5×D3—34no—
39C22×C5×D3—316no—
40C22×C5×D3—34no—
41C22×C5×D3—616no—
42C2×C3×C4×C5C2×D318yescomplemented
43C2×C5×Dic3—38no—
44C4×C5×D3—616no—
45D3×C22⋊C4—34no—
46C2×C32×C5—22no—
47C2×C32×C5C22×C411yescharacteristic
48C2×C32×C5C2×D412yes—
49C5×C3⋊D3—22no—
50C5×C3⋊D3C22⋊C414yesdirect product factor
51C24×C5—91no—
52C22×C4×C5—92no—
53C5×C22⋊C4—91no—
54C5×C22⋊C4—92no—
55C5×C22⋊C4C3⋊D311yescharacteristic, direct product factor
56C23×C32C22×C511yescharacteristic
57C22×C3⋊D3—24no—
58C22×C3⋊D3C4×C514yescomplemented
59C22×C3⋊D3C22×C511yescharacteristic
60C22×C3⋊D3C22×C511yescharacteristic
61C2×C32×C4C22×C512yescomplemented
62C2×C3⋊Dic3C22×C512yescomplemented
63C4×C3⋊D3—24no—
64C22×C3×C5—28no—
65C22×C3×C5C4×D318yescomplemented
66C22×C3×C5C22×D314yes—
67C2×C5×D3—38no—
68C2×C5×D3—316no—
69C2×C5×D3—38no—
70C2×C5×D3—632no—
71C2×C5×D3—68no—
72C3×C4×C5—28no—
73C5×Dic3—68no—
74C23×D3—34no—
75C2×C4×D3—38no—
76C3×C22⋊C4C5×D314yescomplemented
77#217—34no—
78(C2×D3)⋊C4—38no—
79C32×C5C2×C22⋊C411yescharacteristic, complemented, Hall
80C23×C5—91no—
81C23×C5—94no—
82C23×C5—91no—
83C23×C5—184no—
84C23×C5C2×C3⋊D311yescharacteristic
85C2×C4×C5—92no—
86C2×C4×C5—184no—
87C2×C4×C5C2×C3⋊D312yescomplemented
88C22×C32—22no—
89C22×C32C2×C4×C512yescomplemented
90C22×C32C23×C511yescharacteristic
91C2×C3⋊D3—22no—
92C2×C3⋊D3—28no—
93C2×C3⋊D3C2×C4×C512yes—
94C2×C3⋊D3C2×C4×C512yescomplemented
95C2×C3⋊D3C5×D414yes—
96C32×C4—22no—
97C3⋊Dic3—22no—
98C2×C22⋊C4—91noSylow
99C2×C3×C5—28no—
100C2×C3×C5C2×C4×D314yes—
101C2×C3×C5D3×D418yes—
102C5×D3—316no—
103C5×D3—68no—
104C23×C3C2×C5×D314yes—
105C22×D3—34no—
106C22×D3—316no—
107C22×D3—34no—
108C22×D3—616no—
109C2×C3×C4C2×C5×D318yescomplemented
110C2×Dic3—38no—
111C4×D3—616no—
112C22×C5—22no—
113C22×C5—92no—
114C22×C5—94no—
115C22×C5—92no—
116C22×C5—188no—
117C22×C5—182no—
118C22×C5C4×C3⋊D312yescomplemented
119C22×C5C22×C3⋊D311yescharacteristic
120C4×C5—22no—
121C4×C5—182no—
122C2×C32—22no—
123C2×C32C22×C4×C511yescharacteristic
124C2×C32C2×C5×D412yes—
125C3⋊D3—22no—
126C3⋊D3C5×C22⋊C414yesdirect product factor
127C24—91no—
128C22×C4—92no—
129C22⋊C4—91no—
130C22⋊C4—92no—
131C22⋊C4C5×C3⋊D311yescharacteristic, direct product factor
132C3×C5D3×C22⋊C414yescomplemented
133C22×C3—28no—
134C22×C3C4×C5×D318yescomplemented
135C22×C3C22×C5×D314yes—
136C2×D3—38no—
137C2×D3—316no—
138C2×D3—38no—
139C2×D3—632no—
140C2×D3—68no—
141C3×C4—28no—
142Dic3—68no—
143C2×C5—22no—
144C2×C5—94no—
145C2×C5—182no—
146C2×C5C2×C4×C3⋊D311yescharacteristic
147C2×C5D4×C3⋊D312yes—
148C32C2×C5×C22⋊C411yescharacteristic, complemented, Sylow
149C23—91no—
150C23—94no—
151C23—91no—
152C23—184no—
153C23C2×C5×C3⋊D311yescharacteristic
154C2×C4—92no—
155C2×C4—184no—
156C2×C4C2×C5×C3⋊D312yescomplemented
157C2×C3—28no—
158C2×C3C2×C4×C5×D314yes—
159C2×C3C5×D3×D418yes—
160D3—316no—
161D3—68no—
162C5C22⋊C4×C3⋊D311yescharacteristic, direct product factor, Sylow
163C22—22no—
164C22—92no—
165C22—94no—
166C22—92no—
167C22—188no—
168C22—182no—
169C22C4×C5×C3⋊D312yescomplemented
170C22C22×C5×C3⋊D311yescharacteristic
171C4—22no—
172C4—182no—
173C3C5×D3×C22⋊C414yescomplemented
174C2—22no—
175C2—94no—
176C2—182no—
177C2C2×C4×C5×C3⋊D311yescharacteristic
178C2C5×D4×C3⋊D312yes—
subgroupG/H
centerC22×C5C22×C3⋊D3
commutatorC2×C32C22×C4×C5
FrattiniC22C22×C5×C3⋊D3
FittingC32×C5×C22⋊C4C2
socleC22×C32×C5C23
prime radicalC23×C5×C3⋊D3C2
cosocleC22×C32C23×C5
hypercenterC5×C22⋊C4C3⋊D3
hypocenterC32C2×C5×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C5 ◁ C5×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C5×C3⋊D3C2semidirect
3. C32×C5×C22⋊C4C2semidirect
4. C5×#3757C2semidirect
5. C5×#3752C2semidirect
9. C22×C5×C3⋊D3C4semidirect
12. C2×C32×C4×C5C22semidirect
13. C2×C5×C3⋊Dic3C22semidirect
15. C22⋊C4×C3⋊D3C5direct (N × H)
18. C3×C5×C22⋊C4D3semidirect
22. C22×C32×C5C2×C4semidirect
27. C2×C5×C3⋊D3C2×C4semidirect
33. C2×C4×C3⋊D3C2×C5semidirect
34. C32×C22⋊C4C2×C5semidirect
35. #3757C2×C5semidirect
36. #3752C2×C5semidirect
42. C2×C3×C4×C5C2×D3semidirect
50. C5×C3⋊D3C22⋊C4direct (N × H)
55. C5×C22⋊C4C3⋊D3direct (N × H)
58. C22×C3⋊D3C4×C5semidirect
61. C2×C32×C4C22×C5semidirect
62. C2×C3⋊Dic3C22×C5semidirect
65. C22×C3×C5C4×D3semidirect
76. C3×C22⋊C4C5×D3semidirect
79. C32×C5C2×C22⋊C4semidirect
87. C2×C4×C5C2×C3⋊D3semidirect
89. C22×C32C2×C4×C5semidirect
94. C2×C3⋊D3C2×C4×C5semidirect
109. C2×C3×C4C2×C5×D3semidirect
118. C22×C5C4×C3⋊D3semidirect
126. C3⋊D3C5×C22⋊C4direct (N × H)
131. C22⋊C4C5×C3⋊D3direct (N × H)
132. C3×C5D3×C22⋊C4semidirect
134. C22×C3C4×C5×D3semidirect
148. C32C2×C5×C22⋊C4semidirect
156. C2×C4C2×C5×C3⋊D3semidirect
162. C5C22⋊C4×C3⋊D3direct (N × H)
169. C22C4×C5×C3⋊D3semidirect
173. C3C5×D3×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C23×C5×C3⋊D32
C2×C4×C5×C3⋊D32
C32×C5×C22⋊C42
C5×#37572
C5×#37522
C5×D3×C22⋊C43
C22⋊C4×C3⋊D35