Finite Group Databasebeta

← C5×M16×C3⋊D3 #13088089

Subgroups — C5×M16×C3⋊D3 #13088089

Order 1440.

408 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 150 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×C4×C5×C3⋊D3C211yesmaximal, characteristic
2C32×C5×M16C211yesmaximal, characteristic, complemented
3C5×#3748C211yesmaximal, characteristic, complemented
4C5×#3743C212yesmaximal, complemented
5C5×C8×C3⋊D3C212yesmaximal, complemented
6C5×D3×M16—34nomaximal
7C22×C5×C3⋊D3C411yescharacteristic
8C2×C32×C4×C5C2211yescharacteristic
9C2×C5×C3⋊Dic3C411yescharacteristic
10C4×C5×C3⋊D3C411yescharacteristic
11C4×C5×C3⋊D3C411yescharacteristic
12C4×C5×C3⋊D3C2211yescharacteristic
13C4×C5×C3⋊D3C2211yescharacteristic
14C32×C5×C8C2212yescomplemented
15C5×C3⋊(C3⋊C8)C2212yescomplemented
16M16×C3⋊D3C511yesmaximal, characteristic, direct product factor, Hall
17C2×C4×C5×D3—34no—
18C3×C5×M16D314yescomplemented
19C5×#208—34no—
20C5×ΓL(1,𝔽25)—38no—
21C5×D3×C8—38no—
22C22×C32×C5C2×C411yescharacteristic
23C2×C5×C3⋊D3—22no—
24C2×C5×C3⋊D3C2×C411yescharacteristic
25C2×C5×C3⋊D3C2×C411yescharacteristic
26C32×C4×C5C2×C411yescharacteristic
27C32×C4×C5C2311yescharacteristic
28C5×C3⋊Dic3C2×C411yescharacteristic
29C5×C3⋊Dic3C2×C411yescharacteristic
30C2×C5×M16—91noHall
31C2×C4×C3⋊D3C2×C511yescharacteristic
32C32×M16C2×C511yescharacteristic, complemented
33#3748C2×C511yescharacteristic, complemented
34#3743C2×C512yescomplemented
35C8×C3⋊D3C2×C512yescomplemented
36C22×C5×D3—34no—
37C2×C3×C4×C5C2×D314yes—
38C2×C5×Dic3—34no—
39C4×C5×D3—34no—
40C4×C5×D3—34no—
41C4×C5×D3—34no—
42C4×C5×D3—34no—
43C3×C5×C8C2×D318yescomplemented
44C5×C3⋊C8—38no—
45D3×M16—34no—
46C2×C32×C5—21no—
47C2×C32×C5C22×C411yescharacteristic
48C5×C3⋊D3—21no—
49C5×C3⋊D3M1612yesdirect product factor
50C22×C4×C5—91no—
51C5×M16—91no—
52C5×M16—92no—
53C5×M16C3⋊D311yescharacteristic, direct product factor
54C2×C5×C8—92no—
55C22×C3⋊D3C4×C511yescharacteristic
56C2×C32×C4C22×C511yescharacteristic
57C2×C3⋊Dic3C4×C511yescharacteristic
58C4×C3⋊D3C4×C511yescharacteristic
59C4×C3⋊D3C4×C511yescharacteristic
60C4×C3⋊D3C22×C511yescharacteristic
61C4×C3⋊D3C22×C511yescharacteristic
62C32×C8C22×C512yescomplemented
63C3⋊(C3⋊C8)C22×C512yescomplemented
64C22×C3×C5C4×D314yes—
65C2×C5×D3—34no—
66C2×C5×D3—34no—
67C2×C5×D3—68no—
68C3×C4×C5C4×D314yes—
69C3×C4×C5C22×D314yes—
70C5×Dic3—34no—
71C5×Dic3—34no—
72C2×C4×D3—34no—
73C3×M16C5×D314yescomplemented
74#208—34no—
75ΓL(1,𝔽25)—38no—
76D3×C8—38no—
77C32×C5C2×M1611yescharacteristic, complemented, Hall
78C23×C5—91no—
79C2×C4×C5—91no—
80C2×C4×C5—91no—
81C2×C4×C5—91no—
82C2×C4×C5—91no—
83C2×C4×C5—91no—
84C2×C4×C5C2×C3⋊D311yescharacteristic
85C5×C8—92no—
86C5×C8C2×C3⋊D312yescomplemented
87C22×C32C2×C4×C511yescharacteristic
88C2×C3⋊D3—22no—
89C2×C3⋊D3C2×C4×C511yescharacteristic
90C2×C3⋊D3C2×C4×C511yescharacteristic
91C32×C4C2×C4×C511yescharacteristic
92C32×C4C23×C511yescharacteristic
93C3⋊Dic3C2×C4×C511yescharacteristic
94C3⋊Dic3C2×C4×C511yescharacteristic
95C2×M16—91noSylow
96C2×C3×C5—24no—
97C2×C3×C5C2×C4×D314yes—
98C5×D3—38no—
99C5×D3—64no—
100C22×D3—34no—
101C2×C3×C4C2×C5×D314yes—
102C2×Dic3—34no—
103C4×D3—34no—
104C4×D3—34no—
105C4×D3—34no—
106C4×D3—34no—
107C3×C8C2×C5×D318yescomplemented
108C3⋊C8—38no—
109C22×C5—91no—
110C22×C5—91no—
111C22×C5—182no—
112C22×C5C4×C3⋊D311yescharacteristic
113C4×C5—91no—
114C4×C5—91no—
115C4×C5C4×C3⋊D311yescharacteristic
116C4×C5C22×C3⋊D311yescharacteristic
117C2×C32—21no—
118C2×C32C22×C4×C511yescharacteristic
119C3⋊D3—21no—
120C3⋊D3C5×M1612yesdirect product factor
121C22×C4—91no—
122M16—91no—
123M16—92no—
124M16C5×C3⋊D311yescharacteristic, direct product factor
125C2×C8—92no—
126C3×C5D3×M1614yescomplemented
127C22×C3C4×C5×D314yes—
128C2×D3—34no—
129C2×D3—34no—
130C2×D3—68no—
131C3×C4C4×C5×D314yes—
132C3×C4C22×C5×D314yes—
133Dic3—34no—
134Dic3—34no—
135C2×C5—21no—
136C2×C5—92no—
137C2×C5—181no—
138C2×C5C2×C4×C3⋊D311yescharacteristic
139C32C2×C5×M1611yescharacteristic, complemented, Sylow
140C23—91no—
141C2×C4—91no—
142C2×C4—91no—
143C2×C4—91no—
144C2×C4—91no—
145C2×C4—91no—
146C2×C4C2×C5×C3⋊D311yescharacteristic
147C8—92no—
148C8C2×C5×C3⋊D312yescomplemented
149C2×C3—24no—
150C2×C3C2×C4×C5×D314yes—
151D3—38no—
152D3—64no—
153C5M16×C3⋊D311yescharacteristic, direct product factor, Sylow
154C22—91no—
155C22—91no—
156C22—182no—
157C22C4×C5×C3⋊D311yescharacteristic
158C4—91no—
159C4—91no—
160C4C4×C5×C3⋊D311yescharacteristic
161C4C22×C5×C3⋊D311yescharacteristic
162C3C5×D3×M1614yescomplemented
163C2—21no—
164C2—92no—
165C2—181no—
166C2C2×C4×C5×C3⋊D311yescharacteristic
subgroupG/H
centerC4×C5C22×C3⋊D3
commutatorC2×C32C22×C4×C5
FrattiniC4C22×C5×C3⋊D3
FittingC32×C5×M16C2
socleC2×C32×C5C22×C4
prime radicalC22×C5×C3⋊D3C4
cosocleC32×C4C23×C5
hypercenterC5×M16C3⋊D3
hypocenterC32C2×C5×M16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C4×C5 ◁ C5×M16

Complements

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

NH ≅ G/Ntype
2. C32×C5×M16C2semidirect
3. C5×#3748C2semidirect
4. C5×#3743C2semidirect
5. C5×C8×C3⋊D3C2semidirect
14. C32×C5×C8C22semidirect
15. C5×C3⋊(C3⋊C8)C22semidirect
16. M16×C3⋊D3C5direct (N × H)
18. C3×C5×M16D3semidirect
32. C32×M16C2×C5semidirect
33. #3748C2×C5semidirect
34. #3743C2×C5semidirect
35. C8×C3⋊D3C2×C5semidirect
43. C3×C5×C8C2×D3semidirect
49. C5×C3⋊D3M16direct (N × H)
53. C5×M16C3⋊D3direct (N × H)
62. C32×C8C22×C5semidirect
63. C3⋊(C3⋊C8)C22×C5semidirect
73. C3×M16C5×D3semidirect
77. C32×C5C2×M16semidirect
86. C5×C8C2×C3⋊D3semidirect
107. C3×C8C2×C5×D3semidirect
120. C3⋊D3C5×M16direct (N × H)
124. M16C5×C3⋊D3direct (N × H)
126. C3×C5D3×M16semidirect
139. C32C2×C5×M16semidirect
148. C8C2×C5×C3⋊D3semidirect
153. C5M16×C3⋊D3direct (N × H)
162. C3C5×D3×M16semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×C3⋊D32
C32×C5×M162
C5×#37482
C5×#37432
C5×C8×C3⋊D32
C5×D3×M163
M16×C3⋊D35