Finite Group Databasebeta

← C5×SD16×C3⋊D3 #13088096

Subgroups — C5×SD16×C3⋊D3 #13088096

Order 1440.

408 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 114 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×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C5×D4×C3⋊D3C211yesmaximal, characteristic
3C32×C5×SD16C211yesmaximal, characteristic, complemented
4C5×#3755C211yesmaximal, characteristic, complemented
5C5×#3754C211yesmaximal, characteristic, complemented
6C5×#3744C211yesmaximal, characteristic, complemented
7C5×C8×C3⋊D3C211yesmaximal, characteristic, complemented
8C5×D3×SD16—34nomaximal
9C22×C5×C3⋊D3—21no—
10C32×C5×Q8C2211yescharacteristic, complemented
11C32×C5×D4C2211yescharacteristic
12C5×#638—21no—
13C5×C4⋊(C3⋊D3)C2211yescharacteristic
14C4×C5×C3⋊D3—21no—
15C4×C5×C3⋊D3C2211yescharacteristic
16C5×#634—21no—
17C5×#634C2211yescharacteristic, complemented
18C32×C5×C8C2211yescharacteristic, complemented
19C5×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
20SD16×C3⋊D3C511yesmaximal, characteristic, direct product factor, Hall
21C5×D3×Q8—34no—
22C5×D3×D4—34no—
23C3×C5×SD16D314yescomplemented
24C5×#215—34no—
25C5×#214—34no—
26C5×#204—34no—
27C5×D3×C8—34no—
28C22×C32×C5—21no—
29C2×C5×C3⋊D3—21no—
30C2×C5×C3⋊D3—42no—
31C2×C5×C3⋊D3D411yescharacteristic
32C32×C4×C5—21no—
33C32×C4×C5C2311yescharacteristic
34C5×C3⋊Dic3—21no—
35C5×C3⋊Dic3D411yescharacteristic
36C2×C5×SD16—91noHall
37Q8×C3⋊D3C2×C511yescharacteristic, complemented
38D4×C3⋊D3C2×C511yescharacteristic
39C32×SD16C2×C511yescharacteristic, complemented
40#3755C2×C511yescharacteristic, complemented
41#3754C2×C511yescharacteristic, complemented
42#3744C2×C511yescharacteristic, complemented
43C8×C3⋊D3C2×C511yescharacteristic, complemented
44C22×C5×D3—64no—
45C3×C5×Q8C2×D314yescomplemented
46C3×C5×D4C2×D314yes—
47C5×#67—64no—
48C5×D12—34no—
49C4×C5×D3—34no—
50C4×C5×D3—64no—
51C5×Dic6—34no—
52C5×Dic6—64no—
53C3×C5×C8C2×D314yescomplemented
54C5×C3⋊C8—34no—
55D3×SD16—34no—
56C2×C32×C5—41no—
57C2×C32×C5C2×D411yescharacteristic
58C5×C3⋊D3—41no—
59C5×C3⋊D3SD1612yesdirect product factor
60C2×C5×Q8—91no—
61C2×C5×D4—91no—
62C5×SD16—91no—
63C5×SD16—91no—
64C5×SD16—91no—
65C5×SD16C3⋊D311yescharacteristic, direct product factor
66C2×C5×C8—91no—
67C22×C3⋊D3—21no—
68C32×Q8C22×C511yescharacteristic, complemented
69C32×D4C22×C511yescharacteristic
70#638—21no—
71C4⋊(C3⋊D3)C22×C511yescharacteristic
72C4×C3⋊D3—21no—
73C4×C3⋊D3C22×C511yescharacteristic
74#634—21no—
75#634C22×C511yescharacteristic, complemented
76C32×C8C22×C511yescharacteristic, complemented
77C3⋊(C3⋊C8)C22×C511yescharacteristic, complemented
78C22×C3×C5—24no—
79C2×C5×D3—34no—
80C2×C5×D3—64no—
81C2×C5×D3—128no—
82C3×C4×C5—24no—
83C3×C4×C5C22×D314yes—
84C5×Dic3—34no—
85C5×Dic3—64no—
86D3×Q8—34no—
87D3×D4—34no—
88C3×SD16C5×D314yescomplemented
89#215—34no—
90#214—34no—
91#204—34no—
92D3×C8—34no—
93C32×C5C2×SD1611yescharacteristic, complemented, Hall
94C23×C5—181no—
95C5×Q8—91no—
96C5×Q8—181no—
97C5×Q8C2×C3⋊D311yescharacteristic, complemented
98C5×D4—91no—
99C5×D4—181no—
100C5×D4C2×C3⋊D311yescharacteristic
101C2×C4×C5—91no—
102C2×C4×C5—181no—
103C5×C8—91no—
104C5×C8C2×C3⋊D311yescharacteristic, complemented
105C22×C32—21no—
106C2×C3⋊D3—21no—
107C2×C3⋊D3—42no—
108C2×C3⋊D3C5×D411yescharacteristic
109C32×C4—21no—
110C32×C4C23×C511yescharacteristic
111C3⋊Dic3—21no—
112C3⋊Dic3C5×D411yescharacteristic
113C2×SD16—91noSylow
114C2×C3×C5—44no—
115C2×C3×C5D3×D414yes—
116C5×D3—38no—
117C5×D3—124no—
118C22×D3—64no—
119C3×Q8C2×C5×D314yescomplemented
120C3×D4C2×C5×D314yes—
121#67—64no—
122D12—34no—
123C4×D3—34no—
124C4×D3—64no—
125Dic6—34no—
126Dic6—64no—
127C3×C8C2×C5×D314yescomplemented
128C3⋊C8—34no—
129C22×C5—21no—
130C22×C5—91no—
131C22×C5—181no—
132C22×C5—362no—
133C4×C5—21no—
134C4×C5—91no—
135C4×C5—181no—
136C4×C5C22×C3⋊D311yescharacteristic
137C2×C32—41no—
138C2×C32C2×C5×D411yescharacteristic
139C3⋊D3—41no—
140C3⋊D3C5×SD1612yesdirect product factor
141C2×Q8—91no—
142C2×D4—91no—
143SD16—91no—
144SD16—91no—
145SD16—91no—
146SD16C5×C3⋊D311yescharacteristic, direct product factor
147C2×C8—91no—
148C3×C5D3×SD1614yescomplemented
149C22×C3—24no—
150C2×D3—34no—
151C2×D3—64no—
152C2×D3—128no—
153C3×C4—24no—
154C3×C4C22×C5×D314yes—
155Dic3—34no—
156Dic3—64no—
157C2×C5—41no—
158C2×C5—92no—
159C2×C5—361no—
160C2×C5D4×C3⋊D311yescharacteristic
161C32C2×C5×SD1611yescharacteristic, complemented, Sylow
162C23—181no—
163Q8—91no—
164Q8—181no—
165Q8C2×C5×C3⋊D311yescharacteristic, complemented
166D4—91no—
167D4—181no—
168D4C2×C5×C3⋊D311yescharacteristic
169C2×C4—91no—
170C2×C4—181no—
171C8—91no—
172C8C2×C5×C3⋊D311yescharacteristic, complemented
173C2×C3—44no—
174C2×C3C5×D3×D414yes—
175D3—38no—
176D3—124no—
177C5SD16×C3⋊D311yescharacteristic, direct product factor, Sylow
178C22—21no—
179C22—91no—
180C22—181no—
181C22—362no—
182C4—21no—
183C4—91no—
184C4—181no—
185C4C22×C5×C3⋊D311yescharacteristic
186C3C5×D3×SD1614yescomplemented
187C2—41no—
188C2—92no—
189C2—361no—
190C2C5×D4×C3⋊D311yescharacteristic
subgroupG/H
centerC2×C5D4×C3⋊D3
commutator, cosocleC32×C4C23×C5
FrattiniC4C22×C5×C3⋊D3
FittingC32×C5×SD16C2
socleC2×C32×C5C2×D4
prime radicalC5×D4×C3⋊D3C2
hypercenterC5×SD16C3⋊D3
hypocenterC32C2×C5×SD16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×SD16

Complements

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

NH ≅ G/Ntype
1. C5×Q8×C3⋊D3C2semidirect
3. C32×C5×SD16C2semidirect
4. C5×#3755C2semidirect
5. C5×#3754C2semidirect
6. C5×#3744C2semidirect
7. C5×C8×C3⋊D3C2semidirect
10. C32×C5×Q8C22semidirect
17. C5×#634C22semidirect
18. C32×C5×C8C22semidirect
19. C5×C3⋊(C3⋊C8)C22semidirect
20. SD16×C3⋊D3C5direct (N × H)
23. C3×C5×SD16D3semidirect
37. Q8×C3⋊D3C2×C5semidirect
39. C32×SD16C2×C5semidirect
40. #3755C2×C5semidirect
41. #3754C2×C5semidirect
42. #3744C2×C5semidirect
43. C8×C3⋊D3C2×C5semidirect
45. C3×C5×Q8C2×D3semidirect
53. C3×C5×C8C2×D3semidirect
59. C5×C3⋊D3SD16direct (N × H)
65. C5×SD16C3⋊D3direct (N × H)
68. C32×Q8C22×C5semidirect
75. #634C22×C5semidirect
76. C32×C8C22×C5semidirect
77. C3⋊(C3⋊C8)C22×C5semidirect
88. C3×SD16C5×D3semidirect
93. C32×C5C2×SD16semidirect
97. C5×Q8C2×C3⋊D3semidirect
104. C5×C8C2×C3⋊D3semidirect
119. C3×Q8C2×C5×D3semidirect
127. C3×C8C2×C5×D3semidirect
140. C3⋊D3C5×SD16direct (N × H)
146. SD16C5×C3⋊D3direct (N × H)
148. C3×C5D3×SD16semidirect
161. C32C2×C5×SD16semidirect
165. Q8C2×C5×C3⋊D3semidirect
172. C8C2×C5×C3⋊D3semidirect
177. C5SD16×C3⋊D3direct (N × H)
186. C3C5×D3×SD16semidirect

Maximal subgroups

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

subgroupindex
C5×Q8×C3⋊D32
C5×D4×C3⋊D32
C32×C5×SD162
C5×#37552
C5×#37542
C5×#37442
C5×C8×C3⋊D32
C5×D3×SD163
SD16×C3⋊D35