Finite Group Databasebeta

← #13107297

Subgroups — #13107297

Order 1600.

1072 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 219 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
1#11717522C212yesmaximal, complemented
2C52×#135C211yesmaximal, characteristic, complemented
3#11717269C212yesmaximal, complemented
4#11717239C212yesmaximal, complemented
5#11717234C214yesmaximal, complemented
6D8×C5⋊D5C212yesmaximal, complemented
7C2×#87801C211yesmaximal, characteristic, complemented
8#11717221C211yesmaximal, characteristic, complemented
9C52×#41C2212yescomplemented
10#87904C2214yescomplemented
11D4×C5⋊D5—24no—
12D4×C5⋊D5C2214yescomplemented
13#87900—22no—
14#87900C2211yescharacteristic
15C2×C4⋊(C5⋊D5)—22no—
16C2×C4⋊(C5⋊D5)C2212yescomplemented
17C52×Q16C2211yescharacteristic, complemented
18C52×SD16C2212yescomplemented
19C52×D8C2211yescharacteristic, complemented
20C2×C52×C8C2211yescharacteristic, complemented
21#87811C2214yescomplemented
22#87809C2214yescomplemented
23#87804C2211yescharacteristic, complemented
24#87801C2212yescomplemented
25#87801C2212yescomplemented
26#87799C2212yescomplemented
27C8×C5⋊D5C2212yescomplemented
28#66103—56nomaximal
29C22×C5⋊D5—22no—
30C22×C5⋊D5—24no—
31C52×Q8C2312yes—
32C52×D4—22no—
33C52×D4C2312yes—
34C2×C4×C52—22no—
35C2×C4×C52C2311yescharacteristic
36C22⋊(C5⋊D5)—24no—
37C22⋊(C5⋊D5)D412yes—
38C4⋊(C5⋊D5)—24no—
39C4⋊(C5⋊D5)—22no—
40C4⋊(C5⋊D5)D411yescharacteristic
41C4⋊(C5⋊D5)C2314yes—
42C4×C5⋊D5—24no—
43C4×C5⋊D5C2312yes—
44#6045D411yescharacteristic
45C52×C8C2311yescharacteristic
46C52×C8C2311yescharacteristic
47#6029C2312yes—
48#4149—512no—
49C5×#135D516yescomplemented
50#4095—512no—
51#4065—512no—
52#4060—524no—
53D5×D8—512no—
54C2×D40—56no—
55#4047—56no—
56C22×C52—22no—
57C22×C52C2×D411yescharacteristic
58C2×C5⋊D5—24no—
59C2×C5⋊D5—84no—
60C2×C5⋊D5—82no—
61C2×C5⋊D5C2×D412yes—
62C4×C52—22no—
63C4×C52C2×D411yescharacteristic
64C4×C52C2411yescharacteristic
65#1039C2×D412yes—
66C5×#41C2×D5112yescomplemented
67#713—524no—
68D4×D5—524no—
69D4×D5—1024no—
70#709—56no—
71#709—1012no—
72C2×D20—512no—
73C2×D20—1012no—
74C5×Q16C2×D516yescomplemented
75C5×SD16C2×D5112yescomplemented
76C5×D8C2×D516yescomplemented
77C2×C5×C8C2×D516yescomplemented
78#688—524no—
79#686—524no—
80#681—56no—
81D40—512no—
82D40—512no—
83#676—512no—
84C8×D5—512no—
85#576—251noSylow
86C2×C52—21no—
87C2×C52—42no—
88C2×C52C22×D411yescharacteristic
89C5⋊D5—22no—
90C5⋊D5—44no—
91C22×D5—1024no—
92C22×D5—1012no—
93C5×Q8C22×D5112yes—
94C5×D4—212no—
95C5×D4C22×D5112yes—
96C2×C4×C5—212no—
97C2×C4×C5C22×D516yes—
98C22⋊D5—512no—
99C22⋊D5—1024no—
100D20—56no—
101D20—524no—
102D20—1024no—
103D20—1012no—
104C4×D5—512no—
105C4×D5—1024no—
106Dic10—56no—
107C5×C8C22×D516yes—
108C5×C8C22×D516yes—
109#168—512no—
110H(5,𝔽2)—252no—
111AGL(1,ℤ/8)—252no—
112AGL(1,ℤ/8)—254no—
113#135—252no—
114#135C5⋊D511yescharacteristic, complemented
115C2×D8—252no—
116C2×D8—251no—
117#131—251no—
118C52#57611yescharacteristic, complemented, Sylow
119C22×C5—212no—
120C22×C5D4×D516yes—
121C2×D5—512no—
122C2×D5—1024no—
123C2×D5—4024no—
124C2×D5—4012no—
125C4×C5—212no—
126C4×C5D4×D516yes—
127C4×C5C23×D516yes—
128Dic5—512no—
129#41—251no—
130#41—254no—
131#41—502no—
132#41C2×C5⋊D512yescomplemented
133C2×D4—254no—
134C2×D4—252no—
135C2×D4—502no—
136C2×D4—504no—
137Q16C2×C5⋊D511yescharacteristic, complemented
138SD16—254no—
139SD16C2×C5⋊D512yescomplemented
140D8—254no—
141D8—252no—
142D8—252no—
143D8C2×C5⋊D511yescharacteristic, complemented
144M16—251no—
145M16—252no—
146C2×C8—252no—
147C2×C8C2×C5⋊D511yescharacteristic, complemented
148C2×C5—26no—
149C2×C5—412no—
150C2×C5C2×D4×D516yes—
151D5—1012no—
152D5—2024no—
153C23—504no—
154C23—502no—
155Q8—251no—
156Q8C22×C5⋊D512yes—
157D4—22no—
158D4—252no—
159D4—251no—
160D4—254no—
161D4—504no—
162D4—504no—
163D4—502no—
164D4C22×C5⋊D512yes—
165C2×C4—22no—
166C2×C4—252no—
167C2×C4—504no—
168C2×C4C22×C5⋊D511yescharacteristic
169C8—252no—
170C8C22×C5⋊D511yescharacteristic
171C8C22×C5⋊D511yescharacteristic
172C5#6610316yescomplemented
173C22—22no—
174C22—252no—
175C22—504no—
176C22—2002no—
177C22—2004no—
178C22D4×C5⋊D511yescharacteristic
179C4—22no—
180C4—252no—
181C4D4×C5⋊D511yescharacteristic
182C4C23×C5⋊D511yescharacteristic
183C2—21no—
184C2—42no—
185C2—502no—
186C2—1004no—
187C2C2×D4×C5⋊D511yescharacteristic
subgroupG/H
centerC2C2×D4×C5⋊D5
commutator, cosocleC4×C52C24
FrattiniC4C23×C5⋊D5
FittingC52×#135C2
socleC2×C52C22×D4
hypercenter#135C5⋊D5
hypocenterC52#576
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #11717522C2semidirect
2. C52×#135C2semidirect
3. #11717269C2semidirect
4. #11717239C2semidirect
5. #11717234C2semidirect
6. D8×C5⋊D5C2semidirect
7. C2×#87801C2semidirect
8. #11717221C2semidirect
9. C52×#41C22semidirect
10. #87904C22semidirect
12. D4×C5⋊D5C22semidirect
16. C2×C4⋊(C5⋊D5)C22semidirect
17. C52×Q16C22semidirect
18. C52×SD16C22semidirect
19. C52×D8C22semidirect
20. C2×C52×C8C22semidirect
21. #87811C22semidirect
22. #87809C22semidirect
23. #87804C22semidirect
24. #87801C22semidirect
25. #87801C22semidirect
26. #87799C22semidirect
27. C8×C5⋊D5C22semidirect
49. C5×#135D5semidirect
66. C5×#41C2×D5semidirect
74. C5×Q16C2×D5semidirect
75. C5×SD16C2×D5semidirect
76. C5×D8C2×D5semidirect
77. C2×C5×C8C2×D5semidirect
114. #135C5⋊D5semidirect
118. C52#576semidirect
132. #41C2×C5⋊D5semidirect
137. Q16C2×C5⋊D5semidirect
139. SD16C2×C5⋊D5semidirect
143. D8C2×C5⋊D5semidirect
147. C2×C8C2×C5⋊D5semidirect
172. C5#66103semidirect

Maximal subgroups

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

subgroupindex
#117175222
C52×#1352
#117172692
#117172392
#117172342
D8×C5⋊D52
C2×#878012
#117172212
#661035