Finite Group Databasebeta

← #13107303

Subgroups — #13107303

Order 1600.

1032 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1032 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#11717523C211yesmaximal, characteristic, complemented
2#11717517C211yesmaximal, characteristic, complemented
3C52×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4#11717270C211yesmaximal, characteristic, complemented
5C2×#87810C211yesmaximal, characteristic, complemented
6#11717235C212yesmaximal, complemented
7SD16×C5⋊D5C212yesmaximal, complemented
8#11717232C212yesmaximal, complemented
9#11717231C212yesmaximal, complemented
10#11717229C211yesmaximal, characteristic, complemented
11#11717227C211yesmaximal, characteristic, complemented
12C52×#41C2211yescharacteristic, complemented
13C2×C52×D4C2211yescharacteristic
14C2×C22⋊(C5⋊D5)—22no—
15Q8×C5⋊D5C2212yescomplemented
16#87902—22no—
17#87902—21no—
18#87902C2212yes—
19#87902C2212yescomplemented
20D4×C5⋊D5—21no—
21D4×C5⋊D5C2212yes—
22#87900—21no—
23#87900C2211yescharacteristic
24#87900C2211yescharacteristic
25C2×#6045—21no—
26C2×#6045C2211yescharacteristic, complemented
27C52×SD16C2212yescomplemented
28C52×D8C2212yescomplemented
29C52×M16C2211yescharacteristic, complemented
30#87812C2211yescharacteristic, complemented
31#87811C2211yescharacteristic, complemented
32#87810C2212yescomplemented
33#87810C2211yescharacteristic, complemented
34#87810C2212yescomplemented
35#87809C2211yescharacteristic, complemented
36C2×#6029C2211yescharacteristic, complemented
37#87802C2212yescomplemented
38#87800C2212yescomplemented
39#87799C2212yescomplemented
40C8×C5⋊D5C2212yescomplemented
41#66109—56nomaximal
42C23×C52—21no—
43C22×C5⋊D5—22no—
44C52×Q8C2311yescharacteristic
45C52×D4—21no—
46C52×D4—21no—
47C52×D4C2311yescharacteristic
48C52×D4C2312yes—
49C2×C4×C52—21no—
50C2×C4×C52C2311yescharacteristic
51C22⋊(C5⋊D5)—21no—
52C22⋊(C5⋊D5)—22no—
53C22⋊(C5⋊D5)—22no—
54C22⋊(C5⋊D5)—22no—
55C22⋊(C5⋊D5)D412yes—
56C2×#1039—21no—
57C2×#1039—22no—
58C2×#1039—22no—
59C4⋊(C5⋊D5)D411yescharacteristic
60C4⋊(C5⋊D5)C2311yescharacteristic
61C4×C5⋊D5—22no—
62C4×C5⋊D5—21no—
63C4×C5⋊D5C2312yes—
64#6045—21no—
65#6045—22no—
66#6045D411yescharacteristic
67#6045C2312yes—
68#6045C2311yescharacteristic
69C52×C8C2312yes—
70#6029C2311yescharacteristic
71#6029C2311yescharacteristic
72#4150—56no—
73#4144—56no—
74C5×AGL(1,ℤ/8)D516yescomplemented
75#4096—56no—
76C2×#687—56no—
77#4061—512no—
78D5×SD16—512no—
79#4058—512no—
80#4057—512no—
81#4055—56no—
82#4053—56no—
83C22×C52—21no—
84C22×C52—22no—
85C22×C52—81no—
86C22×C52C2×D411yescharacteristic
87C2×C5⋊D5—21no—
88C2×C5⋊D5—82no—
89C2×C5⋊D5C2×D412yes—
90C4×C52—21no—
91C4×C52C2×D411yescharacteristic
92C4×C52C2411yescharacteristic
93#1039—22no—
94#1039—21no—
95#1039C2×D412yes—
96C5×#41C2×D516yescomplemented
97C2×C5×D4C2×D516yes—
98C2×C22⋊D5—1012no—
99Q8×D5—512no—
100#711—512no—
101#711—512no—
102#711—106no—
103#711—1012no—
104D4×D5—512no—
105D4×D5—106no—
106#709—56no—
107#709—56no—
108#709—106no—
109C2×Dic10—56no—
110C2×Dic10—106no—
111C5×SD16C2×D5112yescomplemented
112C5×D8C2×D5112yescomplemented
113C5×M16C2×D516yescomplemented
114#689—56no—
115#688—56no—
116#687—56no—
117#687—512no—
118#687—512no—
119#686—56no—
120C2×#168—56no—
121Dic20—512no—
122#677—512no—
123#676—512no—
124C8×D5—512no—
125#577—251noSylow
126C2×C52—21no—
127C2×C52—42no—
128C2×C52—41no—
129C2×C52C22×D411yescharacteristic
130C5⋊D5—22no—
131C5⋊D5—41no—
132C23×C5—26no—
133C22×D5—1012no—
134C5×Q8C22×D516yes—
135C5×D4—26no—
136C5×D4—26no—
137C5×D4C22×D516yes—
138C5×D4C22×D5112yes—
139C2×C4×C5—26no—
140C2×C4×C5C22×D516yes—
141C22⋊D5—512no—
142C22⋊D5—1012no—
143C22⋊D5—1012no—
144C22⋊D5—1012no—
145C22⋊D5—106no—
146C2×Dic5—1012no—
147C2×Dic5—1012no—
148C2×Dic5—106no—
149D20—56no—
150D20—56no—
151C4×D5—512no—
152C4×D5—1012no—
153C4×D5—106no—
154Dic10—56no—
155Dic10—512no—
156Dic10—56no—
157Dic10—1012no—
158Dic10—106no—
159C5×C8C22×D5112yes—
160#168—56no—
161#168—56no—
1622−1+4—251no—
163H(5,𝔽2)—251no—
164#137—252no—
165#137—251no—
166AGL(1,ℤ/8)—252no—
167AGL(1,ℤ/8)C5⋊D511yescharacteristic, complemented
168#135—251no—
169#135—252no—
170C2×SD16—251no—
171C2×SD16—252no—
172#131—251no—
173C52#57711yescharacteristic, complemented, Sylow
174C22×C5—26no—
175C22×C5—212no—
176C22×C5—86no—
177C22×C5D4×D516yes—
178C2×D5—512no—
179C2×D5—106no—
180C2×D5—4012no—
181C4×C5—26no—
182C4×C5D4×D516yes—
183C4×C5C23×D516yes—
184Dic5—512no—
185Dic5—1012no—
186Dic5—106no—
187#41—251no—
188#41—252no—
189#41—252no—
190#41—251no—
191#41—501no—
192#41—502no—
193#41—501no—
194#41C2×C5⋊D511yescharacteristic, complemented
195C2×Q8—252no—
196C2×Q8—251no—
197C2×Q8—501no—
198C2×D4—252no—
199C2×D4—501no—
200C2×D4—502no—
201C2×D4C2×C5⋊D511yescharacteristic
202Q16—251no—
203Q16—252no—
204SD16—251no—
205SD16—252no—
206SD16—252no—
207SD16—251no—
208SD16—252no—
209SD16C2×C5⋊D512yescomplemented
210D8—251no—
211D8C2×C5⋊D512yescomplemented
212M16—252no—
213M16C2×C5⋊D511yescharacteristic, complemented
214C2×C8—251no—
215C2×C8—252no—
216C2×C5—26no—
217C2×C5—412no—
218C2×C5—46no—
219C2×C5C2×D4×D516yes—
220D5—1012no—
221D5—206no—
222C23—21no—
223C23—502no—
224Q8—251no—
225Q8—252no—
226Q8—251no—
227Q8—502no—
228Q8—501no—
229Q8C22×C5⋊D511yescharacteristic
230D4—21no—
231D4—21no—
232D4—252no—
233D4—251no—
234D4—251no—
235D4—502no—
236D4—502no—
237D4—502no—
238D4—501no—
239D4C22×C5⋊D511yescharacteristic
240D4C22×C5⋊D512yes—
241C2×C4—21no—
242C2×C4—252no—
243C2×C4—502no—
244C2×C4—502no—
245C2×C4—502no—
246C2×C4—501no—
247C2×C4—501no—
248C2×C4C22×C5⋊D511yescharacteristic
249C8—251no—
250C8—251no—
251C8C22×C5⋊D512yes—
252C5#6610916yescomplemented
253C22—21no—
254C22—22no—
255C22—81no—
256C22—252no—
257C22—501no—
258C22—2002no—
259C22D4×C5⋊D511yescharacteristic
260C4—21no—
261C4—252no—
262C4—501no—
263C4—502no—
264C4D4×C5⋊D511yescharacteristic
265C4C23×C5⋊D511yescharacteristic
266C2—21no—
267C2—42no—
268C2—41no—
269C2—502no—
270C2—1001no—
271C2C2×D4×C5⋊D511yescharacteristic
subgroupG/H
centerC2C2×D4×C5⋊D5
commutator, cosocleC4×C52C24
FrattiniC4C23×C5⋊D5
FittingC52×AGL(1,ℤ/8)C2
socleC2×C52C22×D4
hypercenterAGL(1,ℤ/8)C5⋊D5
hypocenterC52#577
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #11717523C2semidirect
2. #11717517C2semidirect
3. C52×AGL(1,ℤ/8)C2semidirect
4. #11717270C2semidirect
5. C2×#87810C2semidirect
6. #11717235C2semidirect
7. SD16×C5⋊D5C2semidirect
8. #11717232C2semidirect
9. #11717231C2semidirect
10. #11717229C2semidirect
11. #11717227C2semidirect
12. C52×#41C22semidirect
15. Q8×C5⋊D5C22semidirect
19. #87902C22semidirect
26. C2×#6045C22semidirect
27. C52×SD16C22semidirect
28. C52×D8C22semidirect
29. C52×M16C22semidirect
30. #87812C22semidirect
31. #87811C22semidirect
32. #87810C22semidirect
33. #87810C22semidirect
34. #87810C22semidirect
35. #87809C22semidirect
36. C2×#6029C22semidirect
37. #87802C22semidirect
38. #87800C22semidirect
39. #87799C22semidirect
40. C8×C5⋊D5C22semidirect
74. C5×AGL(1,ℤ/8)D5semidirect
96. C5×#41C2×D5semidirect
111. C5×SD16C2×D5semidirect
112. C5×D8C2×D5semidirect
113. C5×M16C2×D5semidirect
167. AGL(1,ℤ/8)C5⋊D5semidirect
173. C52#577semidirect
194. #41C2×C5⋊D5semidirect
209. SD16C2×C5⋊D5semidirect
211. D8C2×C5⋊D5semidirect
213. M16C2×C5⋊D5semidirect
252. C5#66109semidirect

Maximal subgroups

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

subgroupindex
#117175232
#117175172
C52×AGL(1,ℤ/8)2
#117172702
C2×#878102
#117172352
SD16×C5⋊D52
#117172322
#117172312
#117172292
#117172272
#661095