Finite Group Databasebeta

← #13106520

Subgroups — #13106520

Order 1600.

800 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 156 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×Q8×C5⋊D5C211yesmaximal, characteristic, complemented
2C2×C4×D52C211yesmaximal, characteristic
3C5×#4092C212yesmaximal, complemented
4#11717039C212yesmaximal
5#11717018C211yesmaximal, characteristic, complemented
6#11717015C214yesmaximal, complemented
7#11717001C212yesmaximal, complemented
8#11716975C212yesmaximal, complemented
9C22×D52C2211yescharacteristic
10C2×C52×Q8C2211yescharacteristic, complemented
11Q8×C5⋊D5—24no—
12C2×C4×C5⋊D5C2212yes—
13C2×C4×C5⋊D5C2211yescharacteristic
14C2×#6045C2211yescharacteristic, complemented
15C2×#6045C2212yescomplemented
16C2×C4×C5×D5C2212yes—
17C2×#6036C2211yescharacteristic
18C2×#6036C2212yes—
19C2×D5×Dic5C2212yes—
20C4×D52—24no—
21C5×#685C2214yes—
22C5×C4⋊Dic5C2212yescomplemented
23C5×#683C2214yescomplemented
24#87781C2212yescomplemented
25#87780C2214yescomplemented
26#87778C2214yes—
27D5×C22⋊Q8—52nomaximal
28C22×C5⋊D5C2311yescharacteristic
29C22×C5×D5C2312yes—
30C2×D52—22no—
31C2×D52—22no—
32C2×D52Q814yescomplemented
33C52×Q8—22no—
34C2×C4×C52C2312yes—
35C2×C4×C52C2311yescharacteristic
36C2×#1039C2312yes—
37C2×#1039C2311yescharacteristic
38C4×C5⋊D5—24no—
39C4×C5⋊D5D414yes—
40#6045—22no—
41#6045—24no—
42C2×C5×Dic5C2312yes—
43C2×C5×Dic5C2314yes—
44C4×C5×D5—24no—
45#6036—22no—
46#6036—24no—
47D5×Dic5—24no—
48C2×Q8×D5—52no—
49C2×Q8×D5—102no—
50C22×C4×D5—52no—
51C5×C22⋊Q8—52no—
52#4092D512yescomplemented
53#4070—52no—
54#4043—52no—
55#4042—54no—
56D5×C4⋊C4—52no—
57D5×C4⋊C4—54no—
58D5×C22⋊C4—54no—
59#4024—54no—
60C22×C52C2411yescharacteristic
61C2×C5⋊D5C2×D412yes—
62C2×C5⋊D5C2×Q812yes—
63C2×C5⋊D5#4112yes—
64C2×C5×D5—22no—
65C2×C5×D5—22no—
66C2×C5×D5C2×Q814yescomplemented
67D52—28no—
68C4×C52—22no—
69C4×C52C2×D412yes—
70#1039—22no—
71#1039C2×D412yes—
72C5×Dic5—22no—
73C5×Dic5—24no—
74C23×D5—52no—
75C2×C5×Q8—22no—
76C2×C5×Q8C2×D512yescomplemented
77C22×C4×C5—52no—
78C22×Dic5—52no—
79Q8×D5—108no—
80Q8×D5—1016no—
81C2×C4×D5—52no—
82C2×C4×D5—52no—
83C2×C4×D5—54no—
84C2×C4×D5—52no—
85C2×C4×D5—54no—
86C2×C4×D5—102no—
87C2×C4×D5—104no—
88C2×C4×D5—108no—
89C2×C4×D5C2×D512yes—
90C2×Dic10—54no—
91C2×Dic10—52no—
92C2×Dic10—102no—
93C2×Dic10—104no—
94C5×C4⋊C4—54no—
95C5×C4⋊C4—52no—
96C5×C22⋊C4—54no—
97C22⋊Dic5—54no—
98#685—54no—
99#685C2×D514yes—
100C4⋊Dic5—54no—
101C4⋊Dic5C2×D512yescomplemented
102#683—54no—
103#683—54no—
104#683C2×D514yescomplemented
105C2×C22⋊Q8—251noSylow
106C2×C52C22×D411yescharacteristic
107C2×C52C22×Q811yescharacteristic
108C2×C52C2×#4111yescharacteristic
109C5⋊D5C22⋊Q814yescomplemented
110C5×D5—24no—
111C23×C5—52no—
112C22×D5—52no—
113C22×D5—58no—
114C22×D5—102no—
115C22×D5—104no—
116C22×D5—104no—
117C22×D5C22×D512yes—
118C5×Q8—28no—
119C5×Q8—24no—
120C2×C4×C5—24no—
121C2×C4×C5—22no—
122C2×C4×C5—52no—
123C2×C4×C5—54no—
124C2×C4×C5—104no—
125C2×C4×C5C22×D514yes—
126C2×C4×C5C22×D512yes—
127C2×Dic5—52no—
128C2×Dic5—54no—
129C2×Dic5—102no—
130C2×Dic5—104no—
131C2×Dic5—104no—
132C2×Dic5C22×D514yes—
133C2×Dic5C22×D512yes—
134C4×D5—24no—
135C4×D5—58no—
136C4×D5—108no—
137C4×D5—108no—
138C4×D5—104no—
139C4×D5—104no—
140C4×D5—108no—
141C4×D5—1016no—
142Dic10—108no—
143Dic10—1016no—
144Dic10—108no—
145Dic10—104no—
146C22×Q8—251no—
147C23×C4—251no—
148C22⋊Q8—52no—
149C22⋊Q8—254no—
150C22⋊Q8—252no—
151C2×C4⋊C4—252no—
152C2×C4⋊C4—251no—
153C2×C22⋊C4—252no—
154C52C2×C22⋊Q811yescharacteristic, complemented, Sylow
155C22×C5—22no—
156C22×C5—54no—
157C22×C5—102no—
158C22×C5—102no—
159C22×C5C23×D512yes—
160C2×D5—22no—
161C2×D5—22no—
162C2×D5—54no—
163C2×D5—54no—
164C2×D5—54no—
165C2×D5—104no—
166C2×D5—104no—
167C2×D5—104no—
168C2×D5—1016no—
169C2×D5Q8×D514yescomplemented
170C4×C5—28no—
171C4×C5—24no—
172C4×C5—24no—
173C4×C5—102no—
174C4×C5—104no—
175C4×C5D4×D514yes—
176Dic5—22no—
177Dic5—24no—
178Dic5—54no—
179Dic5—104no—
180Dic5—108no—
181Dic5—104no—
182C24—251no—
183C2×Q8—252no—
184C2×Q8—251no—
185C2×Q8—504no—
186C2×Q8D5211yescharacteristic, complemented
187C22×C4—52no—
188C22×C4—252no—
189C22×C4—251no—
190C22×C4—252no—
191C22×C4—251no—
192C22×C4—252no—
193C22×C4—504no—
194C4⋊C4—54no—
195C4⋊C4—52no—
196C4⋊C4—252no—
197C4⋊C4—254no—
198C22⋊C4—54no—
199C22⋊C4—254no—
200C2×C5—22no—
201C2×C5—22no—
202C2×C5—22no—
203C2×C5—104no—
204C2×C5C2×D4×D512yes—
205C2×C5C2×Q8×D512yes—
206C2×C5D5×#4112yes—
207D5—24no—
208D5—58no—
209D5—108no—
210C23—52no—
211C23—254no—
212C23—251no—
213C23—502no—
214C23—502no—
215Q8—22no—
216Q8—504no—
217Q8—502no—
218C2×C4—54no—
219C2×C4—52no—
220C2×C4—104no—
221C2×C4—251no—
222C2×C4—254no—
223C2×C4—252no—
224C2×C4—504no—
225C2×C4—502no—
226C2×C4—504no—
227C2×C4—504no—
228C2×C4C2×D5212yes—
229C2×C4C2×D5211yescharacteristic
230C5—22no—
231C5D5×C22⋊Q812yescomplemented
232C22—54no—
233C22—102no—
234C22—102no—
235C22—252no—
236C22—252no—
237C22—252no—
238C22—508no—
239C22C22×D5211yescharacteristic
240C4—22no—
241C4—104no—
242C4—102no—
243C4—252no—
244C4—502no—
245C4#8788612yes—
246C2—104no—
247C2—254no—
248C2Q8×D5211yescharacteristic
249C2#1171748411yescharacteristic
250C2C2×#8788611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC2×C52×Q8C22
prime radicalC22×D52C22
hypercenterC2×Q8D52
hypocenterC52C2×C22⋊Q8
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C5⋊D5C2semidirect
3. C5×#4092C2semidirect
5. #11717018C2semidirect
6. #11717015C2semidirect
7. #11717001C2semidirect
8. #11716975C2semidirect
10. C2×C52×Q8C22semidirect
14. C2×#6045C22semidirect
15. C2×#6045C22semidirect
22. C5×C4⋊Dic5C22semidirect
23. C5×#683C22semidirect
24. #87781C22semidirect
25. #87780C22semidirect
32. C2×D52Q8semidirect
52. #4092D5semidirect
66. C2×C5×D5C2×Q8semidirect
76. C2×C5×Q8C2×D5semidirect
101. C4⋊Dic5C2×D5semidirect
104. #683C2×D5semidirect
109. C5⋊D5C22⋊Q8semidirect
154. C52C2×C22⋊Q8semidirect
169. C2×D5Q8×D5semidirect
186. C2×Q8D52semidirect
231. C5D5×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C5⋊D52
C2×C4×D522
C5×#40922
#117170392
#117170182
#117170152
#117170012
#117169752
D5×C22⋊Q85