Finite Group Databasebeta

← C2×#11717041 #13106162

Subgroups — C2×#11717041 #13106162

Order 1600.

1560 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 1560 conjugacy classes of subgroups — too many to draw. Only its 200 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
1C23×D52C211yesmaximal, characteristic, complemented
2C22×C4⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C22×#6038C212yesmaximal, complemented
4C2×C5×#685C212yesmaximal, complemented
5C2×#87779C211yesmaximal, characteristic, complemented
6#11717041C218yesmaximal, direct product factor
7C23×C5⋊D5C2211yescharacteristic
8C23×C5⋊D5C2211yescharacteristic, complemented
9C23×C5×D5C2212yes—
10C22×D52—24no—
11C22×D52—28no—
12C22×D52C2214yescomplemented
13C22×C4×C52C2211yescharacteristic, complemented
14C2×C4⋊(C5⋊D5)—24no—
15C2×C4⋊(C5⋊D5)C2214yescomplemented
16C22×C5×Dic5C2212yescomplemented
17C2×#6038—28no—
18C2×#6038C2218yescomplemented
19C5×#685C2218yescomplemented
20#87779C2214yescomplemented
21C2×#4028—52nomaximal
22C23×C52C2311yescharacteristic
23C22×C5⋊D5—24no—
24C22×C5⋊D5—22no—
25C22×C5⋊D5—24no—
26C22×C5⋊D5D414yescomplemented
27C22×C5⋊D5C2312yes—
28C22×C5⋊D5C2312yescomplemented
29C22×C5×D5—24no—
30C22×C5×D5—24no—
31C22×C5×D5D418yescomplemented
32C22×C5×D5C2314yes—
33C2×D52—232no—
34C2×D52—28no—
35C2×D52—216no—
36C2×C4×C52—22no—
37C2×C4×C52C2312yescomplemented
38C4⋊(C5⋊D5)—28no—
39C2×C5×Dic5—24no—
40C2×C5×Dic5C2314yescomplemented
41#6038—216no—
42C24×D5—52no—
43C22×C22⋊D5—52no—
44C22×D20—52no—
45C22×D20—52no—
46C22×D20—102no—
47C2×C5×C22⋊C4—52no—
48C2×#685—52no—
49C2×#685D512yescomplemented
50#4028—516no—
51C22×C52C2×D414yes—
52C22×C52C2×D412yes—
53C22×C52C2411yescharacteristic
54C2×C5⋊D5—28no—
55C2×C5⋊D5—24no—
56C2×C5⋊D5—22no—
57C2×C5⋊D5—24no—
58C2×C5⋊D5—44no—
59C2×C5⋊D5C2×D414yescomplemented
60C2×C5×D5—216no—
61C2×C5×D5—24no—
62C2×C5×D5—24no—
63C2×C5×D5C2×D418yescomplemented
64D52—232no—
65C4×C52—22no—
66C5×Dic5—24no—
67C24×C5—52no—
68C23×D5—52no—
69C23×D5—52no—
70C23×D5—58no—
71C23×D5—102no—
72C23×D5—102no—
73C23×D5—108no—
74C23×D5—108no—
75C23×D5—108no—
76C23×D5C2×D512yes—
77C22×C4×C5—22no—
78C22×C4×C5—52no—
79C22×C4×C5C2×D512yescomplemented
80C2×C22⋊D5—58no—
81C2×C22⋊D5—108no—
82C22×Dic5C2×D512yescomplemented
83C2×D20—58no—
84C2×D20—58no—
85C2×D20—108no—
86C2×D20—108no—
87C2×D20—1016no—
88C2×D20—108no—
89C5×C22⋊C4—58no—
90#685—58no—
91#685C2×D518yescomplemented
92C2×#120—251noSylow
93C2×C52#12014yescomplemented
94C2×C52C22×D412yes—
95C2×C52C22×D411yescharacteristic
96C5⋊D5—24no—
97C5⋊D5—42no—
98C5×D5—28no—
99C23×C5—22no—
100C23×C5—58no—
101C23×C5—54no—
102C23×C5—104no—
103C23×C5—104no—
104C23×C5C22×D512yes—
105C22×D5—24no—
106C22×D5—24no—
107C22×D5—58no—
108C22×D5—54no—
109C22×D5—54no—
110C22×D5—108no—
111C22×D5—104no—
112C22×D5—104no—
113C22×D5—1016no—
114C22×D5—1016no—
115C22×D5—1064no—
116C22×D5—104no—
117C22×D5—104no—
118C22×D5—1016no—
119C22×D5—108no—
120C22×D5—104no—
121C22×D5—104no—
122C22×D5—104no—
123C22×D5—208no—
124C22×D5—208no—
125C22×D5D2018yescomplemented
126C22×D5C22×D514yes—
127C2×C4×C5—28no—
128C2×C4×C5—24no—
129C2×C4×C5—24no—
130C2×C4×C5—54no—
131C2×C4×C5—104no—
132C2×C4×C5C22×D514yescomplemented
133C22⋊D5—1016no—
134C2×Dic5—24no—
135C2×Dic5C22×D514yescomplemented
136D20—1016no—
137D20—1032no—
138D20—1016no—
139C25—251no—
140C22×D4—252no—
141C22×D4—251no—
142#120—258no—
143C2×C22⋊C4—52no—
144C2×C22⋊C4—251no—
145C52C2×#12011yescharacteristic, complemented, Sylow
146C22×C5—28no—
147C22×C5—24no—
148C22×C5—22no—
149C22×C5—58no—
150C22×C5—104no—
151C22×C5—104no—
152C22×C5—1016no—
153C22×C5C2×D2014yes—
154C22×C5D4×D514yes—
155C22×C5D4×D514yes—
156C22×C5C23×D512yes—
157C2×D5—24no—
158C2×D5—24no—
159C2×D5—216no—
160C2×D5—58no—
161C2×D5—108no—
162C2×D5—1064no—
163C2×D5—104no—
164C2×D5—104no—
165C2×D5—1016no—
166C2×D5—108no—
167C2×D5—104no—
168C2×D5—104no—
169C2×D5—104no—
170C2×D5—208no—
171C2×D5—2016no—
172C2×D5—208no—
173C2×D5—2016no—
174C2×D5—208no—
175C2×D5C2×D2018yescomplemented
176C4×C5—28no—
177C4×C5—24no—
178C4×C5—104no—
179Dic5—24no—
180C24—52no—
181C24—254no—
182C24—251no—
183C24—251no—
184C24—508no—
185C24—504no—
186C2×D4—258no—
187C2×D4—254no—
188C2×D4—504no—
189C2×D4—508no—
190C22×C4—52no—
191C22×C4D5211yescharacteristic, complemented
192C22⋊C4—58no—
193C22⋊C4—254no—
194C2×C5—24no—
195C2×C5—22no—
196C2×C5—28no—
197C2×C5—108no—
198C2×C5#402818yescomplemented
199C2×C5C22×D2012yes—
200C2×C5C2×D4×D512yes—
201C2×C5C2×D4×D512yes—
202D5—28no—
203D5—108no—
204D5—208no—
205D5—208no—
206D5—204no—
207C23—58no—
208C23—54no—
209C23—104no—
210C23—104no—
211C23—254no—
212C23—252no—
213C23—252no—
214C23—5016no—
215C23—508no—
216C23—5032no—
217C23—504no—
218C23—504no—
219C23—502no—
220C23C2×D5211yescharacteristic
221D4—508no—
222D4—5016no—
223C2×C4—22no—
224C2×C4—54no—
225C2×C4—104no—
226C2×C4C2×D5212yescomplemented
227C5—22no—
228C5C2×#402812yescomplemented
229C22—58no—
230C22—104no—
231C22—104no—
232C22—1016no—
233C22—254no—
234C22—5032no—
235C22—504no—
236C22—508no—
237C22—504no—
238C22—502no—
239C22—1004no—
240C22D5×D2014yes—
241C22#8788612yes—
242C22C22×D5211yescharacteristic
243C4—22no—
244C4—104no—
245C2—108no—
246C2—504no—
247C2—1002no—
248C2#1171704114yesdirect product factor
249C2C2×D5×D2012yes—
250C2C2×#8788611yescharacteristic
subgroupG/H
centerC23C2×D52
commutator, cosocleC22×C52C24
FrattiniC22C22×D52
FittingC22×C4×C52C22
socleC23×C52C23
hypercenterC22×C4D52
hypocenterC52C2×#120
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C23×D52C2semidirect
2. C22×C4⋊(C5⋊D5)C2semidirect
3. C22×#6038C2semidirect
4. C2×C5×#685C2semidirect
5. C2×#87779C2semidirect
6. #11717041C2direct (N × H)
8. C23×C5⋊D5C22semidirect
12. C22×D52C22semidirect
13. C22×C4×C52C22semidirect
15. C2×C4⋊(C5⋊D5)C22semidirect
16. C22×C5×Dic5C22semidirect
18. C2×#6038C22semidirect
19. C5×#685C22semidirect
20. #87779C22semidirect
26. C22×C5⋊D5D4semidirect
28. C22×C5⋊D5C23semidirect
31. C22×C5×D5D4semidirect
37. C2×C4×C52C23semidirect
40. C2×C5×Dic5C23semidirect
49. C2×#685D5semidirect
59. C2×C5⋊D5C2×D4semidirect
63. C2×C5×D5C2×D4semidirect
79. C22×C4×C5C2×D5semidirect
82. C22×Dic5C2×D5semidirect
91. #685C2×D5semidirect
93. C2×C52#120semidirect
125. C22×D5D20semidirect
132. C2×C4×C5C22×D5semidirect
135. C2×Dic5C22×D5semidirect
145. C52C2×#120semidirect
175. C2×D5C2×D20semidirect
191. C22×C4D52semidirect
198. C2×C5#4028semidirect
226. C2×C4C2×D52semidirect
228. C5C2×#4028semidirect
248. C2#11717041direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D522
C22×C4⋊(C5⋊D5)2
C22×#60382
C2×C5×#6852
C2×#877792
#117170412
C2×#40285