Finite Group Databasebeta

← #13106225

Subgroups — #13106225

Order 1600.

904 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 904 conjugacy classes of subgroups — too many to draw. Only its 136 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×D4×C5⋊D5C211yesmaximal, characteristic, complemented
2C2×#87871C211yesmaximal, characteristic, complemented
3C5×#4086C211yesmaximal, characteristic, complemented
4C5×#4082C211yesmaximal, characteristic, complemented
5#11717099C214yesmaximal, complemented
6#11717089C214yesmaximal, complemented
7#11717029C211yesmaximal, characteristic, complemented
8#11716992C211yesmaximal, characteristic, complemented
9#11716982C211yesmaximal, characteristic, complemented
10C23×C5⋊D5C2212yes—
11C2×C52×D4C2211yescharacteristic
12C2×C22⋊(C5⋊D5)C2212yes—
13D4×C5⋊D5—24no—
14C2×C4⋊(C5⋊D5)C2211yescharacteristic
15C2×C4×C5⋊D5C2211yescharacteristic
16C2×C5×C22⋊D5C2214yescomplemented
17C2×C5×D20C2211yescharacteristic, complemented
18C2×C5×Dic10C2211yescharacteristic, complemented
19C2×#6038C2212yes—
20C2×#6038C2214yescomplemented
21C2×D5×Dic5C2212yescomplemented
22#87871—24no—
23C5×C22⋊Dic5C2214yescomplemented
24C4×C5×Dic5C2211yescharacteristic, complemented
25C4×C5×Dic5C2211yescharacteristic, complemented
26#87781C2212yescomplemented
27#87779C2212yes—
28#87779C2214yescomplemented
29#66049—51nomaximal
30#66008—51nomaximal
31C23×C52C2312yes—
32C22×C5⋊D5—24no—
33C22×C5⋊D5—44no—
34C22×C5⋊D5C2312yes—
35C22×C5⋊D5C2311yescharacteristic
36C22×C5×D5C2312yes—
37C52×D4—22no—
38C2×C4×C52C2311yescharacteristic
39C22⋊(C5⋊D5)—24no—
40C2×#1039C2311yescharacteristic
41C4⋊(C5⋊D5)—22no—
42C4×C5⋊D5D414yescomplemented
43C5×C22⋊D5—44no—
44C2×C5×Dic5C2312yes—
45C2×C5×Dic5C2312yes—
46C2×C5×Dic5C2312yes—
47C5×D20—22no—
48C5×Dic10—22no—
49#6038—24no—
50#6038—44no—
51D5×Dic5—24no—
52C2×#713—51no—
53C2×#711—51no—
54C2×D4×D5—51no—
55C2×D4×D5—51no—
56C2×D4×D5—102no—
57C5×#127—51no—
58C5×#124—51no—
59#4093—51no—
60#4086—51no—
61#4086D511yescharacteristic, complemented
62#4085—54no—
63#4083—54no—
64#4082D511yescharacteristic, complemented
65#4030—54no—
66#4028—54no—
67#4021—51no—
68#4020—51no—
69#4018—51no—
70#4018—51no—
71C22×C52—22no—
72C22×C52—24no—
73C22×C52C2411yescharacteristic
74C2×C5⋊D5—22no—
75C2×C5⋊D5—22no—
76C2×C5⋊D5—24no—
77C2×C5⋊D5—48no—
78C2×C5⋊D5C2×D412yes—
79C2×C5×D5—22no—
80C2×C5×D5—24no—
81C4×C52C2×D412yes—
82#1039C2×D412yes—
83C5×Dic5—22no—
84C5×Dic5—22no—
85C5×Dic5—22no—
86C23×D5—52no—
87C23×D5—52no—
88C23×D5—104no—
89C2×C5×Q8—51no—
90C2×C5×D4—22no—
91C2×C5×D4—54no—
92C2×C5×D4—51no—
93C2×C5×D4C2×D511yescharacteristic
94C2×C5×D4C2×D511yescharacteristic
95C2×C22⋊D5—52no—
96C2×C22⋊D5—52no—
97C2×C22⋊D5—52no—
98C2×C22⋊D5—54no—
99C2×C22⋊D5—104no—
100C2×C22⋊D5C2×D514yescomplemented
101C22×Dic5—52no—
102#713—104no—
103#711—104no—
104D4×D5—104no—
105D4×D5—104no—
106D4×D5—1016no—
107C2×D20—52no—
108C2×D20—51no—
109C2×D20—51no—
110C2×D20—54no—
111C2×D20—102no—
112C2×D20C2×D511yescharacteristic, complemented
113C2×C4×D5—51no—
114C2×C4×D5—51no—
115C2×C4×D5—52no—
116C2×C4×D5—102no—
117C2×Dic10C2×D511yescharacteristic, complemented
118C5×C22⋊C4—54no—
119C42×C5—51no—
120C42×C5—51no—
121C22⋊Dic5C2×D514yescomplemented
122#685—52no—
123#685—52no—
124#685—54no—
125#685—54no—
126#683—52no—
127#683—52no—
128C4×Dic5C2×D511yescharacteristic, complemented
129C4×Dic5C2×D511yescharacteristic, complemented
130#535—251noSylow
131C2×C52—42no—
132C2×C52C22×D411yescharacteristic
133C2×C52H(5,𝔽2)12yes—
134C5⋊D5—22no—
135C5⋊D5—42no—
136C5×D5—42no—
137C23×C5—24no—
138C23×C5—52no—
139C23×C5C22×D512yes—
140C23×C5C22×D512yes—
141C22×D5—51no—
142C22×D5—51no—
143C22×D5—52no—
144C22×D5—52no—
145C22×D5—102no—
146C22×D5—104no—
147C22×D5—104no—
148C22×D5—104no—
149C22×D5—1016no—
150C22×D5—204no—
151C22×D5—204no—
152C22×D5—2016no—
153C22×D5C22×D512yes—
154C5×Q8—102no—
155C5×D4—28no—
156C5×D4—22no—
157C5×D4—22no—
158C5×D4—102no—
159C5×D4—204no—
160C2×C4×C5—22no—
161C2×C4×C5—52no—
162C2×C4×C5—52no—
163C2×C4×C5—52no—
164C2×C4×C5C22×D511yescharacteristic
165C2×C4×C5C22×D511yescharacteristic
166C22⋊D5—44no—
167C22⋊D5—104no—
168C22⋊D5—104no—
169C22⋊D5—104no—
170C22⋊D5—1016no—
171C22⋊D5—204no—
172C2×Dic5—51no—
173C2×Dic5—51no—
174C2×Dic5—102no—
175C2×Dic5—104no—
176C2×Dic5C22×D512yes—
177C2×Dic5C22×D512yes—
178C2×Dic5C22×D512yes—
179D20—22no—
180D20—108no—
181D20—104no—
182D20—102no—
183D20—102no—
184D20—204no—
185C4×D5—54no—
186C4×D5—54no—
187C4×D5—108no—
188C4×D5—104no—
189Dic10—22no—
190C2×#41—251no—
191C22×D4—251no—
192#127—51no—
193#127—251no—
194#124—51no—
195#124—251no—
196#121—254no—
197#120—254no—
198#117—251no—
199C52#53511yescharacteristic, complemented, Sylow
200C22×C5—28no—
201C22×C5—22no—
202C22×C5—22no—
203C22×C5—24no—
204C22×C5—24no—
205C22×C5—22no—
206C22×C5—48no—
207C22×C5—102no—
208C22×C5—104no—
209C22×C5C23×D511yescharacteristic
210C22×C5C23×D511yescharacteristic
211C2×D5—22no—
212C2×D5—24no—
213C2×D5—52no—
214C2×D5—52no—
215C2×D5—104no—
216C2×D5—108no—
217C2×D5—102no—
218C2×D5—102no—
219C2×D5—108no—
220C2×D5—102no—
221C2×D5—102no—
222C2×D5—104no—
223C2×D5—104no—
224C2×D5—208no—
225C2×D5—2032no—
226C2×D5—208no—
227C2×D5—208no—
228C4×C5—24no—
229C4×C5—102no—
230C4×C5—102no—
231C4×C5—102no—
232C4×C5D4×D512yes—
233C4×C5D4×D512yes—
234Dic5—22no—
235Dic5—22no—
236Dic5—22no—
237Dic5—52no—
238Dic5—52no—
239Dic5—104no—
240C24—252no—
241#41—504no—
242C2×Q8—51no—
243C2×D4—54no—
244C2×D4—51no—
245C2×D4—252no—
246C2×D4—254no—
247C2×D4—252no—
248C2×D4—251no—
249C2×D4—504no—
250C2×D4D5211yescharacteristic
251C22×C4—252no—
252C22×C4—251no—
253C4⋊C4—252no—
254C22⋊C4—54no—
255C22⋊C4—252no—
256C22⋊C4—254no—
257C42—51no—
258C42—51no—
259C2×C5—24no—
260C2×C5—22no—
261C2×C5—48no—
262C2×C5—42no—
263C2×C5—42no—
264C2×C5—202no—
265C2×C5C2×D4×D511yescharacteristic
266C2×C5C2×D4×D511yescharacteristic
267C2×C5#414412yes—
268C2×C5#414912yes—
269D5—42no—
270D5—108no—
271D5—102no—
272D5—102no—
273D5—208no—
274D5—202no—
275D5—202no—
276C23—52no—
277C23—251no—
278C23—252no—
279C23—504no—
280C23—1004no—
281C23C2×D5212yes—
282Q8—102no—
283D4—22no—
284D4—102no—
285D4—204no—
286D4—504no—
287D4—504no—
288D4—502no—
289D4—1004no—
290C2×C4—52no—
291C2×C4—52no—
292C2×C4—52no—
293C2×C4—251no—
294C2×C4—254no—
295C2×C4—504no—
296C2×C4C2×D5211yescharacteristic
297C5—22no—
298C5#6600811yescharacteristic, complemented
299C5#6604911yescharacteristic, complemented
300C22—24no—
301C22—22no—
302C22—104no—
303C22—102no—
304C22—252no—
305C22—502no—
306C22—504no—
307C22—502no—
308C22—1008no—
309C22C22×D5211yescharacteristic
310C4—102no—
311C4—102no—
312C4—102no—
313C4—252no—
314C4#8788612yes—
315C2—42no—
316C2—202no—
317C2—502no—
318C2—1002no—
319C2#1171747912yes—
320C2C2×#8788611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC2×C52×D4C22
hypercenterC2×D4D52
hypocenterC52#535
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C5⋊D5C2semidirect
2. C2×#87871C2semidirect
3. C5×#4086C2semidirect
4. C5×#4082C2semidirect
5. #11717099C2semidirect
6. #11717089C2semidirect
7. #11717029C2semidirect
8. #11716992C2semidirect
9. #11716982C2semidirect
16. C2×C5×C22⋊D5C22semidirect
17. C2×C5×D20C22semidirect
18. C2×C5×Dic10C22semidirect
20. C2×#6038C22semidirect
21. C2×D5×Dic5C22semidirect
23. C5×C22⋊Dic5C22semidirect
24. C4×C5×Dic5C22semidirect
25. C4×C5×Dic5C22semidirect
26. #87781C22semidirect
28. #87779C22semidirect
42. C4×C5⋊D5D4semidirect
61. #4086D5semidirect
64. #4082D5semidirect
100. C2×C22⋊D5C2×D5semidirect
112. C2×D20C2×D5semidirect
117. C2×Dic10C2×D5semidirect
121. C22⋊Dic5C2×D5semidirect
128. C4×Dic5C2×D5semidirect
129. C4×Dic5C2×D5semidirect
199. C52#535semidirect
298. C5#66008semidirect
299. C5#66049semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C5⋊D52
C2×#878712
C5×#40862
C5×#40822
#117170992
#117170892
#117170292
#117169922
#117169822
#660495
#660085