Finite Group Databasebeta

← D5×#3969 #13101843

Subgroups — D5×#3969 #13101843

Order 1600.

384 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C5×D5×#41C211yesmaximal, characteristic
2C4×D5×Dic5C211yesmaximal, characteristic, complemented
3D5×#681C211yesmaximal, characteristic, complemented
4#11716704C211yesmaximal, characteristic, complemented
5C5×#3969C211yesmaximal, characteristic, complemented
6#11716610C211yesmaximal, characteristic, complemented
7#11716609C211yesmaximal, characteristic, complemented
8C52×#41C2211yescharacteristic
9C5×#713C411yescharacteristic, complemented
10C5×Q8×D5C411yescharacteristic, complemented
11C5×#711—21no—
12C5×#711C411yescharacteristic, complemented
13C5×D4×D5—21no—
14C5×D4×D5C411yescharacteristic, complemented
15C5×#709—21no—
16C5×#709C2211yescharacteristic
17C2×C4×C5×D5—21no—
18C2×C4×C5×D5C2211yescharacteristic
19C2×D5×Dic5—21no—
20C4×#1039C2211yescharacteristic, complemented
21#87804C2211yescharacteristic, complemented
22C4×C5×Dic5C2211yescharacteristic, complemented
23C5×#681C2211yescharacteristic, complemented
24Dic52—21no—
25#87768—21no—
26D5×#168—21no—
27C2×#3969—51nomaximal
28D5×#104—51nomaximal
29C22×C5×D5—21no—
30C22×C5×D5D411yescharacteristic
31C52×Q8C2×C411yescharacteristic, complemented
32C52×D4—21no—
33C52×D4C2×C411yescharacteristic, complemented
34C2×C4×C52—21no—
35C2×C4×C52C2311yescharacteristic
36C2×#1039—21no—
37C5×C22⋊D5—21no—
38C5×C22⋊D5—21no—
39C5×C22⋊D5—21no—
40C2×C5×Dic5—21no—
41C2×C5×Dic5—21no—
42C2×C5×Dic5D411yescharacteristic
43C5×D20—21no—
44C5×D20C2×C411yescharacteristic, complemented
45C4×C5×D5—21no—
46C4×C5×D5—21no—
47C4×C5×D5—21no—
48C4×C5×D5C2×C411yescharacteristic
49C4×C5×D5C2×C411yescharacteristic
50C4×C5×D5D411yescharacteristic
51C4×C5×D5D411yescharacteristic
52C5×Dic10—21no—
53C5×Dic10C2×C411yescharacteristic, complemented
54D5×Dic5—24no—
55#6029—21no—
56C5×#168—21no—
57C2×C5×#41—51no—
58D5×#41D511yescharacteristic
59C2×C4×Dic5—51no—
60C2×#681—51no—
61D5×M16—51no—
62C42×D5—51no—
63C5×#104—51no—
64#3969—51no—
65#3969—51no—
66#3969—51no—
67#3969—51no—
68#3969—102no—
69#3969D511yescharacteristic, direct product factor
70#3957—51no—
71#3937—51no—
72C22×C52—21no—
73C22×C52C2×D411yescharacteristic
74C2×C5×D5—22no—
75C2×C5×D5—21no—
76C2×C5×D5—42no—
77C2×C5×D5C22⋊C411yescharacteristic
78C2×C5×D5C22⋊C411yescharacteristic
79C4×C52—21no—
80C4×C52C22×C411yescharacteristic
81C4×C52C2×D411yescharacteristic
82#1039—22no—
83C5×Dic5—22no—
84C5×Dic5—21no—
85C5×Dic5C22⋊C411yescharacteristic
86C5×Dic5C22⋊C411yescharacteristic
87C5×#41—22no—
88C5×#41—51no—
89C5×#41—51no—
90C5×#41—51no—
91C5×#41—101no—
92C5×#41—101no—
93C5×#41C2×D511yescharacteristic
94C5×#41C2×D511yescharacteristic
95C2×C5×Q8—51no—
96C2×C5×D4—51no—
97C2×C5×D4—101no—
98C22×C4×C5—51no—
99C22×C4×C5—101no—
100C22×Dic5—101no—
101#713Dic511yescharacteristic, complemented
102Q8×D5Dic511yescharacteristic, complemented
103#711—21no—
104#711Dic511yescharacteristic, complemented
105D4×D5—21no—
106D4×D5Dic511yescharacteristic, complemented
107#709—21no—
108#709C2×D511yescharacteristic
109C2×C4×D5—21no—
110C2×C4×D5—101no—
111C2×C4×D5C2×D511yescharacteristic
112C5×M16—51no—
113C42×C5—51no—
114C4×Dic5—51no—
115C4×Dic5—51no—
116C4×Dic5—102no—
117C4×Dic5—101no—
118C4×Dic5—101no—
119C4×Dic5C2×D511yescharacteristic, complemented
120#681—51no—
121#681—51no—
122#681—102no—
123#681—101no—
124#681C2×D511yescharacteristic, complemented
125C2×#168—101no—
126#676—101no—
127C8×D5—101no—
128C2×#104—251noSylow
129C2×C52—21no—
130C2×C52—41no—
131C2×C52C2×C22⋊C411yescharacteristic
132C5×D5—21no—
133C5×D5—41no—
134C5×D5#10412yescomplemented
135C23×C5—51no—
136C23×C5—101no—
137C22×D5—21no—
138C22×D5C22⋊D511yescharacteristic
139C5×Q8—22no—
140C5×Q8—51no—
141C5×Q8—101no—
142C5×Q8C4×D511yescharacteristic, complemented
143C5×Q8C2×Dic511yescharacteristic, complemented
144C5×D4—21no—
145C5×D4—21no—
146C5×D4—22no—
147C5×D4—42no—
148C5×D4—51no—
149C5×D4—101no—
150C5×D4—101no—
151C5×D4—101no—
152C5×D4—101no—
153C5×D4C4×D511yescharacteristic, complemented
154C5×D4C2×Dic511yescharacteristic, complemented
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—22no—
158C2×C4×C5—42no—
159C2×C4×C5—51no—
160C2×C4×C5—51no—
161C2×C4×C5—51no—
162C2×C4×C5—51no—
163C2×C4×C5—51no—
164C2×C4×C5—101no—
165C2×C4×C5—101no—
166C2×C4×C5—101no—
167C2×C4×C5—101no—
168C2×C4×C5—101no—
169C2×C4×C5C22×D511yescharacteristic
170C2×C4×C5C22×D511yescharacteristic
171C22⋊D5—21no—
172C22⋊D5—21no—
173C22⋊D5—21no—
174C2×Dic5—21no—
175C2×Dic5—21no—
176C2×Dic5—104no—
177C2×Dic5—101no—
178C2×Dic5—101no—
179C2×Dic5—202no—
180C2×Dic5C22⋊D511yescharacteristic
181D20—21no—
182D20C2×Dic511yescharacteristic, complemented
183C4×D5—21no—
184C4×D5—21no—
185C4×D5—21no—
186C4×D5—104no—
187C4×D5C2×Dic511yescharacteristic
188C4×D5C2×Dic511yescharacteristic
189C4×D5C22⋊D511yescharacteristic
190C4×D5C22⋊D511yescharacteristic
191Dic10—21no—
192Dic10C2×Dic511yescharacteristic, complemented
193C5×C8—101no—
194#168—21no—
195#168—101no—
196#168—101no—
197#168—202no—
198C2×#41—51no—
199C2×M16—251no—
200C2×C42—251no—
201#104—51no—
202#104—251no—
203#104—251no—
204#104—251no—
205C52C2×#10411yescharacteristic, complemented, Sylow
206C22×C5—21no—
207C22×C5—21no—
208C22×C5—22no—
209C22×C5—42no—
210C22×C5—51no—
211C22×C5—51no—
212C22×C5—102no—
213C22×C5—101no—
214C22×C5—202no—
215C22×C5D4×D511yescharacteristic
216C22×C5C2×C22⋊D511yescharacteristic
217C2×D5—22no—
218C2×D5—21no—
219C2×D5—42no—
220C2×D5C22⋊Dic511yescharacteristic
221C2×D5C22⋊Dic511yescharacteristic
222C4×C5—21no—
223C4×C5—21no—
224C4×C5—22no—
225C4×C5—22no—
226C4×C5—42no—
227C4×C5—51no—
228C4×C5—51no—
229C4×C5—102no—
230C4×C5—101no—
231C4×C5C2×C4×D511yescharacteristic
232C4×C5D4×D511yescharacteristic
233C4×C5C22×Dic511yescharacteristic
234C4×C5C2×C22⋊D511yescharacteristic
235Dic5—22no—
236Dic5—21no—
237Dic5—102no—
238Dic5—102no—
239Dic5—204no—
240Dic5C22⋊Dic511yescharacteristic
241Dic5C22⋊Dic511yescharacteristic
242#41—51no—
243#41—51no—
244#41—51no—
245#41—101no—
246#41—101no—
247#41D5211yescharacteristic
248C2×Q8—51no—
249C2×D4—51no—
250C2×D4—101no—
251C22×C4—51no—
252C22×C4—101no—
253C22×C4—501no—
254M16—51no—
255M16—251no—
256M16—501no—
257C2×C8—501no—
258C42—51no—
259C42—251no—
260C42—501no—
261C2×C5—21no—
262C2×C5—21no—
263C2×C5—22no—
264C2×C5—42no—
265C2×C5—41no—
266C2×C5—41no—
267C2×C5—52no—
268C2×C5—82no—
269C2×C5—101no—
270C2×C5—201no—
271C2×C5D5×C22⋊C411yescharacteristic
272C2×C5C2×C22⋊Dic511yescharacteristic
273D5—21no—
274D5—41no—
275D5#396912yesdirect product factor
276C23—51no—
277C23—101no—
278Q8—51no—
279Q8—101no—
280Q8D5×Dic511yescharacteristic, complemented
281D4—21no—
282D4—51no—
283D4—101no—
284D4—101no—
285D4—101no—
286D4—101no—
287D4D5×Dic511yescharacteristic, complemented
288C2×C4—21no—
289C2×C4—51no—
290C2×C4—51no—
291C2×C4—51no—
292C2×C4—51no—
293C2×C4—51no—
294C2×C4—101no—
295C2×C4—101no—
296C2×C4—101no—
297C2×C4—101no—
298C2×C4—101no—
299C2×C4—504no—
300C2×C4—501no—
301C2×C4C2×D5211yescharacteristic
302C8—101no—
303C8—501no—
304C5—22no—
305C5D5×#10411yescharacteristic, complemented
306C5C2×#396911yescharacteristic, complemented
307C22—21no—
308C22—51no—
309C22—51no—
310C22—102no—
311C22—101no—
312C22—202no—
313C22D5×C22⋊D511yescharacteristic
314C4—21no—
315C4—51no—
316C4—51no—
317C4—102no—
318C4—101no—
319C4—502no—
320C4C2×D5×Dic511yescharacteristic
321C4D5×C22⋊D511yescharacteristic
322C2—21no—
323C2—41no—
324C2—52no—
325C2—101no—
326C2—201no—
327C2D5×C22⋊Dic511yescharacteristic
subgroupG/H
centerC4D5×C22⋊D5
commutatorC4×C52C22×C4
FrattiniC2×C4C2×D52
FittingC52×#41C22
socleC2×C52C2×C22⋊C4
prime radicalC5×D5×#41C2
cosocleC2×C4×C52C23
hypercenter#41D52
hypocenterC52C2×#104
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
2. C4×D5×Dic5C2semidirect
3. D5×#681C2semidirect
4. #11716704C2semidirect
5. C5×#3969C2semidirect
6. #11716610C2semidirect
7. #11716609C2semidirect
9. C5×#713C4semidirect
10. C5×Q8×D5C4semidirect
12. C5×#711C4semidirect
14. C5×D4×D5C4semidirect
20. C4×#1039C22semidirect
21. #87804C22semidirect
22. C4×C5×Dic5C22semidirect
23. C5×#681C22semidirect
31. C52×Q8C2×C4semidirect
33. C52×D4C2×C4semidirect
44. C5×D20C2×C4semidirect
53. C5×Dic10C2×C4semidirect
69. #3969D5direct (N × H)
101. #713Dic5semidirect
102. Q8×D5Dic5semidirect
104. #711Dic5semidirect
106. D4×D5Dic5semidirect
119. C4×Dic5C2×D5semidirect
124. #681C2×D5semidirect
134. C5×D5#104semidirect
142. C5×Q8C4×D5semidirect
143. C5×Q8C2×Dic5semidirect
153. C5×D4C4×D5semidirect
154. C5×D4C2×Dic5semidirect
182. D20C2×Dic5semidirect
192. Dic10C2×Dic5semidirect
205. C52C2×#104semidirect
275. D5#3969direct (N × H)
280. Q8D5×Dic5semidirect
287. D4D5×Dic5semidirect
305. C5D5×#104semidirect
306. C5C2×#3969semidirect

Maximal subgroups

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

subgroupindex
C5×D5×#412
C4×D5×Dic52
D5×#6812
#117167042
C5×#39692
#117166102
#117166092
C2×#39695
D5×#1045