Finite Group Databasebeta

← C3×D5⋊#104 #11752325

Subgroups — C3×D5⋊#104 #11752325

Order 960.

340 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×D5×#41C211yesmaximal, characteristic
2C2×C3×C4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3C3×D5⋊M16C211yesmaximal, characteristic, complemented
4C3×#4010C212yesmaximal, complemented
5C3×#4008C212yesmaximal, complemented
6D5⋊#104C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×AGL(1,𝔽5)—21no—
8C3×C5×#41C411yescharacteristic, complemented
9C3×#713C2211yescharacteristic
10C3×Q8×D5C411yescharacteristic, complemented
11C3×#711—21no—
12C3×#711C2211yescharacteristic
13C3×D4×D5—21no—
14C3×D4×D5C411yescharacteristic, complemented
15C3×#709—21no—
16C3×#709C411yescharacteristic, complemented
17C2×C3×C4×D5—21no—
18C2×C3×C4×D5C2211yescharacteristic
19C3×#704—21no—
20C3×C4×AGL(1,𝔽5)—21no—
21C3×C4×AGL(1,𝔽5)C2212yescomplemented
22C3×#700C2212yescomplemented
23C3×D5⋊C8—21no—
24C2×C3×#104—51nomaximal, Hall
25D5×#41C2×C311yescharacteristic
26C2×C4×AGL(1,𝔽5)C2×C311yescharacteristic, complemented
27D5⋊M16C2×C311yescharacteristic, complemented
28#4010C2×C312yescomplemented
29#4008C2×C312yescomplemented
30C22×C3×D5—21no—
31C22×C3×D5D411yescharacteristic
32C2×C3×AGL(1,𝔽5)—24no—
33C2×C3×AGL(1,𝔽5)—22no—
34C3×C5×Q8C2×C411yescharacteristic, complemented
35C3×C5×D4—21no—
36C3×C5×D4C2×C411yescharacteristic, complemented
37C2×C3×C4×C5—21no—
38C2×C3×C4×C5C2×C411yescharacteristic
39C3×C22⋊D5—21no—
40C3×C22⋊D5—21no—
41C3×C22⋊D5—21no—
42C2×C3×Dic5—21no—
43C2×C3×Dic5D411yescharacteristic
44C3×D20—21no—
45C3×D20C2×C411yescharacteristic, complemented
46C3×C4×D5—21no—
47C3×C4×D5—21no—
48C3×C4×D5—21no—
49C3×C4×D5C2×C411yescharacteristic
50C3×C4×D5D411yescharacteristic
51C3×C4×D5D411yescharacteristic
52C3×C4×D5C2311yescharacteristic
53C3×Dic10—21no—
54C3×Dic10C2×C411yescharacteristic, complemented
55C3×#170—22no—
56C2×C3×#41—51no—
57C2×C3×M16—51no—
58C2×C3×C42—51no—
59C3×#104—52no—
60C3×#104—52no—
61C22×AGL(1,𝔽5)—21no—
62C5×#41C3×C411yescharacteristic, complemented
63#713C22×C311yescharacteristic
64Q8×D5C3×C411yescharacteristic, complemented
65#711—21no—
66#711C22×C311yescharacteristic
67D4×D5—21no—
68D4×D5C3×C411yescharacteristic, complemented
69#709—21no—
70#709C3×C411yescharacteristic, complemented
71C2×C4×D5—21no—
72C2×C4×D5C22×C311yescharacteristic
73#704—21no—
74C4×AGL(1,𝔽5)—21no—
75C4×AGL(1,𝔽5)C22×C312yescomplemented
76#700C22×C312yescomplemented
77D5⋊C8—21no—
78C2×#104—51noSylow
79C22×C3×C5—21no—
80C22×C3×C5C22⋊C411yescharacteristic
81C2×C3×D5—22no—
82C2×C3×D5—21no—
83C2×C3×D5—42no—
84C2×C3×D5C22⋊C411yescharacteristic
85C2×C3×D5C2×D411yescharacteristic
86C3×AGL(1,𝔽5)—24no—
87C3×C4×C5—21no—
88C3×C4×C5C22⋊C411yescharacteristic
89C3×C4×C5C22×C411yescharacteristic
90C3×Dic5—21no—
91C3×Dic5C22⋊C411yescharacteristic
92C3×Dic5C2×D411yescharacteristic
93C3×#41—51no—
94C3×#41—51no—
95C3×#41—51no—
96C3×#41—101no—
97C3×#41—101no—
98C3×#41AGL(1,𝔽5)11yescharacteristic, complemented
99C2×C3×Q8—51no—
100C2×C3×D4—51no—
101C2×C3×D4—101no—
102C22×C3×C4—51no—
103C22×C3×C4—101no—
104C22×C3×C4—101no—
105C3×M16—52no—
106C3×M16—101no—
107C2×C3×C8—101no—
108C3×C42—52no—
109C3×C42—101no—
110C22×D5—21no—
111C22×D5C3×D411yescharacteristic
112C2×AGL(1,𝔽5)—24no—
113C2×AGL(1,𝔽5)—22no—
114C5×Q8C2×C3×C411yescharacteristic, complemented
115C5×D4—21no—
116C5×D4C2×C3×C411yescharacteristic, complemented
117C2×C4×C5—21no—
118C2×C4×C5C2×C3×C411yescharacteristic
119C22⋊D5—21no—
120C22⋊D5—21no—
121C22⋊D5—21no—
122C2×Dic5—21no—
123C2×Dic5C3×D411yescharacteristic
124D20—21no—
125D20C2×C3×C411yescharacteristic, complemented
126C4×D5—21no—
127C4×D5—21no—
128C4×D5—21no—
129C4×D5C2×C3×C411yescharacteristic
130C4×D5C3×D411yescharacteristic
131C4×D5C3×D411yescharacteristic
132C4×D5C23×C311yescharacteristic
133Dic10—21no—
134Dic10C2×C3×C411yescharacteristic, complemented
135#170—22no—
136C2×#41—51no—
137C2×M16—51no—
138C2×C42—51no—
139#104—52no—
140#104—52no—
141C2×C3×C5—21no—
142C2×C3×C5—41no—
143C2×C3×C5C2×C22⋊C411yescharacteristic
144C3×D5—21no—
145C3×D5—41no—
146C3×D5#10412yescomplemented
147C23×C3—51no—
148C23×C3—101no—
149C3×Q8—51no—
150C3×Q8—101no—
151C3×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
152C3×D4—21no—
153C3×D4—51no—
154C3×D4—101no—
155C3×D4—101no—
156C3×D4—101no—
157C3×D4—101no—
158C3×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
159C2×C3×C4—21no—
160C2×C3×C4—51no—
161C2×C3×C4—51no—
162C2×C3×C4—51no—
163C2×C3×C4—51no—
164C2×C3×C4—51no—
165C2×C3×C4—101no—
166C2×C3×C4—101no—
167C2×C3×C4—101no—
168C2×C3×C4—102no—
169C2×C3×C4—104no—
170C2×C3×C4—101no—
171C2×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
172C3×C8—102no—
173C22×C5—21no—
174C22×C5C3×C22⋊C411yescharacteristic
175C2×D5—22no—
176C2×D5—21no—
177C2×D5—42no—
178C2×D5C3×C22⋊C411yescharacteristic
179C2×D5C2×C3×D411yescharacteristic
180AGL(1,𝔽5)—24no—
181C4×C5—21no—
182C4×C5C3×C22⋊C411yescharacteristic
183C4×C5C22×C3×C411yescharacteristic
184Dic5—21no—
185Dic5C3×C22⋊C411yescharacteristic
186Dic5C2×C3×D411yescharacteristic
187#41—51no—
188#41—51no—
189#41—51no—
190#41—101no—
191#41—101no—
192#41C3×AGL(1,𝔽5)11yescharacteristic, complemented
193C2×Q8—51no—
194C2×D4—51no—
195C2×D4—101no—
196C22×C4—51no—
197C22×C4—101no—
198C22×C4—101no—
199M16—52no—
200M16—101no—
201C2×C8—101no—
202C42—52no—
203C42—101no—
204C3×C5C2×#10411yescharacteristic, complemented, Hall
205C22×C3—21no—
206C22×C3—51no—
207C22×C3—51no—
208C22×C3—102no—
209C22×C3—101no—
210C22×C3—202no—
211C22×C3C22⋊AGL(1,𝔽5)11yescharacteristic
212C3×C4—21no—
213C3×C4—51no—
214C3×C4—51no—
215C3×C4—104no—
216C3×C4—101no—
217C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
218C3×C4C22×AGL(1,𝔽5)11yescharacteristic
219C2×C5—21no—
220C2×C5—41no—
221C2×C5C2×C3×C22⋊C411yescharacteristic
222D5—21no—
223D5—41no—
224D5C3×#10412yescomplemented
225C23—51no—
226C23—101no—
227Q8—51no—
228Q8—101no—
229Q8C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
230D4—21no—
231D4—51no—
232D4—101no—
233D4—101no—
234D4—101no—
235D4—101no—
236D4C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
237C2×C4—21no—
238C2×C4—51no—
239C2×C4—51no—
240C2×C4—51no—
241C2×C4—51no—
242C2×C4—51no—
243C2×C4—101no—
244C2×C4—101no—
245C2×C4—101no—
246C2×C4—102no—
247C2×C4—104no—
248C2×C4—101no—
249C2×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
250C8—102no—
251C2×C3—21no—
252C2×C3—41no—
253C2×C3—52no—
254C2×C3—101no—
255C2×C3—201no—
256C2×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
257C5C2×C3×#10411yescharacteristic, complemented, Sylow
258C22—21no—
259C22—51no—
260C22—51no—
261C22—102no—
262C22—101no—
263C22—202no—
264C22C3×C22⋊AGL(1,𝔽5)11yescharacteristic
265C4—21no—
266C4—51no—
267C4—51no—
268C4—104no—
269C4—101no—
270C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
271C4C22×C3×AGL(1,𝔽5)11yescharacteristic
272C3D5⋊#10411yescharacteristic, direct product factor, Sylow
273C2—21no—
274C2—41no—
275C2—52no—
276C2—101no—
277C2—201no—
278C2C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC3×C4C22⋊AGL(1,𝔽5)
commutatorC4×C5C22×C3×C4
FrattiniC4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#41C4
socleC2×C3×C5C2×C22⋊C4
prime radicalC3×D5×#41C2
cosocleC4×D5C23×C3
hypercenterC3×#41AGL(1,𝔽5)
hypocenterC5C2×C3×#104
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×AGL(1,𝔽5)C2semidirect
3. C3×D5⋊M16C2semidirect
4. C3×#4010C2semidirect
5. C3×#4008C2semidirect
6. D5⋊#104C3direct (N × H)
8. C3×C5×#41C4semidirect
10. C3×Q8×D5C4semidirect
14. C3×D4×D5C4semidirect
16. C3×#709C4semidirect
21. C3×C4×AGL(1,𝔽5)C22semidirect
22. C3×#700C22semidirect
26. C2×C4×AGL(1,𝔽5)C2×C3semidirect
27. D5⋊M16C2×C3semidirect
28. #4010C2×C3semidirect
29. #4008C2×C3semidirect
34. C3×C5×Q8C2×C4semidirect
36. C3×C5×D4C2×C4semidirect
45. C3×D20C2×C4semidirect
54. C3×Dic10C2×C4semidirect
62. C5×#41C3×C4semidirect
64. Q8×D5C3×C4semidirect
68. D4×D5C3×C4semidirect
70. #709C3×C4semidirect
75. C4×AGL(1,𝔽5)C22×C3semidirect
76. #700C22×C3semidirect
98. C3×#41AGL(1,𝔽5)semidirect
114. C5×Q8C2×C3×C4semidirect
116. C5×D4C2×C3×C4semidirect
125. D20C2×C3×C4semidirect
134. Dic10C2×C3×C4semidirect
146. C3×D5#104semidirect
151. C3×Q8C2×AGL(1,𝔽5)semidirect
158. C3×D4C2×AGL(1,𝔽5)semidirect
192. #41C3×AGL(1,𝔽5)semidirect
204. C3×C5C2×#104semidirect
224. D5C3×#104semidirect
229. Q8C2×C3×AGL(1,𝔽5)semidirect
236. D4C2×C3×AGL(1,𝔽5)semidirect
257. C5C2×C3×#104semidirect
272. C3D5⋊#104direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×#412
C2×C3×C4×AGL(1,𝔽5)2
C3×D5⋊M162
C3×#40102
C3×#40082
D5⋊#1043
C2×C3×#1045