Finite Group Databasebeta

← C3×D5⋊#99 #11752303

Subgroups — C3×D5⋊#99 #11752303

Order 960.

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

normal subgroups only

This group has 420 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
1C2×C3×D4×D5C211yesmaximal, characteristic
2C2×C3×C22⋊AGL(1,𝔽5)C212yesmaximal, complemented
3C3×#4011C212yesmaximal, complemented
4C3×#3999C212yesmaximal, complemented
5D5⋊#99C311yesmaximal, characteristic, direct product factor, Hall
6C23×C3×D5C411yescharacteristic, complemented
7C23×C3×D5C2211yescharacteristic
8C22×C3×AGL(1,𝔽5)—22no—
9C2×C3×C5×D4C411yescharacteristic, complemented
10C2×C3×C22⋊D5C411yescharacteristic, complemented
11C2×C3×C22⋊D5C2211yescharacteristic
12C3×D4×D5—22no—
13C3×D4×D5—22no—
14C2×C3×D20C2211yescharacteristic
15C2×C3×C4×D5C411yescharacteristic, complemented
16C3×C22⋊AGL(1,𝔽5)—22no—
17C3×C22⋊AGL(1,𝔽5)C2214yescomplemented
18C2×C3×#99—51nomaximal, Hall
19C2×D4×D5C2×C311yescharacteristic
20C2×C22⋊AGL(1,𝔽5)C2×C312yescomplemented
21#4011C2×C312yescomplemented
22#3999C2×C312yescomplemented
23C23×C3×C5C2×C411yescharacteristic
24C23×C3×C5C2×C411yescharacteristic, complemented
25C22×C3×D5—21no—
26C22×C3×D5—21no—
27C22×C3×D5—42no—
28C22×C3×D5—42no—
29C22×C3×D5C2×C411yescharacteristic
30C22×C3×D5C2×C411yescharacteristic, complemented
31C22×C3×D5D412yes—
32C22×C3×D5D412yes—
33C22×C3×D5C2311yescharacteristic
34C2×C3×AGL(1,𝔽5)—24no—
35C2×C3×AGL(1,𝔽5)—44no—
36C3×C5×D4—22no—
37C2×C3×C4×C5C2×C411yescharacteristic, complemented
38C3×C22⋊D5—22no—
39C3×C22⋊D5—22no—
40C2×C3×Dic5C2×C411yescharacteristic, complemented
41C3×D20—22no—
42C3×C4×D5—21no—
43C3×C4×D5—21no—
44C22×C3×D4—51no—
45C2×C3×C22⋊C4—52no—
46C3×#99—52no—
47C3×#99—52no—
48C23×D5C3×C411yescharacteristic, complemented
49C23×D5C22×C311yescharacteristic
50C22×AGL(1,𝔽5)—22no—
51C2×C5×D4C3×C411yescharacteristic, complemented
52C2×C22⋊D5C3×C411yescharacteristic, complemented
53C2×C22⋊D5C22×C311yescharacteristic
54D4×D5—22no—
55D4×D5—22no—
56C2×D20C22×C311yescharacteristic
57C2×C4×D5C3×C411yescharacteristic, complemented
58C22⋊AGL(1,𝔽5)—22no—
59C22⋊AGL(1,𝔽5)C22×C314yescomplemented
60C2×#99—51noSylow
61C22×C3×C5—21no—
62C22×C3×C5—41no—
63C22×C3×C5—41no—
64C22×C3×C5C22⋊C412yes—
65C22×C3×C5C22×C411yescharacteristic
66C2×C3×D5—24no—
67C2×C3×D5—22no—
68C2×C3×D5—21no—
69C2×C3×D5—42no—
70C2×C3×D5—41no—
71C2×C3×D5—42no—
72C2×C3×D5—42no—
73C2×C3×D5—41no—
74C2×C3×D5C22⋊C411yescharacteristic
75C2×C3×D5C22⋊C411yescharacteristic
76C2×C3×D5C2×D412yes—
77C3×AGL(1,𝔽5)—44no—
78C3×C4×C5—21no—
79C3×Dic5—21no—
80C24×C3—51no—
81C24×C3—51no—
82C2×C3×D4—51no—
83C2×C3×D4—51no—
84C2×C3×D4—51no—
85C2×C3×D4—102no—
86C2×C3×D4—102no—
87C2×C3×D4AGL(1,𝔽5)11yescharacteristic, complemented
88C22×C3×C4—51no—
89C22×C3×C4—102no—
90C3×C22⋊C4—54no—
91C3×C22⋊C4—102no—
92C23×C5C2×C3×C411yescharacteristic
93C23×C5C2×C3×C411yescharacteristic, complemented
94C22×D5—21no—
95C22×D5—21no—
96C22×D5—42no—
97C22×D5—42no—
98C22×D5C2×C3×C411yescharacteristic
99C22×D5C2×C3×C411yescharacteristic, complemented
100C22×D5C3×D412yes—
101C22×D5C3×D412yes—
102C22×D5C23×C311yescharacteristic
103C2×AGL(1,𝔽5)—24no—
104C2×AGL(1,𝔽5)—44no—
105C5×D4—22no—
106C2×C4×C5C2×C3×C411yescharacteristic, complemented
107C22⋊D5—22no—
108C22⋊D5—22no—
109C2×Dic5C2×C3×C411yescharacteristic, complemented
110D20—22no—
111C4×D5—21no—
112C4×D5—21no—
113C22×D4—51no—
114C2×C22⋊C4—52no—
115#99—52no—
116#99—52no—
117C2×C3×C5—21no—
118C2×C3×C5—22no—
119C2×C3×C5—41no—
120C2×C3×C5C2×C22⋊C411yescharacteristic
121C3×D5—22no—
122C3×D5—21no—
123C3×D5—41no—
124C3×D5#9912yescomplemented
125C23×C3—52no—
126C23×C3—51no—
127C23×C3—52no—
128C23×C3—51no—
129C23×C3—51no—
130C23×C3—101no—
131C23×C3—101no—
132C23×C3—202no—
133C23×C3—202no—
134C23×C3C2×AGL(1,𝔽5)11yescharacteristic
135C23×C3C2×AGL(1,𝔽5)11yescharacteristic, complemented
136C3×D4—22no—
137C3×D4—102no—
138C3×D4—102no—
139C3×D4—102no—
140C2×C3×C4—51no—
141C2×C3×C4—101no—
142C2×C3×C4—101no—
143C2×C3×C4—104no—
144C2×C3×C4—204no—
145C2×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
146C22×C5—21no—
147C22×C5—41no—
148C22×C5—41no—
149C22×C5C3×C22⋊C412yes—
150C22×C5C22×C3×C411yescharacteristic
151C2×D5—24no—
152C2×D5—22no—
153C2×D5—21no—
154C2×D5—42no—
155C2×D5—41no—
156C2×D5—42no—
157C2×D5—42no—
158C2×D5—41no—
159C2×D5C3×C22⋊C411yescharacteristic
160C2×D5C3×C22⋊C411yescharacteristic
161C2×D5C2×C3×D412yes—
162AGL(1,𝔽5)—44no—
163C4×C5—21no—
164Dic5—21no—
165C24—51no—
166C24—51no—
167C2×D4—51no—
168C2×D4—51no—
169C2×D4—51no—
170C2×D4—102no—
171C2×D4—102no—
172C2×D4C3×AGL(1,𝔽5)11yescharacteristic, complemented
173C22×C4—51no—
174C22×C4—102no—
175C22⋊C4—54no—
176C22⋊C4—102no—
177C3×C5C2×#9911yescharacteristic, complemented, Hall
178C22×C3—21no—
179C22×C3—41no—
180C22×C3—41no—
181C22×C3—51no—
182C22×C3—51no—
183C22×C3—52no—
184C22×C3—104no—
185C22×C3—102no—
186C22×C3—101no—
187C22×C3—201no—
188C22×C3—202no—
189C22×C3—201no—
190C22×C3—202no—
191C22×C3—202no—
192C22×C3C22⋊AGL(1,𝔽5)12yes—
193C22×C3C22×AGL(1,𝔽5)11yescharacteristic
194C3×C4—21no—
195C3×C4—101no—
196C3×C4—204no—
197C2×C5—21no—
198C2×C5—22no—
199C2×C5—41no—
200C2×C5C2×C3×C22⋊C411yescharacteristic
201D5—22no—
202D5—21no—
203D5—41no—
204D5C3×#9912yescomplemented
205C23—52no—
206C23—51no—
207C23—52no—
208C23—51no—
209C23—51no—
210C23—101no—
211C23—101no—
212C23—202no—
213C23—202no—
214C23C2×C3×AGL(1,𝔽5)11yescharacteristic
215C23C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
216D4—22no—
217D4—102no—
218D4—102no—
219D4—102no—
220C2×C4—51no—
221C2×C4—101no—
222C2×C4—101no—
223C2×C4—104no—
224C2×C4—204no—
225C2×C4C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
226C2×C3—21no—
227C2×C3—22no—
228C2×C3—41no—
229C2×C3—52no—
230C2×C3—102no—
231C2×C3—101no—
232C2×C3—201no—
233C2×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
234C5C2×C3×#9911yescharacteristic, complemented, Sylow
235C22—21no—
236C22—41no—
237C22—41no—
238C22—51no—
239C22—52no—
240C22—51no—
241C22—104no—
242C22—102no—
243C22—101no—
244C22—201no—
245C22—202no—
246C22—201no—
247C22—202no—
248C22—202no—
249C22C3×C22⋊AGL(1,𝔽5)12yes—
250C22C22×C3×AGL(1,𝔽5)11yescharacteristic
251C4—21no—
252C4—101no—
253C4—204no—
254C3D5⋊#9911yescharacteristic, direct product factor, Sylow
255C2—21no—
256C2—22no—
257C2—41no—
258C2—52no—
259C2—102no—
260C2—101no—
261C2—201no—
262C2C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2×C3C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C22×C3×C4
FrattiniC22C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C4
socleC2×C3×C5C2×C22⋊C4
prime radicalC2×C3×D4×D5C2
cosocleC22×D5C23×C3
hypercenterC2×C3×D4AGL(1,𝔽5)
hypocenterC5C2×C3×#99
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C22⋊AGL(1,𝔽5)C2semidirect
3. C3×#4011C2semidirect
4. C3×#3999C2semidirect
5. D5⋊#99C3direct (N × H)
6. C23×C3×D5C4semidirect
9. C2×C3×C5×D4C4semidirect
10. C2×C3×C22⋊D5C4semidirect
15. C2×C3×C4×D5C4semidirect
17. C3×C22⋊AGL(1,𝔽5)C22semidirect
20. C2×C22⋊AGL(1,𝔽5)C2×C3semidirect
21. #4011C2×C3semidirect
22. #3999C2×C3semidirect
24. C23×C3×C5C2×C4semidirect
30. C22×C3×D5C2×C4semidirect
37. C2×C3×C4×C5C2×C4semidirect
40. C2×C3×Dic5C2×C4semidirect
48. C23×D5C3×C4semidirect
51. C2×C5×D4C3×C4semidirect
52. C2×C22⋊D5C3×C4semidirect
57. C2×C4×D5C3×C4semidirect
59. C22⋊AGL(1,𝔽5)C22×C3semidirect
87. C2×C3×D4AGL(1,𝔽5)semidirect
93. C23×C5C2×C3×C4semidirect
99. C22×D5C2×C3×C4semidirect
106. C2×C4×C5C2×C3×C4semidirect
109. C2×Dic5C2×C3×C4semidirect
124. C3×D5#99semidirect
135. C23×C3C2×AGL(1,𝔽5)semidirect
145. C2×C3×C4C2×AGL(1,𝔽5)semidirect
172. C2×D4C3×AGL(1,𝔽5)semidirect
177. C3×C5C2×#99semidirect
204. D5C3×#99semidirect
215. C23C2×C3×AGL(1,𝔽5)semidirect
225. C2×C4C2×C3×AGL(1,𝔽5)semidirect
234. C5C2×C3×#99semidirect
254. C3D5⋊#99direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×D52
C2×C3×C22⋊AGL(1,𝔽5)2
C3×#40112
C3×#39992
D5⋊#993
C2×C3×#995