Finite Group Databasebeta

← C3×#65062 #11749670

Subgroups — C3×#65062 #11749670

Order 960.

396 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 90 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, complemented
2C2×C3×#686C211yesmaximal, characteristic, complemented
3C2×C3×D40C211yesmaximal, characteristic, complemented
4C3×#4041C211yesmaximal, characteristic, complemented
5C3×C5×#102C211yesmaximal, characteristic, complemented
6C3×#3952C211yesmaximal, characteristic, complemented
7C3×#3941C211yesmaximal, characteristic, complemented
8#65062C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×D5—21no—
10C2×C3×C5×D4C2211yescharacteristic
11C2×C3×C22⋊D5—21no—
12C3×D4×D5—22no—
13C3×D4×D5—22no—
14C2×C3×D20—21no—
15C2×C3×D20C2211yescharacteristic
16C2×C3×D20C2211yescharacteristic, complemented
17C2×C3×C4×D5C2211yescharacteristic
18C2×C3×C5×C8C2211yescharacteristic, complemented
19C3×C5×C4⋊C4C2211yescharacteristic, complemented
20C3×#686—22no—
21C3×#685—21no—
22C2×C3×#168C2211yescharacteristic, complemented
23C3×D40—22no—
24C3×#447—51nomaximal, Hall
25C2×D4×D5C2×C311yescharacteristic, complemented
26C2×#686C2×C311yescharacteristic, complemented
27C2×D40C2×C311yescharacteristic, complemented
28#4041C2×C311yescharacteristic, complemented
29C5×#102C2×C311yescharacteristic, complemented
30#3952C2×C311yescharacteristic, complemented
31#3941C2×C311yescharacteristic, complemented
32C23×C3×C5—21no—
33C22×C3×D5—24no—
34C22×C3×D5—21no—
35C22×C3×D5—21no—
36C22×C3×D5—42no—
37C22×C3×D5—42no—
38C22×C3×D5D411yescharacteristic
39C3×C5×D4—21no—
40C3×C5×D4D412yescomplemented
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5C2311yescharacteristic
43C3×C22⋊D5—24no—
44C2×C3×Dic5D411yescharacteristic
45C3×D20—21no—
46C3×D20—21no—
47C3×D20—21no—
48C3×D20—42no—
49C3×D20D412yescomplemented
50C3×C4×D5—21no—
51C3×C4×D5—21no—
52C3×C5×C8—21no—
53C3×#168—21no—
54C22×C3×D4—51no—
55C2×C3×D8—51no—
56C2×C3×D8—51no—
57C3×#121—51no—
58C3×#102—51no—
59C3×#102D511yescharacteristic, complemented
60C3×C22⋊C8—51no—
61C23×D5—21no—
62C2×C5×D4C22×C311yescharacteristic
63C2×C22⋊D5—21no—
64D4×D5—22no—
65D4×D5—22no—
66C2×D20—21no—
67C2×D20C22×C311yescharacteristic
68C2×D20C22×C311yescharacteristic, complemented
69C2×C4×D5C22×C311yescharacteristic
70C2×C5×C8C22×C311yescharacteristic, complemented
71C5×C4⋊C4C22×C311yescharacteristic, complemented
72#686—22no—
73#685—21no—
74C2×#168C22×C311yescharacteristic, complemented
75D40—22no—
76#447—51noSylow
77C22×C3×C5—22no—
78C22×C3×C5—41no—
79C22×C3×C5—41no—
80C22×C3×C5C2×D411yescharacteristic
81C2×C3×D5—21no—
82C2×C3×D5—21no—
83C2×C3×D5—22no—
84C2×C3×D5—48no—
85C2×C3×D5—41no—
86C2×C3×D5—41no—
87C2×C3×D5—41no—
88C2×C3×D5—41no—
89C2×C3×D5—41no—
90C2×C3×D5D812yescomplemented
91C3×C4×C5—41no—
92C3×C4×C5C2×D411yescharacteristic
93C3×C4×C5C2×D411yescharacteristic
94C3×Dic5—21no—
95C24×C3—101no—
96C2×C3×D4—51no—
97C2×C3×D4—51no—
98C2×C3×D4—101no—
99C2×C3×D4—101no—
100C2×C3×D4—102no—
101C2×C3×D4—102no—
102C2×C3×D4C2×D511yescharacteristic
103C22×C3×C4—51no—
104C3×D8—102no—
105C3×D8—102no—
106C2×C3×C8—51no—
107C2×C3×C8C2×D511yescharacteristic, complemented
108C3×C4⋊C4C2×D511yescharacteristic, complemented
109C3×C22⋊C4—101no—
110C23×C5—21no—
111C22×D5—24no—
112C22×D5—21no—
113C22×D5—21no—
114C22×D5—42no—
115C22×D5—42no—
116C22×D5C3×D411yescharacteristic
117C5×D4—21no—
118C5×D4C3×D412yescomplemented
119C2×C4×C5—21no—
120C2×C4×C5C23×C311yescharacteristic
121C22⋊D5—24no—
122C2×Dic5C3×D411yescharacteristic
123D20—21no—
124D20—21no—
125D20—21no—
126D20—42no—
127D20C3×D412yescomplemented
128C4×D5—21no—
129C4×D5—21no—
130C5×C8—21no—
131#168—21no—
132C22×D4—51no—
133C2×D8—51no—
134C2×D8—51no—
135#121—51no—
136#102—51no—
137#102C3×D511yescharacteristic, complemented
138C22⋊C8—51no—
139C2×C3×C5—42no—
140C2×C3×C5#12011yescharacteristic
141C2×C3×C5C2×D811yescharacteristic
142C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
143C3×D5—22no—
144C3×D5—42no—
145C3×D5—81no—
146C23×C3—21no—
147C23×C3—51no—
148C23×C3—104no—
149C23×C3—101no—
150C23×C3—101no—
151C23×C3—202no—
152C23×C3—202no—
153C3×D4—21no—
154C3×D4—52no—
155C3×D4—104no—
156C3×D4—101no—
157C3×D4—101no—
158C3×D4—101no—
159C3×D4—202no—
160C3×D4D2012yescomplemented
161C2×C3×C4—21no—
162C2×C3×C4—51no—
163C2×C3×C4—101no—
164C2×C3×C4—101no—
165C2×C3×C4C22×D511yescharacteristic
166C3×C8—21no—
167C3×C8—101no—
168C22×C5—22no—
169C22×C5—41no—
170C22×C5—41no—
171C22×C5C2×C3×D411yescharacteristic
172C2×D5—21no—
173C2×D5—21no—
174C2×D5—22no—
175C2×D5—48no—
176C2×D5—41no—
177C2×D5—41no—
178C2×D5—41no—
179C2×D5—41no—
180C2×D5—41no—
181C2×D5C3×D812yescomplemented
182C4×C5—41no—
183C4×C5C2×C3×D411yescharacteristic
184C4×C5C2×C3×D411yescharacteristic
185Dic5—21no—
186C24—101no—
187C2×D4—51no—
188C2×D4—51no—
189C2×D4—101no—
190C2×D4—101no—
191C2×D4—102no—
192C2×D4—102no—
193C2×D4C2×C3×D511yescharacteristic
194C22×C4—51no—
195D8—102no—
196D8—102no—
197C2×C8—51no—
198C2×C8C2×C3×D511yescharacteristic, complemented
199C4⋊C4C2×C3×D511yescharacteristic, complemented
200C22⋊C4—101no—
201C3×C5#44711yescharacteristic, complemented, Hall
202C22×C3—22no—
203C22×C3—41no—
204C22×C3—41no—
205C22×C3—52no—
206C22×C3—101no—
207C22×C3—101no—
208C22×C3—102no—
209C22×C3—208no—
210C22×C3—201no—
211C22×C3—201no—
212C22×C3—201no—
213C22×C3—201no—
214C22×C3—201no—
215C22×C3D4×D511yescharacteristic
216C3×C4—41no—
217C3×C4—101no—
218C3×C4C2×D2011yescharacteristic
219C3×C4D4×D511yescharacteristic
220C2×C5—42no—
221C2×C5C3×#12011yescharacteristic
222C2×C5C2×C3×D811yescharacteristic
223C2×C5C3×AGL(1,ℤ/8)11yescharacteristic
224D5—22no—
225D5—42no—
226D5—81no—
227C23—21no—
228C23—51no—
229C23—104no—
230C23—101no—
231C23—101no—
232C23—202no—
233C23—202no—
234D4—21no—
235D4—52no—
236D4—104no—
237D4—101no—
238D4—101no—
239D4—101no—
240D4—202no—
241D4C3×D2012yescomplemented
242C2×C4—21no—
243C2×C4—51no—
244C2×C4—101no—
245C2×C4—101no—
246C2×C4C22×C3×D511yescharacteristic
247C8—21no—
248C8—101no—
249C2×C3—42no—
250C2×C3—102no—
251C2×C3—202no—
252C2×C3—401no—
253C2×C3#402811yescharacteristic
254C2×C3D5×D811yescharacteristic
255C2×C3#406011yescharacteristic
256C5C3×#44711yescharacteristic, complemented, Sylow
257C22—22no—
258C22—41no—
259C22—41no—
260C22—52no—
261C22—101no—
262C22—101no—
263C22—102no—
264C22—208no—
265C22—201no—
266C22—201no—
267C22—201no—
268C22—201no—
269C22—201no—
270C22C3×D4×D511yescharacteristic
271C4—41no—
272C4—101no—
273C4C2×C3×D2011yescharacteristic
274C4C3×D4×D511yescharacteristic
275C3#6506211yescharacteristic, direct product factor, Sylow
276C2—42no—
277C2—102no—
278C2—202no—
279C2—401no—
280C2C3×#402811yescharacteristic
281C2C3×D5×D811yescharacteristic
282C2C3×#406011yescharacteristic
subgroupG/H
centerC22×C3D4×D5
commutator, cosocleC2×C4×C5C23×C3
FrattiniC2×C4C22×C3×D5
FittingC3×C5×#102C2
socleC22×C3×C5C2×D4
hypercenterC3×#102D5
hypocenterC5C3×#447
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#102

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×D5C2semidirect
2. C2×C3×#686C2semidirect
3. C2×C3×D40C2semidirect
4. C3×#4041C2semidirect
5. C3×C5×#102C2semidirect
6. C3×#3952C2semidirect
7. C3×#3941C2semidirect
8. #65062C3direct (N × H)
16. C2×C3×D20C22semidirect
18. C2×C3×C5×C8C22semidirect
19. C3×C5×C4⋊C4C22semidirect
22. C2×C3×#168C22semidirect
25. C2×D4×D5C2×C3semidirect
26. C2×#686C2×C3semidirect
27. C2×D40C2×C3semidirect
28. #4041C2×C3semidirect
29. C5×#102C2×C3semidirect
30. #3952C2×C3semidirect
31. #3941C2×C3semidirect
40. C3×C5×D4D4semidirect
49. C3×D20D4semidirect
59. C3×#102D5semidirect
68. C2×D20C22×C3semidirect
70. C2×C5×C8C22×C3semidirect
71. C5×C4⋊C4C22×C3semidirect
74. C2×#168C22×C3semidirect
90. C2×C3×D5D8semidirect
107. C2×C3×C8C2×D5semidirect
108. C3×C4⋊C4C2×D5semidirect
118. C5×D4C3×D4semidirect
127. D20C3×D4semidirect
137. #102C3×D5semidirect
160. C3×D4D20semidirect
181. C2×D5C3×D8semidirect
198. C2×C8C2×C3×D5semidirect
199. C4⋊C4C2×C3×D5semidirect
201. C3×C5#447semidirect
241. D4C3×D20semidirect
256. C5C3×#447semidirect
275. C3#65062direct (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×#6862
C2×C3×D402
C3×#40412
C3×C5×#1022
C3×#39522
C3×#39412
#650623
C3×#4475