Finite Group Databasebeta

← #11754325

Subgroups — #11754325

Order 960.

584 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6779C212yesmaximal, complemented
2#91819C211yesmaximal, characteristic, complemented
3C2×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
5#91542C212yesmaximal, complemented
6#91468C211yesmaximal, characteristic, complemented
7#91450C211yesmaximal, characteristic, complemented
8#91419C212yesmaximal, complemented
9#91418C211yesmaximal, characteristic, complemented
10#91413C212yesmaximal, complemented
11D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
12#65841—31nomaximal, Hall
13C22×C3×C4×C5C2211yescharacteristic
14C2×#1220C2212yes—
15C2×D60C2211yescharacteristic
16C22×C5×Dic3C2212yes—
17C2×C3×C22⋊D5C2211yescharacteristic
18C2×C3×C4×D5C2211yescharacteristic
19C2×#1204C2212yes—
20C2×#1202C2212yes—
21C2×#1200C2212yes—
22#6779—28no—
23C2×D5×Dic3C2212yes—
24#6714C2212yes—
25C4⋊Dic15C2211yescharacteristic
26C5×C4⋊Dic3C2211yescharacteristic
27C5×C4⋊Dic3C2212yes—
28C5×C4⋊Dic3C2211yescharacteristic
29C3×C22⋊Dic5C2211yescharacteristic
30C3×#685C2211yescharacteristic
31C3×#683C2211yescharacteristic
32C3×C4×Dic5C2211yescharacteristic
33#6668C2212yes—
34#6668C2212yes—
35#6667C2212yes—
36#6667C2212yes—
37#5555—51nomaximal, Hall
38C2×#709—32no—
39C2×C5×C4⋊C4—31no—
40#4076—31no—
41#4075—32no—
42C4×C22⋊D5D311yescharacteristic, complemented
43#4042—32no—
44#4041—31no—
45#4040—32no—
46#4039—31no—
47D5×C4⋊C4—31no—
48#4034—31no—
49C23×C3×C5C2311yescharacteristic
50C22×D15C2312yes—
51C22×C3×D5C2311yescharacteristic
52C2×C3×C4×C5—22no—
53C2×C3×C4×C5C2311yescharacteristic
54C2×C3×C4×C5C2311yescharacteristic
55#1220—24no—
56C2×Dic15C2312yes—
57D60—22no—
58C2×C5×Dic3—24no—
59C2×C5×Dic3C2312yes—
60C2×C5×Dic3C2312yes—
61C3×C22⋊D5D414yescomplemented
62C2×C3×Dic5C2311yescharacteristic
63C2×C3×Dic5C2311yescharacteristic
64C2×C3×Dic5C2311yescharacteristic
65C3×C4×D5—22no—
66#1204—24no—
67#1202—24no—
68#1200—24no—
69D5×Dic3—24no—
70C2×#237—52no—
71C3×C4×D4—51no—
72#930—51no—
73#930—51no—
74C2×C4⋊Dic3—51no—
75C2×C4⋊Dic3D511yescharacteristic, complemented
76#897—52no—
77#886—52no—
78#886—52no—
79C4×D12—51no—
80#869—51no—
81C22×C4×C5—32no—
82C22×C4×C5C2×D311yescharacteristic
83C2×C22⋊D5—32no—
84C2×C22⋊D5C2×D311yescharacteristic
85#709—68no—
86C2×D20—32no—
87C2×D20—31no—
88C2×C4×D5—32no—
89C2×C4×D5—32no—
90C2×C4×D5C2×D311yescharacteristic
91C2×Dic10—32no—
92C5×C4⋊C4—31no—
93C5×C4⋊C4—31no—
94C5×C4⋊C4—32no—
95C22⋊Dic5C2×D311yescharacteristic
96#685—32no—
97#685—32no—
98#685—32no—
99#685C2×D311yescharacteristic
100C4⋊Dic5—31no—
101#683—32no—
102#683—32no—
103#683C2×D311yescharacteristic
104C4×Dic5C2×D311yescharacteristic
105#547—151noSylow
106C22×C3×C5—21no—
107C22×C3×C5—21no—
108C22×C3×C5C2×D412yes—
109C22×C3×C5C2411yescharacteristic
110C2×D15—22no—
111C2×D15—22no—
112C2×D15—22no—
113C2×C3×D5—21no—
114C2×C3×D5—21no—
115C2×C3×D5C2×D412yes—
116C3×C4×C5—21no—
117C3×C4×C5#4112yescomplemented
118Dic15—22no—
119C3×Dic5—21no—
120C3×Dic5—21no—
121C3×Dic5C2×D412yes—
122C5×Dic3—22no—
123C5×Dic3—22no—
124C2×C3×D4—51no—
125C22×C3×C4—51no—
126C22×C3×C4C2×D511yescharacteristic
127C2×#67—52no—
128C2×#67—52no—
129C22×Dic3—52no—
130C22×Dic3C2×D512yes—
131#237—108no—
132C2×D12—51no—
133C2×C4×D3—52no—
134C2×Dic6—52no—
135C3×C4⋊C4—51no—
136C3×C22⋊C4—51no—
137C3×C22⋊C4—51no—
138C3×C42—51no—
139(C2×D3)⋊C4—52no—
140(C2×D3)⋊C4—52no—
141(C2×D3)⋊C4—52no—
142C4⋊Dic3—51no—
143C4⋊Dic3—52no—
144C4⋊Dic3—52no—
145C4⋊Dic3C2×D511yescharacteristic
146C4⋊Dic3C2×D511yescharacteristic
147C4⋊Dic3C2×D512yes—
148C23×C5C22×D311yescharacteristic
149C22×D5—32no—
150C22×D5C22×D311yescharacteristic
151C2×C4×C5—22no—
152C2×C4×C5—32no—
153C2×C4×C5—32no—
154C2×C4×C5—64no—
155C2×C4×C5C22×D311yescharacteristic
156C2×C4×C5C22×D311yescharacteristic
157C22⋊D5—64no—
158C22⋊D5D1214yescomplemented
159C2×Dic5—32no—
160C2×Dic5C22×D311yescharacteristic
161C2×Dic5C22×D311yescharacteristic
162C2×Dic5C22×D311yescharacteristic
163D20—64no—
164D20—62no—
165C4×D5—22no—
166C4×D5—64no—
167C4×D5—64no—
168Dic10—64no—
169C2×#41—152no—
170C4⋊Q8—151no—
171#123—152no—
172#123—152no—
173C22⋊Q8—152no—
174#121—151no—
175#121—151no—
176C4×D4—51no—
177C4×D4—151no—
178C2×C4⋊C4—31no—
179C2×C4⋊C4—151no—
180C2×C3×C5—22no—
181C2×C3×C5C22×D411yescharacteristic
182C2×C3×C5C2×#4111yescharacteristic
183C2×C3×C52−1+411yescharacteristic
184D15—42no—
185C3×D5—22no—
186C23×C3—51no—
187C23×C3C22×D511yescharacteristic
188C22×D3—52no—
189C3×D4—54no—
190C2×C3×C4—22no—
191C2×C3×C4—51no—
192C2×C3×C4—51no—
193C2×C3×C4—51no—
194C2×C3×C4—102no—
195C2×C3×C4C22×D511yescharacteristic
196C2×C3×C4C22×D511yescharacteristic
197#67—104no—
198#67—104no—
199C2×Dic3—24no—
200C2×Dic3—52no—
201C2×Dic3—104no—
202C2×Dic3C22×D512yes—
203C2×Dic3C22×D512yes—
204D12—102no—
205C4×D3—104no—
206Dic6—104no—
207C22×C5—21no—
208C22×C5—21no—
209C22×C5C2×D1212yes—
210C22×C5C23×D311yescharacteristic
211C2×D5—21no—
212C2×D5—21no—
213C2×D5—62no—
214C2×D5—62no—
215C2×D5—62no—
216C2×D5C2×D1212yes—
217C4×C5—21no—
218C4×C5—62no—
219C4×C5—62no—
220C4×C5#23712yescomplemented
221Dic5—21no—
222Dic5—21no—
223Dic5—62no—
224Dic5C2×D1212yes—
225#41—308no—
226C2×Q8—152no—
227C2×D4—51no—
228C2×D4—152no—
229C2×D4—152no—
230C2×D4—151no—
231C22×C4—32no—
232C22×C4—51no—
233C22×C4—152no—
234C22×C4—152no—
235C22×C4D3×D511yescharacteristic
236C4⋊C4—31no—
237C4⋊C4—31no—
238C4⋊C4—32no—
239C4⋊C4—51no—
240C4⋊C4—152no—
241C4⋊C4—152no—
242C4⋊C4—151no—
243C22⋊C4—51no—
244C22⋊C4—51no—
245C22⋊C4—152no—
246C22⋊C4—152no—
247C22⋊C4—152no—
248C42—51no—
249C3×C5#54711yescharacteristic, complemented, Hall
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—52no—
253C22×C3—101no—
254C22×C3—101no—
255C22×C3D4×D512yes—
256C22×C3C23×D511yescharacteristic
257C2×D3—102no—
258C2×D3—102no—
259C2×D3—102no—
260C3×C4—21no—
261C3×C4—52no—
262C3×C4—101no—
263C3×C4—101no—
264C3×C4#70912yescomplemented
265Dic3—22no—
266Dic3—22no—
267Dic3—102no—
268C2×C5—22no—
269C2×C5C22×D1211yescharacteristic
270C2×C5C2×#23711yescharacteristic
271C2×C5#101011yescharacteristic
272D5—22no—
273D5—122no—
274C23—51no—
275C23—152no—
276C23C2×D3×D511yescharacteristic
277Q8—304no—
278D4—54no—
279D4—304no—
280D4—304no—
281D4—302no—
282C2×C4—22no—
283C2×C4—32no—
284C2×C4—32no—
285C2×C4—51no—
286C2×C4—51no—
287C2×C4—51no—
288C2×C4—64no—
289C2×C4—102no—
290C2×C4—152no—
291C2×C4—304no—
292C2×C4—304no—
293C2×C4C2×D3×D511yescharacteristic
294C2×C4C2×D3×D511yescharacteristic
295C2×C3—22no—
296C2×C3—102no—
297C2×C3C2×#70911yescharacteristic
298C2×C3C2×D4×D511yescharacteristic
299C2×C3#414711yescharacteristic
300D3—202no—
301C5#555511yescharacteristic, complemented, Sylow
302C22—21no—
303C22—21no—
304C22—52no—
305C22—101no—
306C22—101no—
307C22—302no—
308C22—302no—
309C22—302no—
310C22D5×D1212yes—
311C22C22×D3×D511yescharacteristic
312C4—21no—
313C4—52no—
314C4—62no—
315C4—62no—
316C4—101no—
317C4—101no—
318C4—302no—
319C4#677912yescomplemented
320C3#6584111yescharacteristic, complemented, Sylow
321C2—22no—
322C2—102no—
323C2—602no—
324C2#9200011yescharacteristic
325C2C2×D5×D1211yescharacteristic
326C2C2×#677911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC22×C3×C4×C5C22
hypercenterC22×C4D3×D5
hypocenterC3×C5#547
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#6779C2semidirect
2. #91819C2semidirect
3. C2×C5×C4⋊Dic3C2semidirect
4. C3×C4×C22⋊D5C2semidirect
5. #91542C2semidirect
6. #91468C2semidirect
7. #91450C2semidirect
8. #91419C2semidirect
9. #91418C2semidirect
10. #91413C2semidirect
11. D5×C4⋊Dic3C2semidirect
42. C4×C22⋊D5D3semidirect
61. C3×C22⋊D5D4semidirect
75. C2×C4⋊Dic3D5semidirect
117. C3×C4×C5#41semidirect
158. C22⋊D5D12semidirect
220. C4×C5#237semidirect
249. C3×C5#547semidirect
264. C3×C4#709semidirect
301. C5#5555semidirect
319. C4#6779semidirect
320. C3#65841semidirect

Maximal subgroups

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

subgroupindex
C2×#67792
#918192
C2×C5×C4⋊Dic32
C3×C4×C22⋊D52
#915422
#914682
#914502
#914192
#914182
#914132
D5×C4⋊Dic32
#658413
#55555