Finite Group Databasebeta

← #11754407

Subgroups — #11754407

Order 960.

476 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91819C211yesmaximal, characteristic, complemented
2C5×#926C211yesmaximal, characteristic, complemented
3C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4#91562C212yesmaximal, complemented
5#91550C212yesmaximal, complemented
6#91450C211yesmaximal, characteristic, complemented
7#91418C211yesmaximal, characteristic, complemented
8D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
9#91395C212yesmaximal, complemented
10#91388C211yesmaximal, characteristic, complemented
11#91380C212yesmaximal, complemented
12#65864—31nomaximal, Hall
13C22×C3×C4×C5C2211yescharacteristic
14C2×#1220C2212yes—
15C2×D60C2211yescharacteristic
16C2×C3×C22⋊D5C2211yescharacteristic
17C2×C3×C4×D5C2211yescharacteristic
18C2×#1202C2212yes—
19C2×#1200C2212yes—
20C2×D5×Dic3C2212yes—
21#6714C2212yes—
22C4⋊Dic15C2211yescharacteristic
23C5×#217C2212yes—
24C5×C4⋊Dic3C2211yescharacteristic
25C5×C4⋊Dic3C2211yescharacteristic
26C4×C5×Dic3C2212yes—
27C3×C22⋊Dic5C2211yescharacteristic
28C3×#685C2211yescharacteristic
29C3×#683C2211yescharacteristic
30C3×C4×Dic5C2211yescharacteristic
31Dic3⋊Dic5C2212yes—
32#6669C2212yes—
33#6668C2212yes—
34#6667C2212yes—
35#6667C2212yes—
36#5565—51nomaximal, Hall
37C5×#117—31no—
38#4076—31no—
39C4×C22⋊D5D311yescharacteristic, complemented
40#4041—31no—
41#4039—31no—
42D5×C4⋊C4—31no—
43#4036—31no—
44#4030—32no—
45#4029—32no—
46#4022—32no—
47C4×D20—32no—
48C23×C3×C5C2311yescharacteristic
49C22×D15C2312yes—
50C22×C3×D5C2311yescharacteristic
51C2×C3×C4×C5—22no—
52C2×C3×C4×C5C2311yescharacteristic
53C2×C3×C4×C5C2311yescharacteristic
54#1220—42no—
55C2×Dic15C2312yes—
56D60—22no—
57C2×C5×Dic3C2312yes—
58C2×C5×Dic3C2312yes—
59C3×C22⋊D5—22no—
60C2×C3×Dic5C2311yescharacteristic
61C2×C3×Dic5C2311yescharacteristic
62C2×C3×Dic5C2311yescharacteristic
63C3×C4×D5—22no—
64#1202—24no—
65#1200—42no—
66D5×Dic3—42no—
67C3×C4×D4—51no—
68#939—52no—
69#930—51no—
70#930—51no—
71#926D511yescharacteristic, complemented
72C2×C4⋊Dic3—51no—
73#898—52no—
74#883—52no—
75#67⋊C4—52no—
76C4×D12—51no—
77#870—51no—
78C22×C4×C5C2×D311yescharacteristic
79C2×C22⋊D5—32no—
80C2×C22⋊D5C2×D311yescharacteristic
81C2×D20—32no—
82C2×D20—31no—
83C2×C4×D5—32no—
84C2×C4×D5—32no—
85C2×C4×D5C2×D311yescharacteristic
86C5×C4⋊C4—31no—
87C5×C4⋊C4—31no—
88C5×C22⋊C4—32no—
89C42×C5—32no—
90C22⋊Dic5C2×D311yescharacteristic
91#685—32no—
92#685—32no—
93#685—32no—
94#685C2×D311yescharacteristic
95C4⋊Dic5—31no—
96C4⋊Dic5—32no—
97#683—32no—
98#683—32no—
99#683C2×D311yescharacteristic
100C4×Dic5C2×D311yescharacteristic
101#553—151noSylow
102C22×C3×C5—21no—
103C22×C3×C5—21no—
104C22×C3×C5—21no—
105C22×C3×C5C2411yescharacteristic
106C2×D15—22no—
107C2×D15—22no—
108C2×D15—22no—
109C2×C3×D5—21no—
110C2×C3×D5—21no—
111C2×C3×D5#4112yes—
112C3×C4×C5—21no—
113C3×C4×C5#4112yes—
114Dic15—22no—
115C3×Dic5—21no—
116C3×Dic5—21no—
117C3×Dic5—21no—
118C5×Dic3—22no—
119C5×Dic3—22no—
120C2×C3×D4—51no—
121C22×C3×C4—51no—
122C22×C3×C4C2×D511yescharacteristic
123C2×#67—52no—
124C2×#67—52no—
125C22×Dic3—52no—
126C2×D12—51no—
127C2×C4×D3—52no—
128C3×C4⋊C4—51no—
129C3×C22⋊C4—51no—
130C3×C22⋊C4—51no—
131C3×C42—51no—
132#217C2×D512yes—
133(C2×D3)⋊C4—52no—
134(C2×D3)⋊C4—52no—
135(C2×D3)⋊C4—52no—
136C4⋊Dic3—51no—
137C4⋊Dic3—52no—
138C4⋊Dic3C2×D511yescharacteristic
139C4⋊Dic3C2×D511yescharacteristic
140Dic3⋊C4—52no—
141Dic3⋊C4—52no—
142C4×Dic3C2×D512yes—
143C23×C5C22×D311yescharacteristic
144C22×D5—32no—
145C22×D5C22×D311yescharacteristic
146C2×C4×C5—22no—
147C2×C4×C5—32no—
148C2×C4×C5—32no—
149C2×C4×C5C22×D311yescharacteristic
150C2×C4×C5C22×D311yescharacteristic
151C22⋊D5—22no—
152C22⋊D5—122no—
153C2×Dic5—32no—
154C2×Dic5C22×D311yescharacteristic
155C2×Dic5C22×D311yescharacteristic
156C2×Dic5C22×D311yescharacteristic
157D20—64no—
158D20—62no—
159C4×D5—22no—
160C4×D5—122no—
161C4×D5—122no—
162#126—152no—
163#125—151no—
164#123—152no—
165#121—152no—
166#121—151no—
167#121—151no—
168C4×D4—51no—
169C4×D4—152no—
170C4×D4—151no—
171#117—31no—
172C2×C4⋊C4—151no—
173C2×C3×C5—41no—
174C2×C3×C5C2×#4111yescharacteristic
175C2×C3×C5C2×#4111yescharacteristic
176C2×C3×C5H(5,𝔽2)11yescharacteristic
177D15—42no—
178C3×D5—22no—
179C23×C3—51no—
180C23×C3C22×D511yescharacteristic
181C22×D3—52no—
182C3×D4—102no—
183C2×C3×C4—22no—
184C2×C3×C4—51no—
185C2×C3×C4—51no—
186C2×C3×C4—51no—
187C2×C3×C4—102no—
188C2×C3×C4C22×D511yescharacteristic
189C2×C3×C4C22×D511yescharacteristic
190#67—104no—
191#67—202no—
192C2×Dic3—52no—
193C2×Dic3—202no—
194C2×Dic3C22×D512yes—
195C2×Dic3C22×D512yes—
196D12—102no—
197C4×D3—202no—
198C22×C5—21no—
199C22×C5—21no—
200C22×C5—21no—
201C22×C5C23×D311yescharacteristic
202C2×D5—21no—
203C2×D5—21no—
204C2×D5—62no—
205C2×D5—62no—
206C2×D5—62no—
207C2×D5#23512yes—
208C4×C5—21no—
209C4×C5—62no—
210C4×C5—62no—
211C4×C5#23712yes—
212Dic5—21no—
213Dic5—21no—
214Dic5—21no—
215Dic5—62no—
216C2×D4—51no—
217C2×D4—152no—
218C2×D4—152no—
219C2×D4—151no—
220C22×C4—51no—
221C22×C4—152no—
222C22×C4—152no—
223C22×C4D3×D511yescharacteristic
224C4⋊C4—31no—
225C4⋊C4—31no—
226C4⋊C4—51no—
227C4⋊C4—152no—
228C4⋊C4—152no—
229C4⋊C4—152no—
230C4⋊C4—151no—
231C22⋊C4—32no—
232C22⋊C4—51no—
233C22⋊C4—51no—
234C22⋊C4—152no—
235C22⋊C4—152no—
236C22⋊C4—152no—
237C42—32no—
238C42—51no—
239C3×C5#55311yescharacteristic, complemented, Hall
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—52no—
244C22×C3—101no—
245C22×C3—101no—
246C22×C3C23×D511yescharacteristic
247C2×D3—102no—
248C2×D3—102no—
249C2×D3—102no—
250C3×C4—21no—
251C3×C4—101no—
252C3×C4—101no—
253C3×C4—101no—
254C3×C4#70912yes—
255Dic3—22no—
256Dic3—22no—
257Dic3—102no—
258C2×C5—41no—
259C2×C5C2×#23511yescharacteristic
260C2×C5C2×#23711yescharacteristic
261C2×C5#100911yescharacteristic
262D5—22no—
263D5—122no—
264C23—51no—
265C23—152no—
266C23C2×D3×D511yescharacteristic
267D4—102no—
268D4—304no—
269D4—302no—
270D4—602no—
271C2×C4—22no—
272C2×C4—32no—
273C2×C4—32no—
274C2×C4—51no—
275C2×C4—51no—
276C2×C4—51no—
277C2×C4—102no—
278C2×C4—152no—
279C2×C4—602no—
280C2×C4—602no—
281C2×C4C2×D3×D511yescharacteristic
282C2×C4C2×D3×D511yescharacteristic
283C2×C3—41no—
284C2×C3—102no—
285C2×C3C2×#70911yescharacteristic
286C2×C3D5×#4111yescharacteristic
287C2×C3#414911yescharacteristic
288D3—202no—
289C5#556511yescharacteristic, complemented, Sylow
290C22—21no—
291C22—21no—
292C22—21no—
293C22—52no—
294C22—101no—
295C22—101no—
296C22—302no—
297C22—302no—
298C22—302no—
299C22C22×D3×D511yescharacteristic
300C4—21no—
301C4—62no—
302C4—62no—
303C4—101no—
304C4—101no—
305C4—101no—
306C4—302no—
307C4#677912yes—
308C3#6586411yescharacteristic, complemented, Sylow
309C2—41no—
310C2—102no—
311C2—602no—
312C2D5×#23511yescharacteristic
313C2#9201911yescharacteristic
314C2C2×#677911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC22×C3×C4×C5C22
hypercenterC22×C4D3×D5
hypocenterC3×C5#553
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. #91819C2semidirect
2. C5×#926C2semidirect
3. C3×C4×C22⋊D5C2semidirect
4. #91562C2semidirect
5. #91550C2semidirect
6. #91450C2semidirect
7. #91418C2semidirect
8. D5×C4⋊Dic3C2semidirect
9. #91395C2semidirect
10. #91388C2semidirect
11. #91380C2semidirect
39. C4×C22⋊D5D3semidirect
71. #926D5semidirect
239. C3×C5#553semidirect
289. C5#5565semidirect
308. C3#65864semidirect

Maximal subgroups

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

subgroupindex
#918192
C5×#9262
C3×C4×C22⋊D52
#915622
#915502
#914502
#914182
D5×C4⋊Dic32
#913952
#913882
#913802
#658643
#55655