Finite Group Databasebeta

← #11752577

Subgroups — #11752577

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
1C4×D60C211yesmaximal, characteristic, complemented
2C5×#870C211yesmaximal, characteristic, complemented
3C3×C4×D20C211yesmaximal, characteristic, complemented
4#91450C211yesmaximal, characteristic, complemented
5#91450C211yesmaximal, characteristic, complemented
6D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
7#91409C212yesmaximal, complemented
8#91396C212yesmaximal, complemented
9#91358C211yesmaximal, characteristic, complemented
10#91354C212yesmaximal, complemented
11#91345C212yesmaximal, complemented
12#66029—31nomaximal, Hall
13C2×D60C2211yescharacteristic
14C2×C4×D15C2212yes—
15C2×C3×D20C2211yescharacteristic
16C2×C3×C4×D5C2211yescharacteristic
17C2×C3×C4×D5C2211yescharacteristic
18C2×#1202C2212yes—
19C2×#1202C2212yes—
20C2×D5×Dic3C2212yes—
21C3×C42×C5C2211yescharacteristic
22#6714C2212yes—
23C4⋊Dic15C2211yescharacteristic
24C5×C4⋊Dic3C2211yescharacteristic
25C5×C4⋊Dic3C2211yescharacteristic
26C5×Dic3⋊C4C2212yes—
27C5×Dic3⋊C4C2212yes—
28C3×#685C2211yescharacteristic
29C3×#685C2211yescharacteristic
30C3×C4⋊Dic5C2211yescharacteristic
31#6668C2212yes—
32#6667C2212yes—
33#6667C2212yes—
34#6665C2212yes—
35Dic3×Dic5C2212yes—
36#5565—51nomaximal, Hall
37C5×#125—31no—
38#4044—32no—
39#4041—32no—
40#4041—31no—
41#4041—31no—
42#4040—32no—
43#4039—32no—
44#4038—31no—
45D5×C4⋊C4—31no—
46C4×D20—31no—
47C4×D20D311yescharacteristic, complemented
48C22×D15C2312yes—
49C22×C3×D5C2311yescharacteristic
50C22×C3×D5C2311yescharacteristic
51C2×C3×C4×C5C2311yescharacteristic
52C2×C3×C4×C5C2311yescharacteristic
53C2×C3×C4×C5C2311yescharacteristic
54C2×Dic15C2312yes—
55D60—22no—
56C4×D15—42no—
57C2×C5×Dic3C2312yes—
58C2×C5×Dic3C2312yes—
59C2×C3×Dic5C2311yescharacteristic
60C2×C3×Dic5C2311yescharacteristic
61C3×D20—22no—
62C3×C4×D5—22no—
63C3×C4×D5—22no—
64#1202—24no—
65#1202—42no—
66D5×Dic3—42no—
67C3×C4×D4—51no—
68#939—52no—
69#930—51no—
70#930—51no—
71#926—51no—
72C2×C4⋊Dic3—51no—
73#898—52no—
74#883—52no—
75#67⋊C4—52no—
76C4×D12—51no—
77#870D511yescharacteristic, complemented
78C2×D20—32no—
79C2×D20—31no—
80C2×D20—32no—
81C2×D20C2×D311yescharacteristic
82C2×C4×D5—32no—
83C2×C4×D5—32no—
84C2×C4×D5C2×D311yescharacteristic
85C2×C4×D5C2×D311yescharacteristic
86C5×C4⋊C4—32no—
87C5×C4⋊C4—32no—
88C5×C4⋊C4—31no—
89C5×C4⋊C4—31no—
90C42×C5C2×D311yescharacteristic
91#685—32no—
92#685—32no—
93#685—32no—
94#685—32no—
95#685C2×D311yescharacteristic
96#685C2×D311yescharacteristic
97C4⋊Dic5—31no—
98C4⋊Dic5C2×D311yescharacteristic
99#683—32no—
100C4×Dic5—32no—
101#553—151noSylow
102C22×C3×C5C2411yescharacteristic
103C2×D15—22no—
104C2×D15—22no—
105C2×D15—22no—
106C2×C3×D5—21no—
107C2×C3×D5—21no—
108C2×C3×D5—21no—
109C2×C3×D5—21no—
110C2×C3×D5—21no—
111C2×C3×D5#4112yes—
112C3×C4×C5—21no—
113C3×C4×C5—21no—
114C3×C4×C5#4112yes—
115Dic15—22no—
116C3×Dic5—21no—
117C3×Dic5—21no—
118C5×Dic3—22no—
119C5×Dic3—22no—
120C2×C3×D4—51no—
121C22×C3×C4—51no—
122C22×C3×C4—51no—
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×C42C2×D511yescharacteristic
132#217—52no—
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⋊C4C2×D512yes—
141Dic3⋊C4C2×D512yes—
142C4×Dic3—52no—
143C22×D5—32no—
144C22×D5C22×D311yescharacteristic
145C22×D5C22×D311yescharacteristic
146C2×C4×C5—32no—
147C2×C4×C5—32no—
148C2×C4×C5C22×D311yescharacteristic
149C2×C4×C5C22×D311yescharacteristic
150C2×C4×C5C22×D311yescharacteristic
151C2×Dic5—32no—
152C2×Dic5C22×D311yescharacteristic
153C2×Dic5C22×D311yescharacteristic
154D20—22no—
155D20—64no—
156D20—62no—
157D20—122no—
158C4×D5—22no—
159C4×D5—22no—
160C4×D5—122no—
161C4×D5—122no—
162#126—152no—
163#125—31no—
164#123—152no—
165#121—151no—
166#121—151no—
167#121—152no—
168C4×D4—51no—
169C4×D4—152no—
170C4×D4—151no—
171#117—151no—
172C2×C4⋊C4—151no—
173C2×C3×C5C2×#4111yescharacteristic
174C2×C3×C5C2×#4111yescharacteristic
175C2×C3×C5H(5,𝔽2)11yescharacteristic
176D15—42no—
177C3×D5—22no—
178C3×D5—41no—
179C23×C3—51no—
180C23×C3—51no—
181C22×D3—52no—
182C3×D4—102no—
183C2×C3×C4—51no—
184C2×C3×C4—51no—
185C2×C3×C4—102no—
186C2×C3×C4—102no—
187C2×C3×C4C22×D511yescharacteristic
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×C5C23×D311yescharacteristic
199C2×D5—21no—
200C2×D5—21no—
201C2×D5—21no—
202C2×D5—21no—
203C2×D5—21no—
204C2×D5—62no—
205C2×D5—62no—
206C2×D5—62no—
207C2×D5#23512yes—
208C4×C5—21no—
209C4×C5—21no—
210C4×C5—62no—
211C4×C5—62no—
212C4×C5#23712yes—
213Dic5—21no—
214Dic5—21no—
215Dic5—62no—
216C2×D4—51no—
217C2×D4—152no—
218C2×D4—152no—
219C2×D4—151no—
220C22×C4—51no—
221C22×C4—51no—
222C22×C4—152no—
223C22×C4—152no—
224C4⋊C4—31no—
225C4⋊C4—31no—
226C4⋊C4—32no—
227C4⋊C4—32no—
228C4⋊C4—51no—
229C4⋊C4—152no—
230C4⋊C4—151no—
231C22⋊C4—51no—
232C22⋊C4—51no—
233C22⋊C4—152no—
234C22⋊C4—152no—
235C22⋊C4—152no—
236C22⋊C4—152no—
237C42—152no—
238C42D3×D511yescharacteristic
239C3×C5#55311yescharacteristic, complemented, Hall
240C22×C3—52no—
241C22×C3—101no—
242C22×C3—101no—
243C22×C3—101no—
244C22×C3—101no—
245C22×C3—101no—
246C22×C3C23×D511yescharacteristic
247C2×D3—102no—
248C2×D3—102no—
249C2×D3—102no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—101no—
253C3×C4—101no—
254C3×C4#71312yes—
255Dic3—22no—
256Dic3—22no—
257Dic3—102no—
258C2×C5C2×#23511yescharacteristic
259C2×C5C2×#23711yescharacteristic
260C2×C5#100911yescharacteristic
261D5—22no—
262D5—41no—
263D5—122no—
264C23—51no—
265C23—51no—
266C23—152no—
267D4—102no—
268D4—304no—
269D4—302no—
270D4—602no—
271C2×C4—32no—
272C2×C4—32no—
273C2×C4—51no—
274C2×C4—51no—
275C2×C4—102no—
276C2×C4—102no—
277C2×C4—152no—
278C2×C4—602no—
279C2×C4—602no—
280C2×C4C2×D3×D511yescharacteristic
281C2×C4C2×D3×D511yescharacteristic
282C2×C4C2×D3×D511yescharacteristic
283C2×C3—102no—
284C2×C3—201no—
285C2×C3C2×#71311yescharacteristic
286C2×C3D5×#4111yescharacteristic
287C2×C3#414911yescharacteristic
288D3—202no—
289C5#556511yescharacteristic, complemented, Sylow
290C22—52no—
291C22—101no—
292C22—101no—
293C22—101no—
294C22—101no—
295C22—101no—
296C22—302no—
297C22—302no—
298C22—302no—
299C22C22×D3×D511yescharacteristic
300C4—21no—
301C4—21no—
302C4—62no—
303C4—62no—
304C4—101no—
305C4—101no—
306C4—302no—
307C4#676612yes—
308C3#6602911yescharacteristic, complemented, Sylow
309C2—102no—
310C2—201no—
311C2—602no—
312C2C2×#676611yescharacteristic
313C2D5×#23511yescharacteristic
314C2#9201911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
hypercenterC42D3×D5
hypocenterC3×C5#553
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×D60C2semidirect
2. C5×#870C2semidirect
3. C3×C4×D20C2semidirect
4. #91450C2semidirect
5. #91450C2semidirect
6. D5×C4⋊Dic3C2semidirect
7. #91409C2semidirect
8. #91396C2semidirect
9. #91358C2semidirect
10. #91354C2semidirect
11. #91345C2semidirect
47. C4×D20D3semidirect
77. #870D5semidirect
239. C3×C5#553semidirect
289. C5#5565semidirect
308. C3#66029semidirect

Maximal subgroups

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

subgroupindex
C4×D602
C5×#8702
C3×C4×D202
#914502
D5×C4⋊Dic32
#914092
#913962
#913582
#913542
#913452
#660293
#55655