Finite Group Databasebeta

← #11753823

Subgroups — #11753823

Order 960.

480 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 128 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
1#91784C211yesmaximal, characteristic, complemented
2C5×#893C211yesmaximal, characteristic, complemented
3C3×#4036C211yesmaximal, characteristic, complemented
4#91466C211yesmaximal, characteristic, complemented
5#91460C212yesmaximal, complemented
6#91451C211yesmaximal, characteristic, complemented
7#91438C212yesmaximal, complemented
8#91428C211yesmaximal, characteristic, complemented
9#91420C212yesmaximal, complemented
10#91386C211yesmaximal, characteristic, complemented
11#91351C212yesmaximal, complemented
12#65896—31nomaximal, Hall
13C2×D60C2211yescharacteristic
14C2×D60C2212yes—
15C2×C4×D15C2211yescharacteristic
16C2×C5×D12C2211yescharacteristic
17C2×C4×C5×D3C2212yes—
18C2×#1203C2212yes—
19C2×#1203C2212yes—
20C2×#1203C2212yes—
21C2×#1200C2212yes—
22C3×C5×C4⋊C4C2211yescharacteristic
23#6714C2212yes—
24C5×(C2×D3)⋊C4C2212yes—
25C4×C5×Dic3C2211yescharacteristic
26C3×C4⋊Dic5C2211yescharacteristic
27C3×C4⋊Dic5C2212yes—
28C3×#683C2212yes—
29C3×C4×Dic5C2211yescharacteristic
30#6669C2211yescharacteristic
31#6669C2211yescharacteristic
32#6667C2211yescharacteristic
33#6667C2212yes—
34#6667C2211yescharacteristic
35(C2×D3)⋊Dic5C2212yes—
36#5697—51nomaximal, Hall
37C4×C5×D4—31no—
38#4086—31no—
39#4084—31no—
40#4076—32no—
41#4075—32no—
42#4041—31no—
43#4036D311yescharacteristic, complemented
44#4030—32no—
45#4029—32no—
46C4×D20—31no—
47#4018—31no—
48C22×D15C2311yescharacteristic
49C22×D15C2312yes—
50C22×C5×D3C2312yes—
51C2×C3×C4×C5C2312yes—
52C2×C3×C4×C5C2311yescharacteristic
53C2×Dic15C2311yescharacteristic
54D60—22no—
55D60—42no—
56C4×D15—22no—
57C2×C5×Dic3C2311yescharacteristic
58C2×C5×Dic3C2311yescharacteristic
59C5×D12—22no—
60C4×C5×D3—42no—
61C2×C3×Dic5C2312yes—
62C2×C3×Dic5C2311yescharacteristic
63C2×C3×Dic5C2311yescharacteristic
64#1203—42no—
65#1203—42no—
66#1203—42no—
67#1200—42no—
68C3×#125—51no—
69#895—51no—
70#895—52no—
71#895—51no—
72#895—52no—
73#894—52no—
74#894—52no—
75#893—51no—
76#893D511yescharacteristic, complemented
77#874—51no—
78#872—51no—
79C2×C5×D4—31no—
80C22×C4×C5—32no—
81C2×C22⋊D5—32no—
82C2×C22⋊D5—32no—
83C2×C22⋊D5—32no—
84C2×D20—31no—
85C2×D20—32no—
86C2×C4×D5—31no—
87C2×C4×D5—32no—
88C5×C4⋊C4C2×D311yescharacteristic
89C5×C22⋊C4—32no—
90C42×C5—31no—
91C22⋊Dic5—32no—
92#685—32no—
93#685—31no—
94#685—31no—
95#685—32no—
96C4⋊Dic5C2×D311yescharacteristic
97C4⋊Dic5C2×D312yes—
98#683—31no—
99#683—31no—
100#683C2×D312yes—
101C4×Dic5C2×D311yescharacteristic
102#540—151noSylow
103C22×C3×C5C2411yescharacteristic
104C2×D15—21no—
105C2×D15—22no—
106C2×D15—22no—
107C2×D15—21no—
108C2×D15—22no—
109C2×D15—21no—
110C2×C5×D3—22no—
111C2×C5×D3—22no—
112C2×C5×D3—22no—
113C3×C4×C5—22no—
114C3×C4×C5#4112yes—
115Dic15—21no—
116C3×Dic5—22no—
117C3×Dic5—21no—
118C3×Dic5—21no—
119C5×Dic3—21no—
120C5×Dic3—21no—
121C2×D12—51no—
122C2×D12—52no—
123C2×D12—52no—
124C2×D12—52no—
125C2×D12—52no—
126C2×D12C2×D511yescharacteristic
127C2×C4×D3—51no—
128C2×C4×D3—52no—
129C2×C4×D3C2×D512yes—
130C3×C4⋊C4—52no—
131C3×C4⋊C4—51no—
132C3×C4⋊C4—52no—
133C3×C4⋊C4C2×D511yescharacteristic
134C3×C42—51no—
135(C2×D3)⋊C4—52no—
136(C2×D3)⋊C4—52no—
137(C2×D3)⋊C4—51no—
138(C2×D3)⋊C4—51no—
139(C2×D3)⋊C4—52no—
140(C2×D3)⋊C4C2×D512yes—
141Dic3⋊C4—51no—
142Dic3⋊C4—51no—
143C4×Dic3C2×D511yescharacteristic
144C23×C5—32no—
145C22×D5—31no—
146C22×D5—32no—
147C5×D4—62no—
148C2×C4×C5—31no—
149C2×C4×C5—31no—
150C2×C4×C5—122no—
151C2×C4×C5C22×D312yes—
152C2×C4×C5C22×D311yescharacteristic
153C22⋊D5—122no—
154C22⋊D5—122no—
155C22⋊D5—122no—
156C2×Dic5—31no—
157C2×Dic5C22×D311yescharacteristic
158C2×Dic5C22×D311yescharacteristic
159C2×Dic5C22×D312yes—
160D20—62no—
161D20—122no—
162C4×D5—62no—
163C4×D5—122no—
164#127—151no—
165#125—51no—
166#123—152no—
167#123—152no—
168#121—152no—
169#121—152no—
170#121—151no—
171#121—151no—
172C4×D4—31no—
173C4×D4—151no—
174#117—151no—
175C2×C3×C5C2×#4111yescharacteristic
176C2×C3×C5H(5,𝔽2)11yescharacteristic
177C2×C3×C5H(5,𝔽2)11yescharacteristic
178D15—41no—
179D15—42no—
180C5×D3—42no—
181C22×D3—51no—
182C22×D3—52no—
183C22×D3C22×D512yes—
184C2×C3×C4—51no—
185C2×C3×C4—51no—
186C2×C3×C4—52no—
187C2×C3×C4C22×D512yes—
188C2×C3×C4C22×D511yescharacteristic
189C2×Dic3—51no—
190C2×Dic3C22×D511yescharacteristic
191C2×Dic3C22×D511yescharacteristic
192D12—22no—
193D12—102no—
194D12—202no—
195D12—202no—
196D12—202no—
197D12—202no—
198C4×D3—42no—
199C4×D3—102no—
200C4×D3—202no—
201C22×C5—62no—
202C22×C5—62no—
203C22×C5—62no—
204C22×C5C23×D311yescharacteristic
205C2×D5—61no—
206C2×D5—62no—
207C2×D5—62no—
208C2×D5—61no—
209C2×D5—62no—
210C2×D5—61no—
211C4×C5—22no—
212C4×C5—61no—
213C4×C5—61no—
214C4×C5#23912yes—
215Dic5—22no—
216Dic5—21no—
217Dic5—21no—
218Dic5—61no—
219C2×D4—31no—
220C2×D4—152no—
221C2×D4—152no—
222C2×D4—152no—
223C2×D4—151no—
224C2×D4—152no—
225C22×C4—32no—
226C22×C4—152no—
227C22×C4—151no—
228C4⋊C4—51no—
229C4⋊C4—52no—
230C4⋊C4—52no—
231C4⋊C4—151no—
232C4⋊C4—151no—
233C4⋊C4D3×D511yescharacteristic
234C22⋊C4—32no—
235C22⋊C4—151no—
236C22⋊C4—151no—
237C22⋊C4—152no—
238C22⋊C4—152no—
239C22⋊C4—152no—
240C42—31no—
241C42—51no—
242C3×C5#54011yescharacteristic, complemented, Hall
243C22×C3C23×D511yescharacteristic
244C2×D3—22no—
245C2×D3—22no—
246C2×D3—22no—
247C2×D3—101no—
248C2×D3—102no—
249C2×D3—102no—
250C2×D3—101no—
251C2×D3—102no—
252C2×D3—101no—
253C3×C4—22no—
254C3×C4—101no—
255C3×C4—102no—
256C3×C4—101no—
257C3×C4#70912yes—
258Dic3—21no—
259Dic3—21no—
260Dic3—101no—
261C2×C5—122no—
262C2×C5C2×#23911yescharacteristic
263C2×C5#100911yescharacteristic
264C2×C5#100911yescharacteristic
265D5—121no—
266D5—122no—
267C23—32no—
268C23—151no—
269C23—152no—
270D4—62no—
271D4—302no—
272D4—602no—
273D4—602no—
274D4—602no—
275D4—602no—
276C2×C4—31no—
277C2×C4—31no—
278C2×C4—51no—
279C2×C4—51no—
280C2×C4—52no—
281C2×C4—122no—
282C2×C4—151no—
283C2×C4—302no—
284C2×C4—602no—
285C2×C4C2×D3×D512yes—
286C2×C4C2×D3×D511yescharacteristic
287C2×C3C2×#70911yescharacteristic
288C2×C3#414411yescharacteristic
289C2×C3#414911yescharacteristic
290D3—42no—
291D3—201no—
292D3—202no—
293C5#569711yescharacteristic, complemented, Sylow
294C22—62no—
295C22—62no—
296C22—62no—
297C22—301no—
298C22—302no—
299C22—301no—
300C22—302no—
301C22—302no—
302C22—301no—
303C22C22×D3×D511yescharacteristic
304C4—22no—
305C4—61no—
306C4—61no—
307C4—101no—
308C4—102no—
309C4—101no—
310C4—301no—
311C4#676912yes—
312C3#6589611yescharacteristic, complemented, Sylow
313C2—122no—
314C2—601no—
315C2—602no—
316C2C2×#676911yescharacteristic
317C2#9202711yescharacteristic
318C2#9203511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#540
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #91784C2semidirect
2. C5×#893C2semidirect
3. C3×#4036C2semidirect
4. #91466C2semidirect
5. #91460C2semidirect
6. #91451C2semidirect
7. #91438C2semidirect
8. #91428C2semidirect
9. #91420C2semidirect
10. #91386C2semidirect
11. #91351C2semidirect
43. #4036D3semidirect
76. #893D5semidirect
242. C3×C5#540semidirect
293. C5#5697semidirect
312. C3#65896semidirect

Maximal subgroups

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

subgroupindex
#917842
C5×#8932
C3×#40362
#914662
#914602
#914512
#914382
#914282
#914202
#913862
#913512
#658963
#56975