Finite Group Databasebeta

← #11754644

Subgroups — #11754644

Order 960.

692 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 144 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×D5×#67C212yesmaximal, complemented
2#91819C211yesmaximal, characteristic, complemented
3C5×#930C211yesmaximal, characteristic, complemented
4C2×C3×#685C211yesmaximal, characteristic, complemented
5#91566C212yesmaximal, complemented
6#91476C212yesmaximal, complemented
7#91475C212yesmaximal, complemented
8#91414C212yesmaximal, complemented
9#91413C212yesmaximal, complemented
10#65939—31nomaximal, Hall
11C23×C3×D5C2211yescharacteristic
12C22×D3×D5C2212yescomplemented
13C22×C3×C4×C5C2211yescharacteristic, complemented
14C2×#1220C2212yescomplemented
15C2×D60C2211yescharacteristic, complemented
16C2×C5×#67C2212yescomplemented
17C2×C5×D12C2211yescharacteristic, complemented
18C22×C3×Dic5C2211yescharacteristic, complemented
19D5×#67—28no—
20C2×#1203C2212yescomplemented
21C2×#1202C2212yes—
22C2×#1201C2212yes—
23C2×D5×Dic3C2212yescomplemented
24#6714C2212yescomplemented
25C4⋊Dic15C2211yescharacteristic, complemented
26C5×(C2×D3)⋊C4C2212yescomplemented
27C5×C4⋊Dic3C2211yescharacteristic, complemented
28C3×#685C2212yescomplemented
29C3×#685C2212yescomplemented
30#6668C2212yescomplemented
31#6667C2212yescomplemented
32(C2×D3)⋊Dic5C2212yescomplemented
33#5493—51nomaximal, Hall
34C2×D4×D5—32no—
35C5×#121—31no—
36#4085—32no—
37#4083—32no—
38#4076—31no—
39C2×#685D311yescharacteristic, complemented
40#4040—32no—
41#4029—32no—
42#4028—32no—
43C23×C3×C5C2311yescharacteristic
44C22×D15C2312yes—
45C22×C5×D3C2312yes—
46C22×C3×D5—41no—
47C22×C3×D5—41no—
48C22×C3×D5D414yescomplemented
49C22×C3×D5C2312yes—
50C2×D3×D5—24no—
51C2×D3×D5—42no—
52C2×D3×D5—42no—
53C2×C3×C4×C5—41no—
54C2×C3×C4×C5C2311yescharacteristic
55C2×C3×C4×C5C2311yescharacteristic
56#1220—24no—
57C2×Dic15C2312yes—
58D60—41no—
59C5×#67—24no—
60C2×C5×Dic3C2312yes—
61C5×D12—41no—
62C2×C3×Dic5—41no—
63C2×C3×Dic5C2312yes—
64#1203—42no—
65#1202—24no—
66#1201—24no—
67D5×Dic3—24no—
68C22×#67—52no—
69C2×C3×C22⋊C4—51no—
70#930—51no—
71#930—52no—
72#930D511yescharacteristic, complemented
73#886—52no—
74#886—52no—
75#882—52no—
76#882—52no—
77C23×D5—32no—
78C23×D5C2×D311yescharacteristic
79C2×C5×D4—32no—
80C2×C5×D4—31no—
81C22×C4×C5C2×D311yescharacteristic, complemented
82C2×C22⋊D5—32no—
83C2×C22⋊D5—32no—
84C2×C22⋊D5—32no—
85C22×Dic5C2×D311yescharacteristic, complemented
86D4×D5—68no—
87C2×D20—32no—
88C2×D20—31no—
89C2×C4×D5—32no—
90C5×C4⋊C4—31no—
91C5×C22⋊C4—32no—
92C22⋊Dic5—32no—
93#685—32no—
94#685—32no—
95#685C2×D312yescomplemented
96#685C2×D312yescomplemented
97C4⋊Dic5—31no—
98#683—32no—
99#534—151noSylow
100C22×C3×C5—21no—
101C22×C3×C5—21no—
102C22×C3×C5C2×D412yes—
103C22×C3×C5C2411yescharacteristic
104C2×D15—22no—
105C2×D15—22no—
106C2×D15—22no—
107C2×C5×D3—22no—
108C2×C5×D3—22no—
109C2×C5×D3—22no—
110C2×C3×D5—22no—
111C2×C3×D5—22no—
112C2×C3×D5—44no—
113C2×C3×D5C2×D414yes—
114D3×D5—48no—
115C3×C4×C5—21no—
116C3×C4×C5—21no—
117Dic15—22no—
118C3×Dic5—22no—
119C5×Dic3—22no—
120C24×C3—51no—
121C23×D3—52no—
122C22×C3×C4—51no—
123C22×C3×C4C2×D511yescharacteristic, complemented
124C2×#67—52no—
125C2×#67—52no—
126C2×#67—52no—
127C2×#67—108no—
128C2×#67C2×D512yescomplemented
129C22×Dic3—52no—
130C2×D12—52no—
131C2×D12—51no—
132C2×D12C2×D511yescharacteristic, complemented
133C3×C22⋊C4—52no—
134C3×C22⋊C4—52no—
135(C2×D3)⋊C4—52no—
136(C2×D3)⋊C4—52no—
137(C2×D3)⋊C4—52no—
138(C2×D3)⋊C4C2×D512yescomplemented
139C4⋊Dic3—51no—
140C4⋊Dic3—52no—
141C4⋊Dic3C2×D511yescharacteristic, complemented
142C23×C5—32no—
143C23×C5C22×D311yescharacteristic
144C22×D5—32no—
145C22×D5—41no—
146C22×D5—41no—
147C22×D5—64no—
148C22×D5—122no—
149C22×D5—122no—
150C22×D5D1214yescomplemented
151C22×D5C22×D312yes—
152C5×D4—64no—
153C5×D4—121no—
154C2×C4×C5—32no—
155C2×C4×C5—41no—
156C2×C4×C5C22×D311yescharacteristic
157C2×C4×C5C22×D311yescharacteristic
158C22⋊D5—64no—
159C22⋊D5—64no—
160C22⋊D5—122no—
161C2×Dic5—32no—
162C2×Dic5—41no—
163C2×Dic5C22×D312yes—
164D20—64no—
165D20—121no—
166C4×D5—64no—
167C22×D4—152no—
168#123—152no—
169#123—152no—
170#121—31no—
171#121—152no—
172#121—151no—
173#120—152no—
174#120—152no—
175C2×C22⋊C4—51no—
176C2×C3×C5—22no—
177C2×C3×C5C22×D411yescharacteristic
178C2×C3×C5H(5,𝔽2)11yescharacteristic
179C2×C3×C5H(5,𝔽2)11yescharacteristic
180D15—42no—
181C3×D5—24no—
182C5×D3—42no—
183C23×C3—52no—
184C23×C3—54no—
185C23×C3—201no—
186C23×C3—201no—
187C23×C3C22×D511yescharacteristic
188C22×D3—52no—
189C22×D3—104no—
190C22×D3—202no—
191C22×D3—202no—
192C22×D3C22×D512yes—
193C2×C3×C4—41no—
194C2×C3×C4—52no—
195C2×C3×C4—201no—
196C2×C3×C4C22×D511yescharacteristic
197C2×C3×C4C22×D511yescharacteristic
198#67—24no—
199#67—104no—
200#67—104no—
201#67—104no—
202C2×Dic3—52no—
203C2×Dic3—104no—
204C2×Dic3C22×D512yes—
205D12—41no—
206D12—201no—
207D12—202no—
208C22×C5—21no—
209C22×C5—21no—
210C22×C5—62no—
211C22×C5—62no—
212C22×C5—62no—
213C22×C5C2×D1212yes—
214C22×C5C23×D311yescharacteristic
215C2×D5—22no—
216C2×D5—22no—
217C2×D5—44no—
218C2×D5—62no—
219C2×D5—62no—
220C2×D5—62no—
221C2×D5—128no—
222C2×D5C2×D1214yes—
223C4×C5—21no—
224C4×C5—21no—
225C4×C5—62no—
226Dic5—22no—
227Dic5—62no—
228C24—51no—
229C24—152no—
230C2×D4—32no—
231C2×D4—31no—
232C2×D4—152no—
233C2×D4—152no—
234C2×D4—152no—
235C2×D4—152no—
236C2×D4—151no—
237C2×D4—308no—
238C22×C4—51no—
239C22×C4—152no—
240C22×C4D3×D511yescharacteristic, complemented
241C4⋊C4—31no—
242C4⋊C4—152no—
243C4⋊C4—151no—
244C22⋊C4—32no—
245C22⋊C4—52no—
246C22⋊C4—52no—
247C22⋊C4—152no—
248C22⋊C4—152no—
249C22⋊C4—152no—
250C3×C5#53411yescharacteristic, complemented, Hall
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—54no—
254C22×C3—102no—
255C22×C3—102no—
256C22×C3—204no—
257C22×C3D4×D512yes—
258C22×C3C23×D511yescharacteristic
259C2×D3—22no—
260C2×D3—22no—
261C2×D3—22no—
262C2×D3—102no—
263C2×D3—102no—
264C2×D3—102no—
265C2×D3—208no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—102no—
269Dic3—22no—
270Dic3—102no—
271C2×C5—22no—
272C2×C5—122no—
273C2×C5C22×D1211yescharacteristic
274C2×C5#100411yescharacteristic
275C2×C5#100411yescharacteristic
276D5—24no—
277D5—122no—
278C23—32no—
279C23—52no—
280C23—54no—
281C23—152no—
282C23—201no—
283C23—201no—
284C23—304no—
285C23—602no—
286C23—602no—
287C23C2×D3×D511yescharacteristic
288D4—64no—
289D4—121no—
290D4—304no—
291D4—304no—
292D4—304no—
293D4—601no—
294D4—602no—
295C2×C4—32no—
296C2×C4—41no—
297C2×C4—52no—
298C2×C4—152no—
299C2×C4—201no—
300C2×C4—304no—
301C2×C4C2×D3×D511yescharacteristic
302C2×C4C2×D3×D511yescharacteristic
303C2×C3—22no—
304C2×C3—104no—
305C2×C3C2×D4×D511yescharacteristic
306C2×C3#414411yescharacteristic
307C2×C3#414911yescharacteristic
308D3—42no—
309D3—202no—
310C5#549311yescharacteristic, complemented, Sylow
311C22—21no—
312C22—21no—
313C22—54no—
314C22—62no—
315C22—62no—
316C22—62no—
317C22—102no—
318C22—102no—
319C22—204no—
320C22—302no—
321C22—302no—
322C22—302no—
323C22—608no—
324C22D5×D1212yes—
325C22C22×D3×D511yescharacteristic
326C4—21no—
327C4—21no—
328C4—62no—
329C4—102no—
330C4—302no—
331C3#6593911yescharacteristic, complemented, Sylow
332C2—22no—
333C2—104no—
334C2—122no—
335C2—602no—
336C2C2×D5×D1211yescharacteristic
337C2#9201711yescharacteristic
338C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC22×C3×C4×C5C22
hypercenterC22×C4D3×D5
hypocenterC3×C5#534
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×D5×#67C2semidirect
2. #91819C2semidirect
3. C5×#930C2semidirect
4. C2×C3×#685C2semidirect
5. #91566C2semidirect
6. #91476C2semidirect
7. #91475C2semidirect
8. #91414C2semidirect
9. #91413C2semidirect
12. C22×D3×D5C22semidirect
13. C22×C3×C4×C5C22semidirect
14. C2×#1220C22semidirect
15. C2×D60C22semidirect
16. C2×C5×#67C22semidirect
17. C2×C5×D12C22semidirect
18. C22×C3×Dic5C22semidirect
20. C2×#1203C22semidirect
23. C2×D5×Dic3C22semidirect
24. #6714C22semidirect
25. C4⋊Dic15C22semidirect
26. C5×(C2×D3)⋊C4C22semidirect
27. C5×C4⋊Dic3C22semidirect
28. C3×#685C22semidirect
29. C3×#685C22semidirect
30. #6668C22semidirect
31. #6667C22semidirect
32. (C2×D3)⋊Dic5C22semidirect
39. C2×#685D3semidirect
48. C22×C3×D5D4semidirect
72. #930D5semidirect
81. C22×C4×C5C2×D3semidirect
85. C22×Dic5C2×D3semidirect
95. #685C2×D3semidirect
96. #685C2×D3semidirect
123. C22×C3×C4C2×D5semidirect
128. C2×#67C2×D5semidirect
132. C2×D12C2×D5semidirect
138. (C2×D3)⋊C4C2×D5semidirect
141. C4⋊Dic3C2×D5semidirect
150. C22×D5D12semidirect
240. C22×C4D3×D5semidirect
250. C3×C5#534semidirect
310. C5#5493semidirect
331. C3#65939semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#672
#918192
C5×#9302
C2×C3×#6852
#915662
#914762
#914752
#914142
#914132
#659393
#54935