Finite Group Databasebeta

← C2×#91461 #11754552

Subgroups — C2×#91461 #11754552

Order 960.

852 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 176 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
1C22×C4×D15C211yesmaximal, characteristic, complemented
2C22×#1203C211yesmaximal, characteristic, complemented
3C22×#1202C211yesmaximal, characteristic, complemented
4C22×#1201C211yesmaximal, characteristic, complemented
5C2×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C2×C3×#685C211yesmaximal, characteristic, complemented
7C2×#6669C211yesmaximal, characteristic, complemented
8#91461C218yesmaximal, direct product factor
9C2×#4030—31nomaximal, Hall
10C23×D15C2211yescharacteristic
11C23×C5×D3C2211yescharacteristic
12C23×C3×D5C2211yescharacteristic
13C22×C3×C4×C5C2211yescharacteristic
14C22×Dic15C2211yescharacteristic
15C2×C4×D15—24no—
16C2×C4×D15C2214yescomplemented
17C22×C5×Dic3C2211yescharacteristic
18C22×C3×Dic5C2211yescharacteristic
19C2×#1203—24no—
20C2×#1203C2214yescomplemented
21C2×#1202—24no—
22C2×#1202C2214yescomplemented
23C2×#1201—24no—
24C2×#1201C2214yescomplemented
25C5×(C2×D3)⋊C4C2214yescomplemented
26C3×#685C2214yescomplemented
27#6669C2214yescomplemented
28C2×#884—51nomaximal, Hall
29C22×C22⋊D5—31no—
30C22×C22⋊D5—31no—
31C22×D20—31no—
32C22×C4×D5—31no—
33C2×C5×C22⋊C4—31no—
34C2×#685D311yescharacteristic, complemented
35C2×#683—31no—
36#4030—38no—
37C23×C3×C5C2311yescharacteristic
38C22×D15—22no—
39C22×D15—22no—
40C22×D15D414yescomplemented
41C22×D15C2312yes—
42C22×C5×D3—22no—
43C22×C5×D3—22no—
44C22×C5×D3—22no—
45C22×C5×D3C2312yes—
46C22×C3×D5—22no—
47C22×C3×D5—22no—
48C22×C3×D5—22no—
49C22×C3×D5C2312yes—
50C2×C3×C4×C5—22no—
51C2×C3×C4×C5C2312yes—
52C2×Dic15D414yescomplemented
53C2×Dic15C2312yes—
54C4×D15—28no—
55C2×C5×Dic3—22no—
56C2×C5×Dic3C2312yes—
57C2×C3×Dic5—22no—
58C2×C3×Dic5C2312yes—
59#1203—28no—
60#1202—28no—
61#1201—28no—
62C22×#67—51no—
63C22×#67—51no—
64C22×D12—51no—
65C22×C4×D3—51no—
66C2×C3×C22⋊C4—51no—
67C2×(C2×D3)⋊C4D511yescharacteristic, complemented
68C2×Dic3⋊C4—51no—
69#884—58no—
70C24×C5—31no—
71C23×D5—31no—
72C23×D5C2×D311yescharacteristic
73C22×C4×C5—31no—
74C22×C4×C5C2×D311yescharacteristic
75C2×C22⋊D5—34no—
76C2×C22⋊D5—34no—
77C2×C22⋊D5—64no—
78C2×C22⋊D5—64no—
79C22×Dic5—31no—
80C22×Dic5C2×D311yescharacteristic
81C2×D20—34no—
82C2×D20—64no—
83C2×C4×D5—34no—
84C2×C4×D5—64no—
85C5×C22⋊C4—34no—
86#685C2×D314yescomplemented
87#683—34no—
88C2×#121—151noSylow
89C22×C3×C5C2×D412yes—
90C22×C3×C5C2×D412yes—
91C22×C3×C5#4112yes—
92C22×C3×C5C2411yescharacteristic
93C2×D15—28no—
94C2×D15—22no—
95C2×D15—22no—
96C2×D15C2×D414yescomplemented
97C2×C5×D3—22no—
98C2×C5×D3—22no—
99C2×C5×D3—22no—
100C2×C5×D3—44no—
101C2×C3×D5—22no—
102C2×C3×D5—22no—
103C2×C3×D5—22no—
104C2×C3×D5—44no—
105C3×C4×C5—22no—
106Dic15C2×D414yescomplemented
107C3×Dic5—22no—
108C5×Dic3—22no—
109C24×C3—51no—
110C23×D3—51no—
111C23×D3C2×D511yescharacteristic
112C22×C3×C4—51no—
113C22×C3×C4C2×D511yescharacteristic
114C2×#67—54no—
115C2×#67—54no—
116C2×#67—104no—
117C2×#67—104no—
118C22×Dic3—51no—
119C22×Dic3C2×D511yescharacteristic
120C2×D12—54no—
121C2×D12—104no—
122C2×C4×D3—54no—
123C2×C4×D3—104no—
124C3×C22⋊C4—54no—
125(C2×D3)⋊C4C2×D514yescomplemented
126Dic3⋊C4—54no—
127C23×C5—32no—
128C23×C5—62no—
129C23×C5—62no—
130C23×C5—62no—
131C23×C5C22×D311yescharacteristic
132C22×D5—22no—
133C22×D5—22no—
134C22×D5—22no—
135C22×D5—34no—
136C22×D5—32no—
137C22×D5—62no—
138C22×D5—62no—
139C22×D5C22×D312yes—
140C2×C4×C5—22no—
141C2×C4×C5—32no—
142C2×C4×C5—62no—
143C2×C4×C5C22×D312yes—
144C22⋊D5—68no—
145C22⋊D5—68no—
146C2×Dic5—22no—
147C2×Dic5—34no—
148C2×Dic5—32no—
149C2×Dic5C22×D312yes—
150D20—68no—
151C4×D5—68no—
152C22×D4—151no—
153C22×D4—151no—
154C22×D4—151no—
155C23×C4—151no—
156#121—158no—
157C2×C4⋊C4—151no—
158C2×C22⋊C4—31no—
159C2×C22⋊C4—51no—
160C2×C3×C5#12114yescomplemented
161C2×C3×C5C22×D411yescharacteristic
162C2×C3×C5C22×D411yescharacteristic
163C2×C3×C5C2×#4111yescharacteristic
164D15—24no—
165C3×D5—42no—
166C5×D3—42no—
167C23×C3—52no—
168C23×C3—102no—
169C23×C3—102no—
170C23×C3—102no—
171C23×C3C22×D511yescharacteristic
172C22×D3—22no—
173C22×D3—22no—
174C22×D3—22no—
175C22×D3—54no—
176C22×D3—52no—
177C22×D3—102no—
178C22×D3—102no—
179C22×D3C22×D512yes—
180C2×C3×C4—22no—
181C2×C3×C4—52no—
182C2×C3×C4—102no—
183C2×C3×C4C22×D512yes—
184#67—108no—
185#67—108no—
186C2×Dic3—22no—
187C2×Dic3—54no—
188C2×Dic3—52no—
189C2×Dic3C22×D512yes—
190D12—108no—
191C4×D3—108no—
192C22×C5—62no—
193C22×C5—62no—
194C22×C5—62no—
195C22×C5—124no—
196C22×C5#23512yes—
197C22×C5D3×D412yes—
198C22×C5D3×D412yes—
199C22×C5C23×D311yescharacteristic
200C2×D5—22no—
201C2×D5—22no—
202C2×D5—22no—
203C2×D5—34no—
204C2×D5—44no—
205C2×D5—68no—
206C2×D5—62no—
207C2×D5—62no—
208C4×C5—22no—
209C4×C5—62no—
210Dic5—22no—
211Dic5—34no—
212C24—31no—
213C24—51no—
214C24—151no—
215C2×D4—154no—
216C2×D4—154no—
217C2×D4—154no—
218C2×D4—304no—
219C2×D4—304no—
220C2×D4—304no—
221C22×C4—31no—
222C22×C4—51no—
223C22×C4—151no—
224C22×C4—154no—
225C22×C4—304no—
226C22×C4D3×D511yescharacteristic
227C4⋊C4—154no—
228C22⋊C4—34no—
229C22⋊C4—54no—
230C3×C5C2×#12111yescharacteristic, complemented, Hall
231C22×C3—102no—
232C22×C3—102no—
233C22×C3—102no—
234C22×C3—204no—
235C22×C3#70912yes—
236C22×C3D4×D512yes—
237C22×C3D4×D512yes—
238C22×C3C23×D511yescharacteristic
239C2×D3—22no—
240C2×D3—22no—
241C2×D3—22no—
242C2×D3—44no—
243C2×D3—54no—
244C2×D3—102no—
245C2×D3—102no—
246C2×D3—108no—
247C3×C4—22no—
248C3×C4—102no—
249Dic3—22no—
250Dic3—54no—
251C2×C5—122no—
252C2×C5#88414yescomplemented
253C2×C5C2×#23511yescharacteristic
254C2×C5C2×D3×D411yescharacteristic
255C2×C5C2×D3×D411yescharacteristic
256D5—42no—
257D5—64no—
258C23—32no—
259C23—52no—
260C23—62no—
261C23—62no—
262C23—62no—
263C23—102no—
264C23—102no—
265C23—102no—
266C23—154no—
267C23—152no—
268C23—302no—
269C23—302no—
270C23C2×D3×D511yescharacteristic
271D4—308no—
272D4—308no—
273D4—308no—
274C2×C4—22no—
275C2×C4—32no—
276C2×C4—52no—
277C2×C4—62no—
278C2×C4—102no—
279C2×C4—154no—
280C2×C4—152no—
281C2×C4—308no—
282C2×C4C2×D3×D512yes—
283C2×C3—202no—
284C2×C3#403014yescomplemented
285C2×C3C2×#70911yescharacteristic
286C2×C3C2×D4×D511yescharacteristic
287C2×C3C2×D4×D511yescharacteristic
288D3—42no—
289D3—104no—
290C5C2×#88411yescharacteristic, complemented, Sylow
291C22—62no—
292C22—62no—
293C22—62no—
294C22—102no—
295C22—102no—
296C22—102no—
297C22—124no—
298C22—154no—
299C22—204no—
300C22—308no—
301C22—302no—
302C22—302no—
303C22#677112yes—
304C22#677712yes—
305C22#679012yes—
306C22C22×D3×D511yescharacteristic
307C4—22no—
308C4—62no—
309C4—102no—
310C4—154no—
311C3C2×#403011yescharacteristic, complemented, Sylow
312C2—122no—
313C2—202no—
314C2—304no—
315C2#9146114yesdirect product factor
316C2C2×#677111yescharacteristic
317C2C2×#677711yescharacteristic
318C2C2×#679011yescharacteristic
subgroupG/H
centerC23C2×D3×D5
commutator, cosocleC22×C3×C5C24
FrattiniC22C22×D3×D5
FittingC22×C3×C4×C5C22
socleC23×C3×C5C23
hypercenterC22×C4D3×D5
hypocenterC3×C5C2×#121
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×D15C2semidirect
2. C22×#1203C2semidirect
3. C22×#1202C2semidirect
4. C22×#1201C2semidirect
5. C2×C5×(C2×D3)⋊C4C2semidirect
6. C2×C3×#685C2semidirect
7. C2×#6669C2semidirect
8. #91461C2direct (N × H)
16. C2×C4×D15C22semidirect
20. C2×#1203C22semidirect
22. C2×#1202C22semidirect
24. C2×#1201C22semidirect
25. C5×(C2×D3)⋊C4C22semidirect
26. C3×#685C22semidirect
27. #6669C22semidirect
34. C2×#685D3semidirect
40. C22×D15D4semidirect
52. C2×Dic15D4semidirect
67. C2×(C2×D3)⋊C4D5semidirect
86. #685C2×D3semidirect
96. C2×D15C2×D4semidirect
106. Dic15C2×D4semidirect
125. (C2×D3)⋊C4C2×D5semidirect
160. C2×C3×C5#121semidirect
230. C3×C5C2×#121semidirect
252. C2×C5#884semidirect
284. C2×C3#4030semidirect
290. C5C2×#884semidirect
311. C3C2×#4030semidirect
315. C2#91461direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D152
C22×#12032
C22×#12022
C22×#12012
C2×C5×(C2×D3)⋊C42
C2×C3×#6852
C2×#66692
#914612
C2×#40303
C2×#8845