Finite Group Databasebeta

← C2×#91276 #11754005

Subgroups — C2×#91276 #11754005

Order 960.

532 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 136 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×#6768C211yesmaximal, characteristic, complemented
2C2×#6766C211yesmaximal, characteristic, complemented
3C2×C8×D15C211yesmaximal, characteristic, complemented
4C2×C5×#204C211yesmaximal, characteristic, complemented
5C2×C3×#677C211yesmaximal, characteristic, complemented
6C2×#6661C211yesmaximal, characteristic, complemented
7C2×#6652C211yesmaximal, characteristic, complemented
8#91276C218yesmaximal, direct product factor
9C2×#4062—31nomaximal, Hall
10C2×C4×D15C2211yescharacteristic
11C2×C5×D12C2211yescharacteristic
12C2×C5×Dic6C2211yescharacteristic
13C2×C3×D20C2211yescharacteristic
14C2×C3×Dic10C2211yescharacteristic
15C2×#1203—21no—
16C2×#1202—21no—
17C2×D3×Dic5—21no—
18C2×D5×Dic3—21no—
19#6768—22no—
20#6768C2214yescomplemented
21#6766—22no—
22#6766C2214yescomplemented
23C2×C3×C5×C8C2211yescharacteristic
24C2×C3⋊#168C2211yescharacteristic
25C8×D15C2214yescomplemented
26C5×#204C2214yescomplemented
27C3×#677C2214yescomplemented
28#6661C2214yescomplemented
29#6652C2214yescomplemented
30C2×#916—51nomaximal, Hall
31C2×#713—31no—
32C2×#711—31no—
33C2×C5×SD16—31no—
34C2×#689—31no—
35C2×#686—31no—
36#4062—38no—
37C2×#677D311yescharacteristic, complemented
38C2×C8×D5—31no—
39C22×D15D411yescharacteristic
40C22×C5×D3—21no—
41C22×C3×D5—21no—
42C2×C3×C4×C5C2311yescharacteristic
43C2×Dic15D411yescharacteristic
44C4×D15D412yes—
45C4×D15C2312yes—
46C2×C5×Dic3—21no—
47C5×D12—21no—
48C5×D12C2312yes—
49C5×Dic6—21no—
50C5×Dic6C2312yes—
51C2×C3×Dic5—21no—
52C3×D20—21no—
53C3×D20C2312yes—
54C3×Dic10—21no—
55C3×Dic10C2312yes—
56#1203—24no—
57#1202—24no—
58D3×Dic5—24no—
59D5×Dic3—24no—
60C3×C5×C8C2312yes—
61C3⋊#168C2312yes—
62C2×#239—51no—
63C2×#237—51no—
64C2×C3×SD16—51no—
65C2×#216—51no—
66C2×#213—51no—
67#916—58no—
68C2×#204D511yescharacteristic, complemented
69C2×D3×C8—51no—
70C2×C5×Q8—31no—
71C2×C5×D4—31no—
72C2×C22⋊D5—61no—
73C22×Dic5—61no—
74#713—34no—
75#713—62no—
76#711—34no—
77#711—62no—
78C2×D20—61no—
79C2×D20C2×D311yescharacteristic
80C2×C4×D5—31no—
81C2×C4×D5—61no—
82C2×Dic10C2×D311yescharacteristic
83C5×SD16—34no—
84C2×C5×C8C2×D311yescharacteristic
85#689—34no—
86#686—34no—
87C2×#168—31no—
88#677C2×D314yescomplemented
89C8×D5—34no—
90C2×#135—151noSylow
91C22×C3×C5C2×D411yescharacteristic
92C2×D15—22no—
93C2×D15C2×D412yes—
94C2×C5×D3—22no—
95C2×C5×D3—42no—
96C2×C3×D5—22no—
97C2×C3×D5—42no—
98C3×C4×C5C2×D411yescharacteristic
99C3×C4×C5C2411yescharacteristic
100Dic15C2×D412yes—
101C3×Dic5—22no—
102C5×Dic3—22no—
103C2×C3×Q8—51no—
104C2×C3×D4—51no—
105C2×#67—101no—
106C22×Dic3—101no—
107#239—54no—
108#239—102no—
109#237—54no—
110#237—102no—
111C2×D12—101no—
112C2×D12C2×D511yescharacteristic
113C2×C4×D3—51no—
114C2×C4×D3—101no—
115C2×Dic6C2×D511yescharacteristic
116C3×SD16—54no—
117C2×C3×C8C2×D511yescharacteristic
118#216—54no—
119#213—54no—
120C2×C3⋊C8—51no—
121#204C2×D514yescomplemented
122D3×C8—54no—
123C23×C5—61no—
124C22×D5—21no—
125C22×D5—31no—
126C5×Q8—32no—
127C5×Q8—61no—
128C5×D4—32no—
129C5×D4—61no—
130C2×C4×C5—61no—
131C2×C4×C5C22×D311yescharacteristic
132C22⋊D5—64no—
133C2×Dic5—21no—
134C2×Dic5—31no—
135C2×Dic5—64no—
136D20—21no—
137D20—64no—
138D20C22×D312yes—
139C4×D5—32no—
140C4×D5—32no—
141C4×D5—64no—
142Dic10—21no—
143Dic10C22×D312yes—
144C5×C8C22×D312yes—
145#168—32no—
146C2×#41—151no—
147C2×#41—151no—
148#135—158no—
149C2×Q16—151no—
150C2×SD16—31no—
151C2×SD16—51no—
152C2×D8—151no—
153C22×C8—151no—
154C2×C3×C5#13512yescomplemented
155C2×C3×C5C22×D411yescharacteristic
156D15—22no—
157C3×D5—42no—
158C5×D3—42no—
159C23×C3—101no—
160C22×D3—21no—
161C22×D3—51no—
162C3×Q8—52no—
163C3×Q8—101no—
164C3×D4—52no—
165C3×D4—101no—
166C2×C3×C4—101no—
167C2×C3×C4C22×D511yescharacteristic
168#67—104no—
169C2×Dic3—21no—
170C2×Dic3—51no—
171C2×Dic3—104no—
172D12—21no—
173D12—104no—
174D12C22×D512yes—
175C4×D3—52no—
176C4×D3—52no—
177C4×D3—104no—
178Dic6—21no—
179Dic6C22×D512yes—
180C3×C8C22×D512yes—
181C3⋊C8—52no—
182C22×C5—62no—
183C22×C5—122no—
184C22×C5D3×D411yescharacteristic
185C2×D5—22no—
186C2×D5—32no—
187C2×D5—42no—
188C2×D5—62no—
189C4×C5—62no—
190C4×C5D3×D411yescharacteristic
191C4×C5C23×D311yescharacteristic
192Dic5—22no—
193Dic5—32no—
194#41—154no—
195#41—154no—
196#41—302no—
197#41—302no—
198C2×Q8—31no—
199C2×Q8—51no—
200C2×D4—31no—
201C2×D4—51no—
202C2×D4—301no—
203C2×D4—301no—
204C22×C4—151no—
205C22×C4—301no—
206C22×C4—301no—
207Q16—154no—
208SD16—34no—
209SD16—54no—
210D8—154no—
211C2×C8—151no—
212C2×C8—154no—
213C2×C8D3×D511yescharacteristic
214C3×C5C2×#13511yescharacteristic, complemented, Hall
215C22×C3—102no—
216C22×C3—202no—
217C22×C3D4×D511yescharacteristic
218C2×D3—22no—
219C2×D3—42no—
220C2×D3—52no—
221C2×D3—102no—
222C3×C4—102no—
223C3×C4D4×D511yescharacteristic
224C3×C4C23×D511yescharacteristic
225Dic3—22no—
226Dic3—52no—
227C2×C5—122no—
228C2×C5#91612yescomplemented
229C2×C5C2×D3×D411yescharacteristic
230D5—42no—
231D5—62no—
232C23—61no—
233C23—101no—
234C23—151no—
235Q8—32no—
236Q8—52no—
237Q8—61no—
238Q8—101no—
239D4—32no—
240D4—52no—
241D4—61no—
242D4—101no—
243D4—304no—
244D4—304no—
245C2×C4—61no—
246C2×C4—101no—
247C2×C4—151no—
248C2×C4—152no—
249C2×C4—152no—
250C2×C4—304no—
251C2×C4—304no—
252C2×C4C2×D3×D511yescharacteristic
253C8—152no—
254C8C2×D3×D512yes—
255C2×C3—202no—
256C2×C3#406212yescomplemented
257C2×C3C2×D4×D511yescharacteristic
258D3—42no—
259D3—102no—
260C5C2×#91611yescharacteristic, complemented, Sylow
261C22—62no—
262C22—102no—
263C22—122no—
264C22—152no—
265C22—202no—
266C22—302no—
267C22#677711yescharacteristic
268C4—62no—
269C4—102no—
270C4—152no—
271C4#677711yescharacteristic
272C4C22×D3×D511yescharacteristic
273C3C2×#406211yescharacteristic, complemented, Sylow
274C2—122no—
275C2—202no—
276C2—302no—
277C2#9127612yesdirect product factor
278C2C2×#677711yescharacteristic
subgroupG/H
centerC22#6777
commutator, cosocleC3×C4×C5C24
FrattiniC4C22×D3×D5
FittingC2×C3×C5×C8C22
socleC22×C3×C5C2×D4
hypercenterC2×C8D3×D5
hypocenterC3×C5C2×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. C2×#6768C2semidirect
2. C2×#6766C2semidirect
3. C2×C8×D15C2semidirect
4. C2×C5×#204C2semidirect
5. C2×C3×#677C2semidirect
6. C2×#6661C2semidirect
7. C2×#6652C2semidirect
8. #91276C2direct (N × H)
20. #6768C22semidirect
22. #6766C22semidirect
25. C8×D15C22semidirect
26. C5×#204C22semidirect
27. C3×#677C22semidirect
28. #6661C22semidirect
29. #6652C22semidirect
37. C2×#677D3semidirect
68. C2×#204D5semidirect
88. #677C2×D3semidirect
121. #204C2×D5semidirect
154. C2×C3×C5#135semidirect
214. C3×C5C2×#135semidirect
228. C2×C5#916semidirect
256. C2×C3#4062semidirect
260. C5C2×#916semidirect
273. C3C2×#4062semidirect
277. C2#91276direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#67682
C2×#67662
C2×C8×D152
C2×C5×#2042
C2×C3×#6772
C2×#66612
C2×#66522
#912762
C2×#40623
C2×#9165