Finite Group Databasebeta

← C2×C8×#713 #12963733

Subgroups — C2×C8×#713 #12963733

Order 1280.

2566 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#713C211yesmaximal, characteristic
2C2×C5×C8×Q8C211yesmaximal, characteristic, complemented
3C2×Q8×#168C211yesmaximal, characteristic, complemented
4C8×#713C2116yesmaximal, direct product factor
5C2×#65123C213yesmaximal, complemented
6C2×#65122C213yesmaximal, complemented
7C2×C8×D20C213yesmaximal, complemented
8C2×C4×C8×D5C213yesmaximal, complemented
9C22×#713C411yescharacteristic
10C2×C4×C5×Q8C2211yescharacteristic
11C2×Q8×Dic5C411yescharacteristic
12C22×C8×D5C2213yes—
13C22×C8×D5C2213yes—
14C4×#713C418yes—
15C4×#713C2218yes—
16C2×#4039C413yes—
17C2×#4038C413yes—
18C2×C4×D20C2213yes—
19C2×C42×D5C2213yes—
20C5×C8×Q8C2218yescomplemented
21C2×C5×C4⋊C8C2213yes—
22C2×C4×C5×C8C2213yes—
23C2×#3952C2216yes—
24C2×C8×Dic5C2211yescharacteristic
25C2×C8×Dic5C2213yes—
26Q8×#168C2218yescomplemented
27C2×C4⋊#168C2213yes—
28C2×C4×#168C2213yes—
29#65123C22124yescomplemented
30#65122C22124yescomplemented
31C8×D20C22124yescomplemented
32C4×C8×D5C22124yescomplemented
33C2×C8×#41—51nomaximal, Sylow
34C22×C5×Q8C2×C411yescharacteristic
35C2×#713C8116yesdirect product factor
36C2×#713C2×C418yes—
37C22×D20C2×C413yes—
38C22×C4×D5C2×C413yes—
39C22×C4×D5C2×C413yes—
40C22×C4×D5C2313yes—
41C22×C5×C8C2313yes—
42C22×C5×C8C2311yescharacteristic
43C4×C5×Q8C2×C414yes—
44C4×C5×Q8C2314yes—
45C2×C5×C4⋊C4C2×C413yes—
46C2×C42×C5C2313yes—
47Q8×Dic5C2×C418yes—
48C2×#685C2×C416yes—
49C2×C4⋊Dic5C2×C413yes—
50C2×C4×Dic5C2×C413yes—
51C2×C4×Dic5C2×C413yes—
52C2×C4×Dic5C2311yescharacteristic
53C22×#168C2313yes—
54C22×#168C2311yescharacteristic
55C2×C8×D5—212no—
56C2×C8×D5—212no—
57C2×C8×D5C23112yes—
58C2×C8×D5C23112yes—
59#4039C2×C4124yes—
60#4038C2×C4124yes—
61C4×D20C2×C4112yes—
62C4×D20C23112yes—
63C42×D5C2×C4112yes—
64C42×D5C23112yes—
65C5×C4⋊C8C23112yes—
66C4×C5×C8C23112yes—
67#3952C23124yes—
68C8×Dic5C23112yes—
69C8×Dic5C2314yes—
70C4⋊#168C23112yes—
71C4×#168C23112yes—
72C2×C4×#41—51no—
73C8×#41—516no—
74C2×C8×Q8—51no—
75C2×C8×Q8D511yescharacteristic, complemented
76C2×C8×D4—53no—
77C2×C8×D4—53no—
78C2×#431—53no—
79C22×C4×C8—53no—
80C23×D5C22×C413yes—
81C2×C5×Q8C2×C818yescomplemented
82C2×C5×Q8C22×C414yes—
83C22×C4×C5C22×C413yes—
84C22×C4×C5C22×C413yes—
85C22×C4×C5C2411yescharacteristic
86C22×Dic5C22×C413yes—
87C22×Dic5C22×C411yescharacteristic
88C22×Dic5C22×C411yescharacteristic
89#713C2×C8164yesdirect product factor
90C2×D20C2×C8124yescomplemented
91C2×D20C22×C4112yes—
92C2×C4×D5—26no—
93C2×C4×D5—26no—
94C2×C4×D5—212no—
95C2×C4×D5C2×C8124yescomplemented
96C2×C4×D5C22×C4112yes—
97C2×C4×D5C22×C416yes—
98C2×C4×D5C22×C4112yes—
99C2×C4×D5C2416yes—
100C2×C5×C8—26no—
101C2×C5×C8#4114yescomplemented
102C2×C5×C8C2416yes—
103C2×C5×C8C2412yes—
104C5×C4⋊C4C22×C4112yes—
105C42×C5C22×C416yes—
106C42×C5C2416yes—
107#685C22×C4124yes—
108C4⋊Dic5C22×C4112yes—
109C4×Dic5C22×C412yes—
110C4×Dic5C22×C4112yes—
111C4×Dic5C22×C4112yes—
112C4×Dic5C2412yes—
113C2×#168—26no—
114C2×#168#4114yescomplemented
115C2×#168C2416yes—
116C2×#168C2412yes—
117C8×D5—224no—
118C8×D5—224no—
119C22×#41—51no—
120C23×C8—53no—
121C23×C8—53no—
122C4×#41—58no—
123C4×#41—58no—
124C2×C4×Q8—51no—
125C2×C4×Q8C2×D511yescharacteristic
126C2×C4×D4—53no—
127C2×C4×D4—53no—
128C2×#117—53no—
129C22×C42—53no—
130C8×Q8—58no—
131C8×Q8C2×D518yescomplemented
132C8×D4—524no—
133C8×D4—524no—
134#431—524no—
135C2×C4⋊C8—53no—
136C2×C4⋊C8C2×D513yes—
137C2×C22⋊C8—56no—
138C2×C4×C8—53no—
139C2×C4×C8—51no—
140C2×C4×C8—53no—
141C2×C4×C8—524no—
142C2×C4×C8C2×D513yes—
143C23×C5C23×C411yescharacteristic
144C22×D5—26no—
145C22×D5—26no—
146C22×D5C22×C8112yes—
147C22×D5C23×C416yes—
148C5×Q8C22×C8116yescomplemented
149C2×C4×C5—26no—
150C2×C4×C5C22×C8112yes—
151C2×C4×C5C23×C416yes—
152C2×C4×C5C23×C411yescharacteristic
153C2×C4×C5C23×C416yes—
154C2×C4×C5C2×#4112yes—
155C2×C4×C5C2×#4112yes—
156C2×C4×C5C2511yescharacteristic
157C2×Dic5—26no—
158C2×Dic5C22×C814yes—
159C2×Dic5#13114yes—
160C2×Dic5C23×C416yes—
161C2×Dic5C23×C412yes—
162C2×Dic5C23×C412yes—
163D20C22×C8148yescomplemented
164C4×D5—212no—
165C4×D5—26no—
166C4×D5—26no—
167C4×D5—224no—
168C4×D5C22×C8148yescomplemented
169C5×C8—26no—
170C5×C8C2×#4114yescomplemented
171#168—26no—
172#168C2×#4114yescomplemented
173C2×#41—516no—
174C2×#41—58no—
175C22×Q8C4×D511yescharacteristic
176C22×D4—53no—
177C23×C4—53no—
178C23×C4—53no—
179C23×C4—53no—
180C22×C8—51no—
181C22×C8—53no—
182C22×C8—512no—
183C22×C8—512no—
184C22×C8—1012no—
185C22×C8—1012no—
186C22×C8C22×D513yes—
187C22×C8C22×D511yescharacteristic
188C4×Q8—58no—
189C4×Q8C4×D514yes—
190C4×Q8C22×D514yes—
191C4×D4—524no—
192C4×D4—512no—
193C4×D4—512no—
194#117—524no—
195C2×C4⋊C4—53no—
196C2×C4⋊C4C4×D513yes—
197C2×C22⋊C4—56no—
198C2×C42—53no—
199C2×C42—53no—
200C2×C42—51no—
201C2×C42—512no—
202C2×C42—512no—
203C2×C42C22×D513yes—
204C4⋊C8—512no—
205C4⋊C8C22×D5112yes—
206C22⋊C8—524no—
207C4×C8—54no—
208C4×C8—512no—
209C4×C8—512no—
210C4×C8C22×D5112yes—
211C22×C5C4×#4112yes—
212C22×C5C23×C812yes—
213C22×C5C2×#13112yes—
214C22×C5C24×C411yescharacteristic
215C2×D5—26no—
216C2×D5—224no—
217C2×D5—26no—
218C2×D5C23×C8112yes—
219C4×C5—26no—
220C4×C5C4×#4112yes—
221C4×C5C23×C8112yes—
222C4×C5C22×#4111yescharacteristic
223C4×C5C22×#4111yescharacteristic
224Dic5—26no—
225Dic5C23×C814yes—
226Dic5C2×#13114yes—
227C24—53no—
228#41—564no—
229C2×Q8C8×D518yescomplemented
230C2×Q8C2×C4×D514yes—
231C2×D4—512no—
232C2×D4—524no—
233C22×C4—51no—
234C22×C4—51no—
235C22×C4—512no—
236C22×C4—524no—
237C22×C4—53no—
238C22×C4—512no—
239C22×C4—56no—
240C22×C4—56no—
241C22×C4—1012no—
242C22×C4—106no—
243C22×C4—106no—
244C22×C4C2×C4×D513yes—
245C22×C4C2×C4×D513yes—
246C22×C4C23×D511yescharacteristic
247C2×C8—26no—
248C2×C8—54no—
249C2×C8—52no—
250C2×C8—56no—
251C2×C8—1024no—
252C2×C8—106no—
253C2×C8—1024no—
254C2×C8#71314yesdirect product factor
255C2×C8C23×D516yes—
256C2×C8C23×D512yes—
257C4⋊C4—512no—
258C4⋊C4C2×C4×D5112yes—
259C22⋊C4—524no—
260C42—52no—
261C42—512no—
262C42—512no—
263C42—52no—
264C42C2×C4×D516yes—
265C42C23×D516yes—
266C2×C5C8×#4114yescomplemented
267C2×C5C2×C4×#4111yescharacteristic
268C2×C5C24×C811yescharacteristic
269C2×C5C22×#13111yescharacteristic
270D5—212no—
271C23—512no—
272C23—56no—
273C23—106no—
274C23—106no—
275C23C22×C4×D511yescharacteristic
276Q8C2×C8×D5116yescomplemented
277D4—548no—
278C2×C4—26no—
279C2×C4—54no—
280C2×C4—54no—
281C2×C4—52no—
282C2×C4—52no—
283C2×C4—548no—
284C2×C4—56no—
285C2×C4—1024no—
286C2×C4—106no—
287C2×C4—1012no—
288C2×C4—106no—
289C2×C4—106no—
290C2×C4C2×C8×D5112yes—
291C2×C4C22×C4×D516yes—
292C2×C4C22×C4×D516yes—
293C2×C4C22×C4×D511yescharacteristic
294C2×C4C2×#71312yes—
295C2×C4D5×#4112yes—
296C2×C4C24×D511yescharacteristic
297C8—26no—
298C8—54no—
299C8—106no—
300C8C2×#71314yesdirect product factor
301C5C2×C8×#4111yescharacteristic, complemented, Sylow
302C22—512no—
303C22—106no—
304C22—1024no—
305C22—106no—
306C22C4×#71312yes—
307C22C22×C8×D512yes—
308C22D5×#13112yes—
309C22C23×C4×D511yescharacteristic
310C4—26no—
311C4—54no—
312C4—54no—
313C4—106no—
314C4C4×#71312yes—
315C4C22×C8×D5112yes—
316C4C22×#71311yescharacteristic
317C4C2×D5×#4111yescharacteristic
318C2—1012no—
319C2C8×#71314yesdirect product factor
320C2C2×C4×#71311yescharacteristic
321C2C23×C8×D511yescharacteristic
322C2C2×D5×#13111yescharacteristic
subgroupG/H
centerC22×C8C22×D5
commutatorC2×C5C24×C8
FrattiniC2×C4C24×D5
FittingC2×C5×C8×Q8C2
socleC23×C5C23×C4
prime radicalC22×#713C4
cosocleC2×C4×C5C25
hypercenterC2×C8×Q8D5
hypocenterC5C2×C8×#41
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C5×C8×Q8C2semidirect
3. C2×Q8×#168C2semidirect
4. C8×#713C2direct (N × H)
5. C2×#65123C2semidirect
6. C2×#65122C2semidirect
7. C2×C8×D20C2semidirect
8. C2×C4×C8×D5C2semidirect
20. C5×C8×Q8C22semidirect
26. Q8×#168C22semidirect
29. #65123C22semidirect
30. #65122C22semidirect
31. C8×D20C22semidirect
32. C4×C8×D5C22semidirect
35. C2×#713C8direct (N × H)
75. C2×C8×Q8D5semidirect
81. C2×C5×Q8C2×C8semidirect
89. #713C2×C8direct (N × H)
90. C2×D20C2×C8semidirect
95. C2×C4×D5C2×C8semidirect
101. C2×C5×C8#41semidirect
114. C2×#168#41semidirect
131. C8×Q8C2×D5semidirect
148. C5×Q8C22×C8semidirect
163. D20C22×C8semidirect
168. C4×D5C22×C8semidirect
170. C5×C8C2×#41semidirect
172. #168C2×#41semidirect
229. C2×Q8C8×D5semidirect
254. C2×C8#713direct (N × H)
266. C2×C5C8×#41semidirect
276. Q8C2×C8×D5semidirect
300. C8C2×#713direct (N × H)
301. C5C2×C8×#41semidirect
319. C2C8×#713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#7132
C2×C5×C8×Q82
C2×Q8×#1682
C8×#7132
C2×#651232
C2×#651222
C2×C8×D202
C2×C4×C8×D52
C2×C8×#415