Finite Group Databasebeta

← C2×#10611642 #12980202

Subgroups — C2×#10611642 #12980202

Order 1280.

2238 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65904C211yesmaximal, characteristic, complemented
2C2×#65911C211yesmaximal, characteristic
3C2×C5×C8×Q8C211yesmaximal, characteristic, complemented
4#10611642C2116yesmaximal, direct product factor
5C2×#65137C213yesmaximal, complemented
6C2×#65130C213yesmaximal, complemented
7C2×C4×#677C213yesmaximal, complemented
8C2×#64982C213yesmaximal, complemented
9C22×#713—21no—
10C2×C4×C5×Q8C2211yescharacteristic
11C2×Q8×Dic5—21no—
12C22×#677C2213yes—
13C22×#677C2216yes—
14#65911—24no—
15#65911C2218yes—
16#65904—24no—
17#65904C2218yescomplemented
18C2×#4041—23no—
19C2×#4036—23no—
20C2×#4020C2213yes—
21C2×C4×D20C2213yes—
22C2×#4015C2213yes—
23C2×C4×Dic10C2213yes—
24C5×C8×Q8C2218yescomplemented
25C2×C5×C4⋊C8C2213yes—
26C2×C4×C5×C8C2213yes—
27C2×#3953C2213yes—
28C2×#3949C2211yescharacteristic
29C2×#3948C2213yes—
30#65137C22124yescomplemented
31#65130C22124yescomplemented
32#64982C22124yescomplemented
33C4×#677C22124yescomplemented
34C2×#3392—51nomaximal, Sylow
35C22×C5×Q8D411yescharacteristic
36C2×#713—28no—
37C2×#713—48no—
38C22×D20—23no—
39C22×D20—23no—
40C22×D20C2313yes—
41C22×C4×D5—23no—
42C22×Dic10C2313yes—
43C22×C5×C8C2313yes—
44C22×C5×C8C2311yescharacteristic
45C4×C5×Q8D414yes—
46C4×C5×Q8C2314yes—
47C2×C5×C4⋊C4D413yes—
48C2×C42×C5C2313yes—
49Q8×Dic5—28no—
50C2×#685—23no—
51C2×C4⋊Dic5—23no—
52C2×C4⋊Dic5—23no—
53C2×C4⋊Dic5C2311yescharacteristic
54C2×C4⋊Dic5C2311yescharacteristic
55C2×#683—23no—
56C2×C4×Dic5—23no—
57C2×#677—212no—
58C2×#677—412no—
59C2×#677C23112yes—
60C2×#677C23124yes—
61#4041—224no—
62#4036—224no—
63#4020—26no—
64#4020C23112yes—
65C4×D20—26no—
66C4×D20C23112yes—
67#4015—26no—
68#4015C23112yes—
69C4×Dic10—26no—
70C4×Dic10C23112yes—
71C5×C4⋊C8C23112yes—
72C4×C5×C8C23112yes—
73#3953C23112yes—
74#3949C2314yes—
75#3948C23112yes—
76C2×#557—51no—
77C2×#550—51no—
78#3392—516no—
79C2×#492—53no—
80C2×#460—53no—
81C2×#461—53no—
82C2×C8×Q8D511yescharacteristic, complemented
83C2×C4×SD16—53no—
84C23×D5—23no—
85C2×C5×Q8SD1618yescomplemented
86C2×C5×Q8C2×D414yes—
87C22×C4×C5C2×D413yes—
88C22×C4×C5C2×D413yes—
89C22×C4×C5C2411yescharacteristic
90C22×Dic5—23no—
91C22×Dic5—21no—
92C22×Dic5—21no—
93#713—432no—
94C2×D20—26no—
95C2×D20—26no—
96C2×D20—212no—
97C2×D20—23no—
98C2×D20—212no—
99C2×D20—412no—
100C2×D20—86no—
101C2×D20C2416yes—
102C2×C4×D5—212no—
103C2×C4×D5—412no—
104C2×Dic10—26no—
105C2×Dic10—26no—
106C2×Dic10—23no—
107C2×Dic10C2416yes—
108C2×C5×C8—26no—
109C2×C5×C8#4114yescomplemented
110C2×C5×C8C2416yes—
111C2×C5×C8C2412yes—
112C5×C4⋊C4C2×D4112yes—
113C42×C5C2×D416yes—
114C42×C5C2416yes—
115#685—212no—
116C4⋊Dic5—21no—
117C4⋊Dic5—212no—
118C4⋊Dic5—212no—
119C4⋊Dic5—21no—
120C4⋊Dic5C2412yes—
121C4⋊Dic5C2412yes—
122#683—212no—
123C4×Dic5—212no—
124#677—224no—
125#677—424no—
126C22×#41—101no—
127C22×SD16—53no—
128C22×SD16—56no—
129#557—58no—
130#557—104no—
131#550—58no—
132#550—104no—
133C2×C4⋊Q8—53no—
134C2×#127—53no—
135C2×#125—103no—
136C2×#121—103no—
137C2×C4×Q8—53no—
138C2×C4×Q8—101no—
139C2×C4×Q8C2×D511yescharacteristic
140C2×C4×D4—53no—
141#492—524no—
142#461—524no—
143#460—524no—
144C8×Q8C2×D518yescomplemented
145C4×SD16—524no—
146C2×#106—51no—
147C2×C4⋊C8C2×D513yes—
148C2×#103—53no—
149C2×#102—53no—
150C2×C4×C8C2×D513yes—
151C23×C5C22×D411yescharacteristic
152C22×D5—26no—
153C22×D5—46no—
154C22×D5—46no—
155C22×D5—46no—
156C5×Q8C2×SD16116yescomplemented
157C2×C4×C5—26no—
158C2×C4×C5C2×SD16112yes—
159C2×C4×C5C22×D416yes—
160C2×C4×C5C22×D411yescharacteristic
161C2×C4×C5C22×D416yes—
162C2×C4×C5C2×#4112yes—
163C2×C4×C5H(5,𝔽2)12yes—
164C2×C4×C5C2511yescharacteristic
165C2×Dic5—22no—
166C2×Dic5—26no—
167C2×Dic5—22no—
168C2×Dic5—46no—
169C2×Dic5—42no—
170C2×Dic5—42no—
171D20—26no—
172D20—26no—
173D20—46no—
174D20—424no—
175D20—812no—
176C4×D5—424no—
177Dic10—26no—
178Dic10—26no—
179Dic10—46no—
180C5×C8—26no—
181C5×C8C2×#4114yescomplemented
182C2×#41—108no—
183C2×#41—208no—
184C22×Q8—53no—
185C22×Q8D2011yescharacteristic
186C22×D4—53no—
187C22×D4—103no—
188C22×D4—103no—
189C23×C4—103no—
190C2×SD16—512no—
191C2×SD16—524no—
192C2×SD16—1012no—
193C2×SD16—2012no—
194C22×C8C22×D513yes—
195C22×C8C22×D511yescharacteristic
196C4⋊Q8—512no—
197C4⋊Q8—106no—
198#127—512no—
199#127—106no—
200#125—1024no—
201#121—1024no—
202C4×Q8—512no—
203C4×Q8—108no—
204C4×Q8—106no—
205C4×Q8D2014yes—
206C4×Q8C22×D514yes—
207C4×D4—512no—
208C4×D4—106no—
209C2×C4⋊C4—51no—
210C2×C4⋊C4—51no—
211C2×C4⋊C4—103no—
212C2×C4⋊C4—103no—
213C2×C4⋊C4—103no—
214C2×C4⋊C4D2013yes—
215C2×C22⋊C4—103no—
216C2×C42—103no—
217C2×C42C22×D513yes—
218#106—54no—
219C4⋊C8C22×D5112yes—
220#103—512no—
221#102—512no—
222C4×C8C22×D5112yes—
223C22×C5#55012yes—
224C22×C5C22×SD1612yes—
225C22×C5#57712yes—
226C22×C5C23×D411yescharacteristic
227C2×D5—46no—
228C2×D5—46no—
229C2×D5—46no—
230C2×D5—812no—
231C4×C5—26no—
232C4×C5#55012yes—
233C4×C5C22×SD16112yes—
234C4×C5C22×#4111yescharacteristic
235C4×C5C2×H(5,𝔽2)11yescharacteristic
236Dic5—46no—
237Dic5—42no—
238Dic5—42no—
239C24—103no—
240#41—2032no—
241C2×Q8—56no—
242C2×Q8—103no—
243C2×Q8—106no—
244C2×Q8—106no—
245C2×Q8#67718yescomplemented
246C2×Q8C2×D2014yes—
247C2×D4—56no—
248C2×D4—103no—
249C2×D4—1012no—
250C2×D4—1012no—
251C2×D4—106no—
252C2×D4—106no—
253C2×D4—2012no—
254C2×D4—406no—
255C22×C4—101no—
256C22×C4—103no—
257C22×C4—101no—
258C22×C4—1012no—
259C22×C4—2012no—
260C22×C4C2×D2013yes—
261C22×C4C2×D2013yes—
262C22×C4C23×D511yescharacteristic
263SD16—1024no—
264SD16—2024no—
265C2×C8—26no—
266C2×C8#71314yescomplemented
267C2×C8C23×D516yes—
268C2×C8C23×D512yes—
269C4⋊C4—52no—
270C4⋊C4—52no—
271C4⋊C4—101no—
272C4⋊C4—101no—
273C4⋊C4—1012no—
274C4⋊C4—1012no—
275C4⋊C4—1012no—
276C4⋊C4C2×D20112yes—
277C22⋊C4—1012no—
278C42—1012no—
279C42C2×D2016yes—
280C42C23×D516yes—
281C2×C5#339214yescomplemented
282C2×C5C2×#55011yescharacteristic
283C2×C5C23×SD1611yescharacteristic
284C2×C5C2×#57711yescharacteristic
285D5—86no—
286C23—106no—
287C23—206no—
288C23—206no—
289C23—206no—
290C23C22×D2011yescharacteristic
291Q8—106no—
292Q8—106no—
293Q8—206no—
294Q8C2×#677116yescomplemented
295D4—106no—
296D4—106no—
297D4—2024no—
298D4—206no—
299D4—4012no—
300C2×C4—26no—
301C2×C4—102no—
302C2×C4—106no—
303C2×C4—102no—
304C2×C4—202no—
305C2×C4—202no—
306C2×C4—206no—
307C2×C4—2024no—
308C2×C4C2×#677112yes—
309C2×C4C22×D2016yes—
310C2×C4C22×D2016yes—
311C2×C4C22×D2011yescharacteristic
312C2×C4C2×#71312yes—
313C2×C4#414912yes—
314C2×C4C24×D511yescharacteristic
315C8—26no—
316C8C2×#71314yescomplemented
317C5C2×#339211yescharacteristic, complemented, Sylow
318C22—206no—
319C22—206no—
320C22—206no—
321C22—4012no—
322C22#6591112yes—
323C22C22×#67712yes—
324C22#6608512yes—
325C22C23×D2011yescharacteristic
326C4—26no—
327C4—206no—
328C4—202no—
329C4—202no—
330C4#6591112yes—
331C4C22×#677112yes—
332C4C22×#71311yescharacteristic
333C4C2×#414911yescharacteristic
334C2—406no—
335C2#1061164214yesdirect product factor
336C2C2×#6591111yescharacteristic
337C2C23×#67711yescharacteristic
338C2C2×#6608511yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×C8×Q8C2
socleC23×C5C22×D4
prime radicalC2×#65911C2
hypercenterC2×C8×Q8D5
hypocenterC5C2×#3392
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#65904C2semidirect
3. C2×C5×C8×Q8C2semidirect
4. #10611642C2direct (N × H)
5. C2×#65137C2semidirect
6. C2×#65130C2semidirect
7. C2×C4×#677C2semidirect
8. C2×#64982C2semidirect
17. #65904C22semidirect
24. C5×C8×Q8C22semidirect
30. #65137C22semidirect
31. #65130C22semidirect
32. #64982C22semidirect
33. C4×#677C22semidirect
82. C2×C8×Q8D5semidirect
85. C2×C5×Q8SD16semidirect
109. C2×C5×C8#41semidirect
144. C8×Q8C2×D5semidirect
156. C5×Q8C2×SD16semidirect
181. C5×C8C2×#41semidirect
245. C2×Q8#677semidirect
266. C2×C8#713semidirect
281. C2×C5#3392semidirect
294. Q8C2×#677semidirect
316. C8C2×#713semidirect
317. C5C2×#3392semidirect
335. C2#10611642direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659042
C2×#659112
C2×C5×C8×Q82
#106116422
C2×#651372
C2×#651302
C2×C4×#6772
C2×#649822
C2×#33925