Finite Group Databasebeta

← C2×#10601886 #12253867

Subgroups — C2×#10601886 #12253867

Order 1280.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#472C211yesmaximal, characteristic
2C22×#3959C211yesmaximal, characteristic, complemented
3C2×#65432C211yesmaximal, characteristic, complemented
4C2×#65429C211yesmaximal, characteristic, complemented
5C2×#64783C211yesmaximal, characteristic, complemented
6#10601886C218yesmaximal, direct product factor
7C2×#64716C211yesmaximal, characteristic, complemented
8C2×#64713C211yesmaximal, characteristic, complemented
9C2×C5×AGL(1,ℤ/8)—21no—
10C22×C5×D8C2211yescharacteristic
11C2×C5×#131C2211yescharacteristic
12C2×#4097—21no—
13C22×Dic20C2211yescharacteristic
14C5×#472—22no—
15C5×#472C2214yes—
16C2×C5×#108C2211yescharacteristic
17C2×C5×#100—21no—
18C2×#3959—21no—
19C2×#3959—21no—
20C2×#3959—22no—
21C2×#3959C2214yescomplemented
22#65432—22no—
23#65432C2214yescomplemented
24#65429—22no—
25#65429C2214yescomplemented
26C2×#3956—21no—
27C2×#3951C2211yescharacteristic
28C2×#3944—21no—
29C2×#3944C2211yescharacteristic
30C22×#672—21no—
31C22×#672C2211yescharacteristic
32#64783C2214yescomplemented
33#64716C2214yescomplemented
34#64713C2214yescomplemented
35C2×#2223—51nomaximal, Sylow
36C2×C5×#41D411yescharacteristic
37C22×C5×D4—21no—
38C22×Dic10—21no—
39C5×AGL(1,ℤ/8)—24no—
40C5×AGL(1,ℤ/8)—42no—
41C2×C5×SD16—41no—
42C2×C5×D8—21no—
43C2×C5×D8—21no—
44C2×C5×D8—21no—
45C2×C5×D8—21no—
46C2×C5×D8—21no—
47C2×C5×D8—41no—
48C2×C5×D8C2312yes—
49C5×#131—21no—
50C5×#131—21no—
51C5×#131D412yes—
52C5×#131C2312yes—
53C2×C5×M16—21no—
54C2×C5×M16—21no—
55C2×C5×M16D411yescharacteristic
56C22×C5×C8—21no—
57C22×C5×C8C2311yescharacteristic
58#4097—24no—
59#4097—42no—
60C2×#689—41no—
61C2×#687—41no—
62C2×#681—21no—
63C2×Dic20—21no—
64C2×Dic20—21no—
65C2×Dic20—21no—
66C2×Dic20—21no—
67C2×Dic20—21no—
68C2×Dic20C2312yes—
69C5×#108—21no—
70C5×#108C2312yes—
71C5×#100—24no—
72#3959—24no—
73#3959—24no—
74#3956—24no—
75#3951—21no—
76#3951C2312yes—
77#3944—21no—
78#3944—24no—
79#3944C2312yes—
80C2×#672—21no—
81C2×#672—24no—
82C2×#672D411yescharacteristic
83C2×#672D411yescharacteristic
84C2×#672D412yes—
85C2×#672C2312yes—
86C22×SD32—51no—
87C2×#504—51no—
88C2×#473—51no—
89C2×#472D511yescharacteristic
90#2223—58no—
91C2×#368—51no—
92C2×#362—51no—
93C2×#361—51no—
94C24×C5—41no—
95C5×#41—21no—
96C5×#41—21no—
97C5×#41D812yes—
98C5×#41C2×D412yes—
99C2×C5×Q8D811yescharacteristic
100C2×C5×D4—21no—
101C2×C5×D4—22no—
102C2×C5×D4—41no—
103C2×C5×D4—41no—
104C2×C5×D4—41no—
105C2×C5×D4—41no—
106C2×C5×D4—41no—
107C2×C5×D4D811yescharacteristic
108C22×C4×C5—21no—
109C22×C4×C5C2×D411yescharacteristic
110C22×Dic5—41no—
111C2×Dic10—22no—
112C2×Dic10—41no—
113C2×Dic10—41no—
114C2×Dic10—41no—
115C2×Dic10—41no—
116C2×Dic10—41no—
117C5×SD16—44no—
118C5×D8—22no—
119C5×D8—22no—
120C5×D8—44no—
121C5×D8—41no—
122C5×D8—41no—
123C5×M16—21no—
124C5×M16—22no—
125C5×M16—22no—
126C5×M16—22no—
127C5×M16—41no—
128C5×M16C2×D412yes—
129C2×C5×C8—21no—
130C2×C5×C8—22no—
131C2×C5×C8—22no—
132C2×C5×C8—41no—
133C2×C5×C8C2×D411yescharacteristic
134C2×C5×C8C2×D411yescharacteristic
135C2×C5×C8C2×D411yescharacteristic
136C2×C5×C8#4111yescharacteristic
137C2×C5×C8#4111yescharacteristic
138C2×C5×C8C2411yescharacteristic
139#689—44no—
140#687—44no—
141#681—22no—
142#681—41no—
143C2×#168—41no—
144Dic20—22no—
145Dic20—22no—
146Dic20—41no—
147Dic20—41no—
148#672—22no—
149#672C2×D412yes—
150#672C2×D412yes—
151C2×#137—101no—
152C2×AGL(1,ℤ/8)—21no—
153C22×Q16—51no—
154C22×D8C2×D511yescharacteristic
155C2×#131C2×D511yescharacteristic
156C2×SD32—54no—
157C2×SD32—101no—
158C2×SD32—101no—
159C2×SD32—102no—
160#504—54no—
161#504—102no—
162C2×M32—51no—
163C2×M32—101no—
164C22×C16—51no—
165C22×C16—101no—
166#473—54no—
167#473—102no—
168#472—22no—
169#472C2×D514yes—
170C2×#108—51no—
171C2×#108C2×D511yescharacteristic
172C2×#101—101no—
173C2×#100—21no—
174#368—54no—
175#362—54no—
176#361—54no—
177C23×C5—21no—
178C23×C5—42no—
179C23×C5—81no—
180C23×C5—81no—
181C23×C5—162no—
182C23×C5#13511yescharacteristic
183C5×Q8—21no—
184C5×Q8C2×D812yes—
185C5×D4—22no—
186C5×D4—22no—
187C5×D4—21no—
188C5×D4—42no—
189C5×D4—42no—
190C5×D4—81no—
191C5×D4—81no—
192C5×D4C2×D812yes—
193C2×C4×C5—21no—
194C2×C4×C5—22no—
195C2×C4×C5—22no—
196C2×C4×C5#12111yescharacteristic
197C2×C4×C5#12111yescharacteristic
198C2×C4×C5C2×D811yescharacteristic
199C2×C4×C5C2×D811yescharacteristic
200C2×C4×C5#13511yescharacteristic
201C2×C4×C5C22×D411yescharacteristic
202C2×Dic5—42no—
203C2×Dic5—81no—
204C2×Dic5—81no—
205Dic10—42no—
206Dic10—42no—
207Dic10—81no—
208Dic10—81no—
209C5×C8—22no—
210C5×C8—42no—
211C5×C8#12111yescharacteristic
212C5×C8#12111yescharacteristic
213C5×C8C22×D411yescharacteristic
214C5×C8C2×#4111yescharacteristic
215#168—42no—
216C2×#41C22⋊D511yescharacteristic
217C22×Q8—101no—
218C22×D4—21no—
219#137—104no—
220#137—202no—
221AGL(1,ℤ/8)—24no—
222AGL(1,ℤ/8)—42no—
223C2×Q16—52no—
224C2×Q16—101no—
225C2×Q16—101no—
226C2×Q16—101no—
227C2×Q16—101no—
228C2×Q16—101no—
229C2×Q16—201no—
230C2×SD16—41no—
231C2×SD16—201no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—41no—
238C2×D8C22×D512yes—
239#131—21no—
240#131—21no—
241#131C22⋊D512yes—
242#131C22×D512yes—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—101no—
246C2×M16C22⋊D511yescharacteristic
247C22×C8—21no—
248C22×C8C22×D511yescharacteristic
249SD32—104no—
250SD32—104no—
251M32—52no—
252M32—104no—
253M32—101no—
254C2×C16—51no—
255C2×C16—51no—
256C2×C16—52no—
257C2×C16—52no—
258C2×C16—104no—
259C2×C16—101no—
260#108—21no—
261#108—52no—
262#108—101no—
263#108C22×D512yes—
264#101—104no—
265#100—24no—
266C22×C5—22no—
267C22×C5—22no—
268C22×C5—42no—
269C22×C5—82no—
270C22×C5—162no—
271C22×C5—162no—
272C22×C5—162no—
273C22×C5#46611yescharacteristic
274C22×C5#46611yescharacteristic
275C22×C5C2×#13511yescharacteristic
276C4×C5—22no—
277C4×C5#46611yescharacteristic
278C4×C5#46611yescharacteristic
279C4×C5C2×#12111yescharacteristic
280C4×C5C22×D811yescharacteristic
281Dic5—82no—
282C24—41no—
283#41—21no—
284#41—21no—
285#41#68612yes—
286#41C2×C22⋊D512yes—
287C2×Q8—102no—
288C2×Q8—201no—
289C2×Q8—201no—
290C2×Q8—201no—
291C2×Q8—201no—
292C2×Q8—201no—
293C2×Q8#68611yescharacteristic
294C2×D4—21no—
295C2×D4—22no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4#68611yescharacteristic
302C22×C4—21no—
303C22×C4—201no—
304C22×C4C2×C22⋊D511yescharacteristic
305Q16—102no—
306Q16—102no—
307Q16—204no—
308Q16—201no—
309Q16—201no—
310SD16—44no—
311SD16—204no—
312D8—22no—
313D8—22no—
314D8—44no—
315D8—41no—
316D8—41no—
317M16—21no—
318M16—22no—
319M16—22no—
320M16—22no—
321M16—41no—
322M16—102no—
323M16—201no—
324M16C2×C22⋊D512yes—
325C2×C8—21no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—201no—
330C2×C8D4×D511yescharacteristic
331C2×C8D4×D511yescharacteristic
332C2×C8#71111yescharacteristic
333C2×C8#71111yescharacteristic
334C2×C8C2×C22⋊D511yescharacteristic
335C2×C8C23×D511yescharacteristic
336C16—52no—
337C16—52no—
338C16—102no—
339C2×C5—21no—
340C2×C5—21no—
341C2×C5—42no—
342C2×C5—162no—
343C2×C5#222312yescomplemented
344C2×C5C2×#46611yescharacteristic
345C23—21no—
346C23—42no—
347C23—81no—
348C23—81no—
349C23—162no—
350C23#409611yescharacteristic
351Q8—21no—
352Q8—202no—
353Q8—202no—
354Q8—401no—
355Q8—401no—
356Q8C2×#68612yes—
357D4—22no—
358D4—22no—
359D4—21no—
360D4—42no—
361D4—42no—
362D4—81no—
363D4—81no—
364D4C2×#68612yes—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—202no—
369C2×C4—401no—
370C2×C4—401no—
371C2×C4C2×#68611yescharacteristic
372C2×C4C2×#68611yescharacteristic
373C2×C4#408511yescharacteristic
374C2×C4#408511yescharacteristic
375C2×C4#409611yescharacteristic
376C2×C4C22×C22⋊D511yescharacteristic
377C8—22no—
378C8—42no—
379C8—202no—
380C8#408511yescharacteristic
381C8#408511yescharacteristic
382C8C2×D4×D511yescharacteristic
383C8C2×#71111yescharacteristic
384C5C2×#222311yescharacteristic, complemented, Sylow
385C22—22no—
386C22—22no—
387C22—42no—
388C22—82no—
389C22—162no—
390C22—162no—
391C22—162no—
392C22#6532711yescharacteristic
393C22#6532711yescharacteristic
394C22C2×#409611yescharacteristic
395C4—22no—
396C4—402no—
397C4#6532711yescharacteristic
398C4#6532711yescharacteristic
399C4C22×#68611yescharacteristic
400C4C2×#408511yescharacteristic
401C2—21no—
402C2—21no—
403C2—42no—
404C2—162no—
405C2#1060188612yesdirect product factor
406C2C2×#6532711yescharacteristic
subgroupG/H
centerC22#65327
commutator, cosocleC2×C5×C8C24
FrattiniC2×C8C23×D5
Fitting, prime radicalC2×C5×#472C2
socleC22×C5#466
hypercenterC2×#472D5
hypocenterC5C2×#2223
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#472

Complements

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

NH ≅ G/Ntype
2. C22×#3959C2semidirect
3. C2×#65432C2semidirect
4. C2×#65429C2semidirect
5. C2×#64783C2semidirect
6. #10601886C2direct (N × H)
7. C2×#64716C2semidirect
8. C2×#64713C2semidirect
21. C2×#3959C22semidirect
23. #65432C22semidirect
25. #65429C22semidirect
32. #64783C22semidirect
33. #64716C22semidirect
34. #64713C22semidirect
343. C2×C5#2223semidirect
384. C5C2×#2223semidirect
405. C2#10601886direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4722
C22×#39592
C2×#654322
C2×#654292
C2×#647832
#106018862
C2×#647162
C2×#647132
C2×#22235