Finite Group Databasebeta

← C2×#10610201 #12969036

Subgroups — C2×#10610201 #12969036

Order 1280.

2566 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65811C212yesmaximal, complemented
2C22×C4×C5×C8C211yesmaximal, characteristic, complemented
3C2×#65404C214yesmaximal, complemented
4#10610201C2116yesmaximal, direct product factor
5C2×#64984C211yesmaximal, characteristic, complemented
6C2×#64983C212yesmaximal, complemented
7C2×C4×D40C214yesmaximal, complemented
8C2×#64971C211yesmaximal, characteristic, complemented
9C22×#709—22no—
10C23×C5×C8C2212yes—
11C22×C42×C5C2211yescharacteristic
12C2×#4076—22no—
13C2×#4076C2214yes—
14C22×D40C2214yes—
15#65811—28no—
16#65811C22116yescomplemented
17C2×#4021—22no—
18C2×#4020C2212yes—
19C2×C4×D20—22no—
20C2×C4×D20C2214yes—
21C2×#4015C2212yes—
22C2×C4×C5×C8C2212yes—
23C2×C4×C5×C8C2211yescharacteristic
24C2×C4×C5×C8C2211yescharacteristic
25C2×C4×C5×C8C2218yescomplemented
26#65404C22132yescomplemented
27C2×#3953C2218yes—
28C2×#3950C2214yes—
29#64984C2218yescomplemented
30#64983C22116yescomplemented
31C4×D40C22132yescomplemented
32#64971C2218yescomplemented
33C2×#3169—51nomaximal, Sylow
34C23×C4×C5D411yescharacteristic
35C23×C4×C5D411yescharacteristic
36C23×C4×C5C2311yescharacteristic
37C22×C22⋊D5—24no—
38C2×#709—216no—
39C2×#709—416no—
40C22×D20—22no—
41C22×D20—22no—
42C22×D20C2314yes—
43C22×C4×D5—24no—
44C22×Dic10—22no—
45C22×C5×C8—28no—
46C22×C5×C8C2312yes—
47C22×C5×C8C2318yes—
48C22×C5×C8C2312yes—
49C2×C42×C5D411yescharacteristic
50C2×C42×C5D411yescharacteristic
51C2×C42×C5D414yes—
52C2×C42×C5C2311yescharacteristic
53C2×C42×C5C2311yescharacteristic
54C2×C42×C5C2314yes—
55#4076—28no—
56#4076—216no—
57#4076C23116yes—
58C2×#685—24no—
59C2×#685—24no—
60C2×C4⋊Dic5—22no—
61C2×C4⋊Dic5C2314yes—
62C2×D40—216no—
63C2×D40C23116yes—
64#4021—216no—
65#4020—24no—
66#4020C2318yes—
67C4×D20—216no—
68C4×D20—28no—
69C4×D20C23116yes—
70#4015—24no—
71#4015C2318yes—
72C4×C5×C8C2314yes—
73C4×C5×C8C2318yes—
74C4×C5×C8C2314yes—
75#3953C23132yes—
76#3950C23116yes—
77C2×#532—52no—
78#3169—516no—
79C2×#500—51no—
80C2×#493—51no—
81C2×#486—52no—
82C2×#466—54no—
83C2×C4×D8—54no—
84C22×C4×C8D511yescharacteristic, complemented
85C24×C5C2×D411yescharacteristic
86C23×D5—24no—
87C22×C4×C5—24no—
88C22×C4×C5—24no—
89C22×C4×C5D818yescomplemented
90C22×C4×C5C2×D411yescharacteristic
91C22×C4×C5C2×D412yes—
92C22×C4×C5C2×D411yescharacteristic
93C22×C4×C5C2×D414yes—
94C22×C4×C5C2×D411yescharacteristic
95C22×C4×C5C2×D414yes—
96C22×C4×C5C2×D411yescharacteristic
97C22×C4×C5C2×D411yescharacteristic
98C22×C4×C5C2412yes—
99C22×C4×C5C2411yescharacteristic
100C2×C22⋊D5—216no—
101C2×C22⋊D5—416no—
102C22×Dic5—24no—
103#709—464no—
104C2×D20—216no—
105C2×D20—28no—
106C2×D20—28no—
107C2×D20—24no—
108C2×D20—48no—
109C2×D20—48no—
110C2×D20C2418yes—
111C2×C4×D5—216no—
112C2×C4×D5—416no—
113C2×Dic10—28no—
114C2×Dic10—48no—
115C2×C5×C8—24no—
116C2×C5×C8—216no—
117C2×C5×C8#4118yescomplemented
118C2×C5×C8C2414yes—
119C2×C5×C8C2414yes—
120C42×C5C2×D412yes—
121C42×C5C2×D414yes—
122C42×C5C2×D412yes—
123C42×C5C2×D414yes—
124C42×C5C2412yes—
125C42×C5C2412yes—
126#685—216no—
127#685—216no—
128C4⋊Dic5—24no—
129C4⋊Dic5—28no—
130C4⋊Dic5C2418yes—
131D40—232no—
132C22×#41—102no—
133C22×D8—54no—
134C23×C8C2×D512yes—
135#532—516no—
136#532—108no—
137C2×C4⋊Q8—52no—
138C2×#127—52no—
139C2×#124—102no—
140C2×#121—54no—
141C2×#121—102no—
142C2×C4×D4—54no—
143C2×C4×D4—102no—
144C22×C42C2×D511yescharacteristic
145#500—58no—
146#493—58no—
147#486—516no—
148#466—532no—
149C4×D8—532no—
150C2×#107—54no—
151C2×#102—58no—
152C2×C4×C8C2×D511yescharacteristic
153C2×C4×C8C2×D511yescharacteristic
154C2×C4×C8C2×D512yes—
155C2×C4×C8C2×D518yescomplemented
156C23×C5—22no—
157C23×C5—22no—
158C23×C5C2×D814yes—
159C23×C5C22×D412yes—
160C23×C5C22×D411yescharacteristic
161C22×D5—28no—
162C22×D5—48no—
163C22×D5—48no—
164C22×D5—48no—
165C2×C4×C5—22no—
166C2×C4×C5—22no—
167C2×C4×C5—24no—
168C2×C4×C5—28no—
169C2×C4×C5—24no—
170C2×C4×C5C2×D814yes—
171C2×C4×C5C2×D814yes—
172C2×C4×C5C2×D8116yescomplemented
173C2×C4×C5#13514yes—
174C2×C4×C5C22×D412yes—
175C2×C4×C5C22×D412yes—
176C2×C4×C5C22×D411yescharacteristic
177C2×C4×C5C22×D412yes—
178C2×C4×C5C22×D412yes—
179C2×C4×C5C22×D412yes—
180C2×C4×C5C2×#4114yes—
181C2×C4×C5C2511yescharacteristic
182C22⋊D5—432no—
183C2×Dic5—28no—
184C2×Dic5—48no—
185D20—216no—
186D20—48no—
187D20—416no—
188D20—416no—
189C4×D5—432no—
190Dic10—416no—
191C5×C8—24no—
192C5×C8C2×#4118yescomplemented
193C2×#41—1016no—
194C2×#41—2016no—
195C22×Q8—102no—
196C22×D4—54no—
197C22×D4—104no—
198C22×D4—102no—
199C22×D4—102no—
200C23×C4—104no—
201C23×C4D2011yescharacteristic
202C23×C4D2011yescharacteristic
203C23×C4C22×D511yescharacteristic
204C2×D8—516no—
205C2×D8—1016no—
206C22×C8—28no—
207C22×C8C22×D512yes—
208C22×C8C22×D518yes—
209C22×C8C22×D512yes—
210C4⋊Q8—58no—
211C4⋊Q8—104no—
212#127—58no—
213#127—104no—
214#124—1016no—
215#121—516no—
216#121—108no—
217#121—1016no—
218C4×D4—516no—
219C4×D4—108no—
220C4×D4—1016no—
221C2×C4⋊C4—54no—
222C2×C4⋊C4—102no—
223C2×C22⋊C4—104no—
224C2×C22⋊C4—104no—
225C2×C42D2011yescharacteristic
226C2×C42D2014yes—
227C2×C42D2011yescharacteristic
228C2×C42C22×D511yescharacteristic
229C2×C42C22×D514yes—
230C2×C42C22×D511yescharacteristic
231#107—516no—
232#102—532no—
233C4×C8C22×D518yes—
234C4×C8C22×D514yes—
235C4×C8C22×D514yes—
236C22×C5—28no—
237C22×C5—22no—
238C22×C5—22no—
239C22×C5#53212yes—
240C22×C5C22×D814yes—
241C22×C5C22×D812yes—
242C22×C5C2×#13512yes—
243C22×C5C23×D411yescharacteristic
244C2×D5—48no—
245C2×D5—48no—
246C2×D5—48no—
247C2×D5—816no—
248C4×C5—22no—
249C4×C5—22no—
250C4×C5#53212yes—
251C4×C5C22×D814yes—
252C4×C5C22×D814yes—
253C4×C5C2×#13514yes—
254C4×C5C22×#4112yes—
255Dic5—48no—
256C24—104no—
257C24C2×D2011yescharacteristic
258#41—2064no—
259C2×Q8—108no—
260C2×Q8—208no—
261C2×D4—58no—
262C2×D4—1016no—
263C2×D4—108no—
264C2×D4—104no—
265C2×D4—108no—
266C2×D4—1016no—
267C2×D4—2016no—
268C2×D4—208no—
269C2×D4—208no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—104no—
273C22×C4—1016no—
274C22×C4—2016no—
275C22×C4D4018yescomplemented
276C22×C4C2×D2011yescharacteristic
277C22×C4C2×D2012yes—
278C22×C4C2×D2011yescharacteristic
279C22×C4C2×D2014yes—
280C22×C4C2×D2011yescharacteristic
281C22×C4C2×D2014yes—
282C22×C4C2×D2011yescharacteristic
283C22×C4C2×D2011yescharacteristic
284C22×C4C23×D512yes—
285C22×C4C23×D511yescharacteristic
286D8—1032no—
287C2×C8—24no—
288C2×C8—216no—
289C2×C8#70918yescomplemented
290C2×C8C23×D514yes—
291C2×C8C23×D514yes—
292C4⋊C4—58no—
293C4⋊C4—104no—
294C4⋊C4—108no—
295C22⋊C4—1016no—
296C22⋊C4—1016no—
297C42C2×D2014yes—
298C42C2×D2012yes—
299C42C2×D2014yes—
300C42C2×D2012yes—
301C42C23×D512yes—
302C42C23×D512yes—
303C2×C5—24no—
304C2×C5#316914yescomplemented
305C2×C5C2×#53211yescharacteristic
306C2×C5C23×D811yescharacteristic
307C2×C5C22×#13511yescharacteristic
308D5—88no—
309C23—22no—
310C23—22no—
311C23—108no—
312C23—208no—
313C23—208no—
314C23—208no—
315C23C2×D4014yes—
316C23C22×D2012yes—
317C23C22×D2011yescharacteristic
318Q8—2016no—
319D4—1016no—
320D4—2032no—
321D4—208no—
322D4—2016no—
323D4—2016no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—24no—
327C2×C4—28no—
328C2×C4—24no—
329C2×C4—108no—
330C2×C4—208no—
331C2×C4—2032no—
332C2×C4C2×D4014yes—
333C2×C4C2×D4014yes—
334C2×C4C2×D40116yescomplemented
335C2×C4#405014yes—
336C2×C4C22×D2012yes—
337C2×C4C22×D2012yes—
338C2×C4C22×D2011yescharacteristic
339C2×C4C22×D2012yes—
340C2×C4C22×D2012yes—
341C2×C4C22×D2012yes—
342C2×C4C2×#70914yes—
343C2×C4C24×D511yescharacteristic
344C8—24no—
345C8C2×#70918yescomplemented
346C5C2×#316911yescharacteristic, complemented, Sylow
347C22—28no—
348C22—22no—
349C22—22no—
350C22—208no—
351C22—208no—
352C22—208no—
353C22—4016no—
354C22#6581112yes—
355C22C22×D4014yes—
356C22C22×D4012yes—
357C22C2×#405012yes—
358C22C23×D2011yescharacteristic
359C4—22no—
360C4—22no—
361C4—208no—
362C4#6581112yes—
363C4C22×D4014yes—
364C4C22×D4014yes—
365C4C2×#405014yes—
366C4C22×#70912yes—
367C2—24no—
368C2—408no—
369C2#1061020114yesdirect product factor
370C2C2×#6581111yescharacteristic
371C2C23×D4011yescharacteristic
372C2C22×#405011yescharacteristic
subgroupG/H
centerC22×C4C2×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC22×C4×C5×C8C2
socleC23×C5C22×D4
hypercenterC22×C4×C8D5
hypocenterC5C2×#3169
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×C8

Complements

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

NH ≅ G/Ntype
1. C2×#65811C2semidirect
2. C22×C4×C5×C8C2semidirect
3. C2×#65404C2semidirect
4. #10610201C2direct (N × H)
5. C2×#64984C2semidirect
6. C2×#64983C2semidirect
7. C2×C4×D40C2semidirect
8. C2×#64971C2semidirect
16. #65811C22semidirect
25. C2×C4×C5×C8C22semidirect
26. #65404C22semidirect
29. #64984C22semidirect
30. #64983C22semidirect
31. C4×D40C22semidirect
32. #64971C22semidirect
84. C22×C4×C8D5semidirect
89. C22×C4×C5D8semidirect
117. C2×C5×C8#41semidirect
155. C2×C4×C8C2×D5semidirect
172. C2×C4×C5C2×D8semidirect
192. C5×C8C2×#41semidirect
275. C22×C4D40semidirect
289. C2×C8#709semidirect
304. C2×C5#3169semidirect
334. C2×C4C2×D40semidirect
345. C8C2×#709semidirect
346. C5C2×#3169semidirect
369. C2#10610201direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658112
C22×C4×C5×C82
C2×#654042
#106102012
C2×#649842
C2×#649832
C2×C4×D402
C2×#649712
C2×#31695