Finite Group Databasebeta

← C2×#10610260 #12968598

Subgroups — C2×#10610260 #12968598

Order 1280.

2182 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65811C211yesmaximal, characteristic
2C22×#4016C211yesmaximal, characteristic, complemented
3C2×C4×C5×M16C211yesmaximal, characteristic, complemented
4C2×#65422C214yesmaximal, complemented
5#10610260C2116yesmaximal, direct product factor
6C2×#64992C212yesmaximal, complemented
7C2×#65002C212yesmaximal, complemented
8C2×#64986C214yesmaximal, complemented
9C22×#709C2212yes—
10C22×C5×M16C2212yes—
11C22×C42×C5C2211yescharacteristic
12C2×#4076—22no—
13C22×C4⋊Dic5C2212yes—
14C22×#683—22no—
15#65811—24no—
16#65811C2218yes—
17C2×#4021C2212yes—
18C2×#4020C2211yescharacteristic
19C2×C4×D20—22no—
20C2×#4016—22no—
21C2×#4016—24no—
22C2×#4016C2212yes—
23C2×#4016C2212yes—
24C2×#4016C2218yescomplemented
25C2×#4015C2211yescharacteristic
26C4×C5×M16C2218yescomplemented
27C2×C5×#97C2212yes—
28C2×C4×C5×C8C2212yes—
29#65422C22132yescomplemented
30C2×#3953C2218yes—
31C2×#3948C2218yes—
32#65002C22116yescomplemented
33#64992C22116yescomplemented
34#64986C22132yescomplemented
35C2×#3142—51nomaximal, Sylow
36C23×C4×C5D412yes—
37C23×C4×C5C2311yescharacteristic
38C22×C22⋊D5—22no—
39C23×Dic5—22no—
40C2×#709—24no—
41C2×#709—216no—
42C2×#709C2318yes—
43C22×D20—22no—
44C22×D20C2312yes—
45C22×C4×D5—22no—
46C22×Dic10C2312yes—
47C2×C5×M16—28no—
48C2×C5×M16C2318yes—
49C22×C5×C8C2314yes—
50C2×C42×C5D412yes—
51C2×C42×C5D414yes—
52C2×C42×C5C2311yescharacteristic
53C2×C42×C5C2311yescharacteristic
54C2×C42×C5C2314yes—
55#4076—216no—
56C2×#685—24no—
57C2×C4⋊Dic5—22no—
58C2×C4⋊Dic5—22no—
59C2×C4⋊Dic5—24no—
60C2×C4⋊Dic5C2314yes—
61C2×C4⋊Dic5C2318yes—
62C2×#683—24no—
63C2×#683—24no—
64C2×#683—216no—
65#4021—24no—
66#4021C2318yes—
67#4020—22no—
68#4020C2314yes—
69C4×D20—216no—
70#4016—24no—
71#4016—24no—
72#4016—216no—
73#4016C2318yes—
74#4016C2318yes—
75#4015—22no—
76#4015C2314yes—
77C5×#97C2318yes—
78C4×C5×C8C2318yes—
79#3953C23132yes—
80#3948C23132yes—
81C2×#532—51no—
82C22×#125—51no—
83#3142—516no—
84C2×#491—52no—
85C2×#490—52no—
86C2×#488—54no—
87C2×#417—54no—
88C2×C4×M16D511yescharacteristic, complemented
89C24×C5C2×D411yescharacteristic
90C23×D5—22no—
91C22×C4×C5—44no—
92C22×C4×C5C2×D412yes—
93C22×C4×C5C2×D412yes—
94C22×C4×C5C2×D418yes—
95C22×C4×C5C2×D411yescharacteristic
96C22×C4×C5C2×D412yes—
97C22×C4×C5#4118yes—
98C22×C4×C5C2411yescharacteristic
99C22×C4×C5C2412yes—
100C2×C22⋊D5—28no—
101C2×C22⋊D5—48no—
102C22×Dic5—22no—
103C22×Dic5—28no—
104C22×Dic5—24no—
105C22×Dic5—48no—
106#709—232no—
107#709—416no—
108C2×D20—28no—
109C2×D20—28no—
110C2×D20—22no—
111C2×D20—48no—
112C2×D20C2414yes—
113C2×C4×D5—28no—
114C2×C4×D5—48no—
115C2×Dic10—28no—
116C2×Dic10—22no—
117C2×Dic10C2414yes—
118C5×M16—216no—
119C2×C5×C8—28no—
120C2×C5×C8C2418yes—
121C42×C5C2×D412yes—
122C42×C5C2×D418yes—
123C42×C5C2×D412yes—
124C42×C5C2412yes—
125C42×C5C2412yes—
126#685—216no—
127C4⋊Dic5—28no—
128C4⋊Dic5—24no—
129C4⋊Dic5—28no—
130C4⋊Dic5C2418yes—
131#683—216no—
132#683—216no—
133C22×#41—52no—
134C22×M16C2×D512yes—
135#532—58no—
136#532—104no—
137C2×C4⋊Q8—51no—
138C2×#127—51no—
139C2×#125—52no—
140C2×#125—52no—
141C2×#125—58no—
142C2×#125—102no—
143C2×#125—104no—
144C2×#124—52no—
145C2×#121—102no—
146C2×C4×D4—102no—
147C22×C4⋊C4—52no—
148C22×C4⋊C4—102no—
149C22×C42C2×D511yescharacteristic
150#491—516no—
151#490—516no—
152#488—532no—
153#417—532no—
154C2×#103—58no—
155C2×#102—58no—
156C4×M16C2×D518yescomplemented
157C2×#97C2×D512yes—
158C2×C4×C8C2×D512yes—
159C23×C5—24no—
160C23×C5#12414yes—
161C23×C5C22×D412yes—
162C23×C5C22×D411yescharacteristic
163C22×D5—24no—
164C22×D5—44no—
165C22×D5—48no—
166C2×C4×C5—24no—
167C2×C4×C5—24no—
168C2×C4×C5—48no—
169C2×C4×C5#12414yes—
170C2×C4×C5#12418yes—
171C2×C4×C5C22×D414yes—
172C2×C4×C5C22×D414yes—
173C2×C4×C5C22×D411yescharacteristic
174C2×C4×C5C22×D412yes—
175C2×C4×C5C2×#4114yes—
176C2×C4×C5C2×#4118yes—
177C2×C4×C5C2511yescharacteristic
178C22⋊D5—416no—
179C2×Dic5—28no—
180C2×Dic5—24no—
181C2×Dic5—416no—
182C2×Dic5—44no—
183C2×Dic5—48no—
184D20—28no—
185D20—416no—
186D20—44no—
187C4×D5—416no—
188Dic10—28no—
189Dic10—44no—
190C5×C8—28no—
191C2×#41—58no—
192C2×#41—104no—
193C2×#41—1016no—
194C22×Q8—52no—
195C22×D4—52no—
196C22×D4—102no—
197C22×D4—102no—
198C23×C4—102no—
199C23×C4—102no—
200C23×C4D2012yes—
201C23×C4C22×D511yescharacteristic
202C2×M16—28no—
203C2×M16C22×D518yes—
204C22×C8C22×D514yes—
205C4⋊Q8—54no—
206C4⋊Q8—102no—
207#127—54no—
208#127—102no—
209#125—58no—
210#125—58no—
211#125—1016no—
212#125—104no—
213#125—104no—
214#124—58no—
215#124—104no—
216#121—1016no—
217C4×D4—1016no—
218C2×C4⋊C4—54no—
219C2×C4⋊C4—58no—
220C2×C4⋊C4—104no—
221C2×C4⋊C4—102no—
222C2×C4⋊C4—1016no—
223C2×C4⋊C4—104no—
224C2×C4⋊C4—104no—
225C2×C4⋊C4—102no—
226C2×C22⋊C4—104no—
227C2×C42D2012yes—
228C2×C42D2014yes—
229C2×C42C22×D511yescharacteristic
230C2×C42C22×D511yescharacteristic
231C2×C42C22×D514yes—
232#103—532no—
233#102—532no—
234#97C22×D518yes—
235C4×C8C22×D518yes—
236C22×C5—28no—
237C22×C5—24no—
238C22×C5C2×#12414yes—
239C22×C5C2×#12412yes—
240C22×C5#57514yes—
241C22×C5C23×D411yescharacteristic
242C2×D5—44no—
243C2×D5—48no—
244C2×D5—88no—
245C4×C5—24no—
246C4×C5—24no—
247C4×C5C2×#12412yes—
248C4×C5C2×#12414yes—
249C4×C5C22×#4112yes—
250Dic5—44no—
251Dic5—48no—
252C24—102no—
253C24C2×D2011yescharacteristic
254#41—1032no—
255#41—2016no—
256C2×Q8—54no—
257C2×Q8—102no—
258C2×Q8—108no—
259C2×D4—54no—
260C2×D4—108no—
261C2×D4—108no—
262C2×D4—102no—
263C2×D4—108no—
264C2×D4—208no—
265C2×D4—208no—
266C22×C4—44no—
267C22×C4—108no—
268C22×C4—102no—
269C22×C4—104no—
270C22×C4—108no—
271C22×C4—208no—
272C22×C4—208no—
273C22×C4C2×D2012yes—
274C22×C4C2×D2012yes—
275C22×C4C2×D2018yes—
276C22×C4C2×D2012yes—
277C22×C4C2×D2011yescharacteristic
278C22×C4#70918yes—
279C22×C4C23×D512yes—
280C22×C4C23×D511yescharacteristic
281M16—216no—
282C2×C8—28no—
283C2×C8C23×D518yes—
284C4⋊C4—58no—
285C4⋊C4—108no—
286C4⋊C4—104no—
287C4⋊C4—1016no—
288C4⋊C4—1016no—
289C4⋊C4—108no—
290C22⋊C4—1016no—
291C42C2×D2018yes—
292C42C2×D2012yes—
293C42C2×D2012yes—
294C42C23×D512yes—
295C42C23×D512yes—
296C2×C5—24no—
297C2×C5#314214yescomplemented
298C2×C5C22×#12411yescharacteristic
299C2×C5C2×#57512yes—
300D5—84no—
301C23—24no—
302C23—104no—
303C23—204no—
304C23—208no—
305C23#402114yes—
306C23C22×D2012yes—
307C23C22×D2011yescharacteristic
308Q8—108no—
309Q8—204no—
310D4—108no—
311D4—2016no—
312D4—2016no—
313D4—204no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—48no—
317C2×C4—104no—
318C2×C4—108no—
319C2×C4—2016no—
320C2×C4—204no—
321C2×C4—208no—
322C2×C4—2016no—
323C2×C4#402114yes—
324C2×C4#402118yes—
325C2×C4C22×D2014yes—
326C2×C4C22×D2014yes—
327C2×C4C22×D2012yes—
328C2×C4C22×D2011yescharacteristic
329C2×C4C2×#70914yes—
330C2×C4C2×#70918yes—
331C2×C4C24×D511yescharacteristic
332C8—28no—
333C5C2×#314211yescharacteristic, complemented, Sylow
334C22—28no—
335C22—24no—
336C22—208no—
337C22—204no—
338C22—408no—
339C22C2×#402114yes—
340C22C2×#402112yes—
341C22#6608214yes—
342C22C23×D2011yescharacteristic
343C4—24no—
344C4—24no—
345C4—208no—
346C4—204no—
347C4C2×#402114yes—
348C4C2×#402112yes—
349C4C22×#70912yes—
350C2—24no—
351C2—404no—
352C2#1061026014yesdirect product factor
353C2C22×#402111yescharacteristic
354C2C2×#6608212yes—
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C4×C5×M16C2
socleC23×C5C22×D4
prime radicalC2×#65811C2
hypercenterC2×C4×M16D5
hypocenterC5C2×#3142
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
2. C22×#4016C2semidirect
3. C2×C4×C5×M16C2semidirect
4. C2×#65422C2semidirect
5. #10610260C2direct (N × H)
6. C2×#64992C2semidirect
7. C2×#65002C2semidirect
8. C2×#64986C2semidirect
24. C2×#4016C22semidirect
26. C4×C5×M16C22semidirect
29. #65422C22semidirect
32. #65002C22semidirect
33. #64992C22semidirect
34. #64986C22semidirect
88. C2×C4×M16D5semidirect
156. C4×M16C2×D5semidirect
297. C2×C5#3142semidirect
333. C5C2×#3142semidirect
352. C2#10610260direct (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×#40162
C2×C4×C5×M162
C2×#654222
#106102602
C2×#649922
C2×#650022
C2×#649862
C2×#31425