Finite Group Databasebeta

← C2×#10613669 #12968902

Subgroups — C2×#10613669 #12968902

Order 1280.

1942 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66062C212yesmaximal
2C2×C5×#500C211yesmaximal, characteristic, complemented
3C2×#65368C212yesmaximal, complemented
4#10613669C2116yesmaximal, direct product factor
5C2×#65169C214yesmaximal
6C2×#65167C214yesmaximal, complemented
7C2×C4×C8×D5C211yesmaximal, characteristic
8C2×#64971C211yesmaximal, characteristic, complemented
9C2×C5×C4⋊Q8C2212yes—
10C2×#4092—22no—
11C2×Q8×Dic5—22no—
12C22×C8×D5C2212yes—
13#66062—28no—
14#66062C22116yes—
15C2×#4043—22no—
16C2×#4038C2214yes—
17C2×#4036C2214yes—
18C2×#4033—22no—
19C2×C42×D5C2211yescharacteristic
20C2×#4015C2212yes—
21C5×#500C2218yescomplemented
22C2×C5×#107C2214yes—
23C2×C4×C5×C8C2211yescharacteristic
24C2×#3950C2214yes—
25C2×C8×Dic5C2212yes—
26#65368C22116yescomplemented
27C2×#3940C2218yes—
28C2×C4×#168C2211yescharacteristic
29#65169C22132yes—
30#65167C22132yescomplemented
31C4×C8×D5C2218yes—
32#64971C2218yescomplemented
33C2×#3160—51nomaximal, Sylow
34C22×C5×Q8—22no—
35C22×C4×D5D411yescharacteristic
36C22×C4×D5D411yescharacteristic
37C22×C4×D5C2311yescharacteristic
38C22×Dic10—22no—
39C22×C5×C8C2312yes—
40C5×C4⋊Q8—24no—
41C5×C4⋊Q8C2318yes—
42C2×C5×C4⋊C4—22no—
43C2×C5×C4⋊C4C2314yes—
44C2×C42×C5C2311yescharacteristic
45#4092—216no—
46Q8×Dic5—216no—
47C2×#685—24no—
48C2×C4⋊Dic5—22no—
49C2×C4⋊Dic5—24no—
50C2×C4⋊Dic5C2314yes—
51C2×#683—24no—
52C2×C4×Dic5—24no—
53C2×C4×Dic5D411yescharacteristic
54C2×C4×Dic5D411yescharacteristic
55C2×C4×Dic5C2311yescharacteristic
56C22×#168C2312yes—
57C2×C8×D5Q8116yescomplemented
58C2×C8×D5C2318yes—
59#4043—216no—
60#4038—28no—
61#4038C23116yes—
62#4036—28no—
63#4036C23116yes—
64#4033—216no—
65C42×D5D414yes—
66C42×D5C2314yes—
67#4015—24no—
68#4015C2318yes—
69C5×#107C23116yes—
70C4×C5×C8C2314yes—
71#3950C23116yes—
72C8×Dic5C2318yes—
73#3940C23132yes—
74C4×#168C2314yes—
75C2×#533—52no—
76#3160—516no—
77C2×#500—51no—
78C2×#500D511yescharacteristic, complemented
79C2×#499—54no—
80C2×#498—52no—
81C2×#427—54no—
82C22×C4×C8—51no—
83C23×D5C2×D411yescharacteristic
84C2×C5×Q8—28no—
85C2×C5×Q8—48no—
86C22×C4×C5—24no—
87C22×C4×C5C2×D411yescharacteristic
88C22×C4×C5C2×D411yescharacteristic
89C22×C4×C5C2411yescharacteristic
90C22×Dic5—24no—
91C22×Dic5C2×D411yescharacteristic
92C22×Dic5C2×D411yescharacteristic
93C22×Dic5C2×D411yescharacteristic
94C2×C4×D5—24no—
95C2×C4×D5—24no—
96C2×C4×D5C2×D414yes—
97C2×C4×D5C2×D414yes—
98C2×C4×D5C2×D412yes—
99C2×C4×D5C2×Q818yes—
100C2×C4×D5C2412yes—
101C2×Dic10—28no—
102C2×Dic10—48no—
103C2×C5×C8C2×Q818yes—
104C2×C5×C8C2414yes—
105C5×C4⋊C4—28no—
106C5×C4⋊C4—24no—
107C5×C4⋊C4C2418yes—
108C42×C5C2×D412yes—
109C42×C5C2412yes—
110#685—216no—
111C4⋊Dic5—24no—
112C4⋊Dic5—28no—
113C4⋊Dic5—216no—
114C4⋊Dic5C2418yes—
115#683—216no—
116C4×Dic5—216no—
117C4×Dic5C2×D412yes—
118C4×Dic5C2×D414yes—
119C4×Dic5C2×D414yes—
120C4×Dic5C2412yes—
121C2×#168C2×Q818yes—
122C2×#168C2414yes—
123C8×D5C2×Q8132yescomplemented
124C23×C8—52no—
125#533—516no—
126#533—108no—
127C2×C4⋊Q8—52no—
128C2×C4⋊Q8C2×D512yes—
129C2×#125—54no—
130C2×C22⋊Q8—102no—
131C2×C22⋊Q8—102no—
132C2×C4×Q8—102no—
133C2×C4×Q8—102no—
134C2×#117—54no—
135C22×C42—51no—
136#500—58no—
137#500C2×D518yescomplemented
138#499—532no—
139#498—516no—
140#427—532no—
141C2×#107—54no—
142C2×#107C2×D514yes—
143C2×#106—58no—
144C2×C4×C8—52no—
145C2×C4×C8—51no—
146C2×C4×C8—58no—
147C2×C4×C8C2×D511yescharacteristic
148C23×C5C22×D411yescharacteristic
149C22×D5—22no—
150C22×D5—22no—
151C22×D5C4⋊Q814yes—
152C22×D5C22×D412yes—
153C5×Q8—416no—
154C2×C4×C5—28no—
155C2×C4×C5—48no—
156C2×C4×C5#13514yes—
157C2×C4×C5#13514yes—
158C2×C4×C5C22×D411yescharacteristic
159C2×C4×C5C22×D412yes—
160C2×C4×C5C22×D412yes—
161C2×C4×C5C22×Q814yes—
162C2×C4×C5C2511yescharacteristic
163C2×Dic5—22no—
164C2×Dic5—22no—
165C2×Dic5—28no—
166C2×Dic5—48no—
167C2×Dic5C4⋊Q814yes—
168C2×Dic5C22×D412yes—
169C2×Dic5C22×D412yes—
170C2×Dic5C22×D412yes—
171C4×D5—28no—
172C4×D5—28no—
173C4×D5C4⋊Q818yes—
174C4×D5C22×Q818yes—
175Dic10—416no—
176C5×C8C22×Q818yes—
177#168C22×Q818yes—
178C22×Q8—22no—
179C22×Q8—102no—
180C23×C4—51no—
181C23×C4—51no—
182C23×C4—51no—
183C22×C8—52no—
184C22×C8—516no—
185C22×C8—58no—
186C22×C8C22×D512yes—
187C4⋊Q8—24no—
188C4⋊Q8—58no—
189C4⋊Q8—104no—
190C4⋊Q8C22×D518yes—
191#125—516no—
192#125—108no—
193C22⋊Q8—1016no—
194C22⋊Q8—1016no—
195C4×Q8—1016no—
196C4×Q8—1016no—
197#117—516no—
198#117—108no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—54no—
201C2×C4⋊C4—104no—
202C2×C4⋊C4—104no—
203C2×C4⋊C4—102no—
204C2×C4⋊C4C22×D514yes—
205C2×C22⋊C4—104no—
206C2×C42—51no—
207C2×C42—51no—
208C2×C42—51no—
209C2×C42—54no—
210C2×C42—54no—
211C2×C42—104no—
212C2×C42C22×D511yescharacteristic
213#107—516no—
214#107C22×D5116yes—
215#106—532no—
216C4×C8—58no—
217C4×C8—54no—
218C4×C8C22×D514yes—
219C22×C5C2×C4⋊Q812yes—
220C22×C5C2×#13512yes—
221C22×C5C2×#13512yes—
222C22×C5C23×D411yescharacteristic
223C2×D5—28no—
224C2×D5—22no—
225C2×D5—22no—
226C2×D5C2×C4⋊Q814yes—
227C4×C5—48no—
228C4×C5C2×C4⋊Q812yes—
229C4×C5C2×#13514yes—
230C4×C5C2×#13514yes—
231C4×C5C23×Q812yes—
232Dic5—22no—
233Dic5—22no—
234Dic5—48no—
235Dic5C2×C4⋊Q814yes—
236C24—51no—
237C2×Q8—28no—
238C2×Q8—48no—
239C2×Q8—108no—
240C2×Q8—208no—
241C22×C4—24no—
242C22×C4—51no—
243C22×C4—52no—
244C22×C4—58no—
245C22×C4—52no—
246C22×C4—51no—
247C22×C4—51no—
248C22×C4—54no—
249C22×C4—54no—
250C22×C4—104no—
251C22×C4—104no—
252C22×C4—104no—
253C22×C4D4×D511yescharacteristic
254C22×C4D4×D511yescharacteristic
255C22×C4C23×D511yescharacteristic
256C2×C8—58no—
257C2×C8—54no—
258C2×C8—532no—
259C2×C8Q8×D518yes—
260C2×C8C23×D514yes—
261C4⋊C4—28no—
262C4⋊C4—24no—
263C4⋊C4—58no—
264C4⋊C4—1016no—
265C4⋊C4—1016no—
266C4⋊C4—104no—
267C4⋊C4—108no—
268C4⋊C4C23×D518yes—
269C22⋊C4—1016no—
270C42—54no—
271C42—54no—
272C42—52no—
273C42—52no—
274C42—1016no—
275C42D4×D512yes—
276C42C23×D512yes—
277C2×C5#316014yescomplemented
278C2×C5C22×C4⋊Q811yescharacteristic
279C2×C5C22×#13511yescharacteristic
280C2×C5C22×#13511yescharacteristic
281D5—24no—
282C23—54no—
283C23—52no—
284C23—102no—
285C23—102no—
286C23C2×D4×D511yescharacteristic
287Q8—416no—
288Q8—2016no—
289C2×C4—28no—
290C2×C4—48no—
291C2×C4—54no—
292C2×C4—52no—
293C2×C4—58no—
294C2×C4—58no—
295C2×C4—52no—
296C2×C4—52no—
297C2×C4—102no—
298C2×C4—102no—
299C2×C4—108no—
300C2×C4—108no—
301C2×C4—108no—
302C2×C4—208no—
303C2×C4#405814yes—
304C2×C4#406514yes—
305C2×C4C2×D4×D511yescharacteristic
306C2×C4C2×D4×D512yes—
307C2×C4C2×D4×D512yes—
308C2×C4C2×Q8×D514yes—
309C2×C4C24×D511yescharacteristic
310C8—58no—
311C8C2×Q8×D518yes—
312C5C2×#316011yescharacteristic, complemented, Sylow
313C22—54no—
314C22—108no—
315C22—102no—
316C22—102no—
317C22D5×C4⋊Q812yes—
318C22C2×#405812yes—
319C22C2×#406512yes—
320C22C22×D4×D511yescharacteristic
321C4—48no—
322C4—54no—
323C4—102no—
324C4—102no—
325C4—208no—
326C4D5×C4⋊Q812yes—
327C4C2×#405814yes—
328C4C2×#406514yes—
329C4C22×Q8×D512yes—
330C2—104no—
331C2#1061366914yesdirect product factor
332C2C2×D5×C4⋊Q811yescharacteristic
333C2C22×#405811yescharacteristic
334C2C22×#406511yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#500C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
hypercenterC2×#500D5
hypocenterC5C2×#3160
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
2. C2×C5×#500C2semidirect
3. C2×#65368C2semidirect
4. #10613669C2direct (N × H)
6. C2×#65167C2semidirect
8. C2×#64971C2semidirect
21. C5×#500C22semidirect
26. #65368C22semidirect
30. #65167C22semidirect
32. #64971C22semidirect
57. C2×C8×D5Q8semidirect
78. C2×#500D5semidirect
123. C8×D5C2×Q8semidirect
137. #500C2×D5semidirect
277. C2×C5#3160semidirect
312. C5C2×#3160semidirect
331. C2#10613669direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660622
C2×C5×#5002
C2×#653682
#106136692
C2×#651692
C2×#651672
C2×C4×C8×D52
C2×#649712
C2×#31605