Finite Group Databasebeta

← C2×#10613641 #12969145

Subgroups — C2×#10613641 #12969145

Order 1280.

1842 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66031C212yesmaximal
2C2×C5×#499C211yesmaximal, characteristic, complemented
3C2×#65358C212yesmaximal, complemented
4#10613641C2116yesmaximal, direct product factor
5C2×#65176C212yesmaximal
6C2×#65162C212yesmaximal, complemented
7C2×#65157C212yesmaximal
8C2×#65142C212yesmaximal, complemented
9C2×#64988C211yesmaximal, characteristic, complemented
10C2×#64978C211yesmaximal, characteristic
11C2×C5×#125C2212yes—
12C22×Dic20C2212yes—
13C22×Dic20C2212yes—
14C22×#676C2211yescharacteristic
15C22×C8×D5C2211yescharacteristic
16#66031—28no—
17#66031C22116yes—
18C2×#4044—24no—
19C2×#4043C2214yes—
20C2×#4036—24no—
21C2×#4033C2214yes—
22C2×#4018C2211yescharacteristic
23C2×#4015C2212yes—
24C5×#499C2218yescomplemented
25C2×C5×#107C2212yes—
26C2×C5×#106C2212yes—
27C2×C4×C5×C8C2211yescharacteristic
28C2×#3947C2211yescharacteristic
29C2×C8×Dic5C2211yescharacteristic
30#65358C22116yescomplemented
31C2×#3942C2214yes—
32C2×#3942C2214yes—
33C2×#3935C2211yescharacteristic
34#65176C22116yes—
35#65162C22116yescomplemented
36#65157C22116yes—
37#65142C22116yescomplemented
38#64988C2218yescomplemented
39#64978C2218yes—
40C2×#3177—51nomaximal, Sylow
41C22×C4×D5C2311yescharacteristic
42C22×Dic10C2314yes—
43C22×C5×C8C2311yescharacteristic
44C22×C5×C8C2311yescharacteristic
45C5×#125—24no—
46C5×#125C2318yes—
47C2×C5×C4⋊C4—24no—
48C2×C5×C4⋊C4C2314yes—
49C2×C42×C5C2311yescharacteristic
50C2×#685—24no—
51C2×#685D412yes—
52C2×C4⋊Dic5—24no—
53C2×C4⋊Dic5—24no—
54C2×#683—24no—
55C2×#683D412yes—
56C2×C4×Dic5—24no—
57C2×C4×Dic5C2311yescharacteristic
58C22×#168C2311yescharacteristic
59C22×#168C2311yescharacteristic
60C2×Dic20—28no—
61C2×Dic20—28no—
62C2×Dic20C2318yes—
63C2×Dic20C2318yes—
64C2×#676—24no—
65C2×#676C2314yes—
66C2×C8×D5—24no—
67C2×C8×D5C2314yes—
68#4044—232no—
69#4043—28no—
70#4043C23116yes—
71#4036—232no—
72#4033—28no—
73#4033C23116yes—
74#4018D414yes—
75#4018C2314yes—
76#4015—24no—
77#4015C2318yes—
78C5×#107C2318yes—
79C5×#106C2318yes—
80C4×C5×C8C2314yes—
81#3947C2314yes—
82C8×Dic5C2314yes—
83#3942C23116yes—
84#3942C23116yes—
85#3935C2314yes—
86C2×#541—52no—
87#3177—516no—
88C2×#499D511yescharacteristic, complemented
89C2×#494—51no—
90C2×#491—52no—
91C2×#470—52no—
92C2×#467—52no—
93C2×#441—52no—
94C2×C4×Q16—52no—
95C2×#405—51no—
96C23×D5C2×D411yescharacteristic
97C22×C4×C5—24no—
98C22×C4×C5C2×D412yes—
99C22×C4×C5C2411yescharacteristic
100C22×Dic5—24no—
101C22×Dic5C2×D411yescharacteristic
102C22×Dic5C2×D412yes—
103C2×C4×D5—22no—
104C2×C4×D5—22no—
105C2×C4×D5C2×D412yes—
106C2×C4×D5C2412yes—
107C2×Dic10—28no—
108C2×Dic10—28no—
109C2×Dic10—24no—
110C2×Dic10C2418yes—
111C2×C5×C8#4114yes—
112C2×C5×C8#4114yes—
113C2×C5×C8C2412yes—
114C2×C5×C8C2412yes—
115C5×C4⋊C4—216no—
116C5×C4⋊C4—24no—
117C5×C4⋊C4C2418yes—
118C42×C5C2×D412yes—
119C42×C5C2412yes—
120#685—216no—
121#685C2×D418yes—
122C4⋊Dic5—216no—
123C4⋊Dic5—216no—
124#683—216no—
125#683C2×D418yes—
126C4×Dic5—216no—
127C4×Dic5C2×D412yes—
128C4×Dic5C2412yes—
129C2×#168—22no—
130C2×#168—22no—
131C2×#168C2412yes—
132C2×#168C2412yes—
133Dic20—216no—
134Dic20—216no—
135#676—28no—
136C8×D5—28no—
137C22×Q16—52no—
138C22×Q16—52no—
139C22×M16—51no—
140C23×C8—51no—
141#541—516no—
142#541—108no—
143C2×C4⋊Q8—52no—
144C2×#126—104no—
145C2×#125—104no—
146C2×#125C2×D512yes—
147C2×C22⋊Q8—54no—
148C2×C4×Q8—54no—
149C2×#117—51no—
150#499C2×D518yescomplemented
151#494—58no—
152#491—516no—
153#470—516no—
154#467—516no—
155#441—516no—
156C4×Q16—516no—
157C2×#107C2×D512yes—
158C2×#106C2×D512yes—
159C2×#103—54no—
160C2×#103—54no—
161#405—58no—
162C2×#97—51no—
163C2×#97—51no—
164C2×C4×C8—51no—
165C2×C4×C8C2×D511yescharacteristic
166C23×C5C22×D411yescharacteristic
167C22×D5—22no—
168C22×D5—24no—
169C22×D5C22×D412yes—
170C2×C4×C5—24no—
171C2×C4×C5—28no—
172C2×C4×C5—48no—
173C2×C4×C5C22×D414yes—
174C2×C4×C5C22×D411yescharacteristic
175C2×C4×C5C2×#4112yes—
176C2×C4×C5C2×#4112yes—
177C2×C4×C5C2511yescharacteristic
178C2×Dic5—22no—
179C2×Dic5—24no—
180C2×Dic5—28no—
181C2×Dic5—48no—
182C2×Dic5C22×D414yes—
183C2×Dic5C22×D412yes—
184C4×D5—24no—
185C4×D5—22no—
186C4×D5—22no—
187Dic10—28no—
188Dic10—28no—
189Dic10—48no—
190C5×C8C2×#4114yes—
191C5×C8C2×#4114yes—
192#168—22no—
193#168—22no—
194C22×Q8—54no—
195C23×C4—51no—
196C2×Q16—58no—
197C2×Q16—58no—
198C2×Q16—108no—
199C2×Q16—108no—
200C2×M16—54no—
201C2×M16—104no—
202C22×C8—51no—
203C22×C8—51no—
204C22×C8—54no—
205C22×C8—104no—
206C22×C8C22×D511yescharacteristic
207C22×C8C22×D511yescharacteristic
208C4⋊Q8—58no—
209C4⋊Q8—104no—
210#126—1032no—
211#125—24no—
212#125—1032no—
213#125C22×D518yes—
214C22⋊Q8—516no—
215C22⋊Q8—108no—
216C4×Q8—516no—
217C4×Q8—108no—
218#117—54no—
219#117—54no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—52no—
222C2×C4⋊C4—104no—
223C2×C4⋊C4—104no—
224C2×C4⋊C4—104no—
225C2×C4⋊C4C22×D514yes—
226C2×C22⋊C4—52no—
227C2×C22⋊C4—104no—
228C2×C42—51no—
229C2×C42—104no—
230C2×C42C22×D511yescharacteristic
231#107C22×D518yes—
232#106C22×D518yes—
233#103—516no—
234#103—516no—
235#97—54no—
236#97—54no—
237C4×C8—54no—
238C4×C8C22×D514yes—
239C22×C5#53212yes—
240C22×C5#57814yes—
241C22×C5C23×D411yescharacteristic
242C2×D5—22no—
243C2×D5—24no—
244C2×D5—44no—
245C4×C5—24no—
246C4×C5—48no—
247C4×C5#53212yes—
248C4×C5C22×#4111yescharacteristic
249C4×C5C22×#4111yescharacteristic
250Dic5—22no—
251Dic5—24no—
252Dic5—48no—
253C24—51no—
254C2×Q8—58no—
255C2×Q8—104no—
256C2×Q8—108no—
257C2×Q8—108no—
258C22×C4—24no—
259C22×C4—52no—
260C22×C4—51no—
261C22×C4—52no—
262C22×C4—52no—
263C22×C4—102no—
264C22×C4—102no—
265C22×C4—104no—
266C22×C4D4×D512yes—
267C22×C4C23×D511yescharacteristic
268Q16—1016no—
269Q16—1016no—
270M16—108no—
271C2×C8—52no—
272C2×C8—52no—
273C2×C8—102no—
274C2×C8—102no—
275C2×C8—108no—
276C2×C8#71314yes—
277C2×C8#71314yes—
278C2×C8C23×D512yes—
279C2×C8C23×D512yes—
280C4⋊C4—216no—
281C4⋊C4—24no—
282C4⋊C4—58no—
283C4⋊C4—1016no—
284C4⋊C4—1016no—
285C4⋊C4—1016no—
286C4⋊C4C23×D518yes—
287C22⋊C4—58no—
288C22⋊C4—1016no—
289C42—52no—
290C42—52no—
291C42—1016no—
292C42D4×D512yes—
293C42C23×D512yes—
294C2×C5#317714yescomplemented
295C2×C5C2×#53211yescharacteristic
296C2×C5C2×#57812yes—
297D5—42no—
298C23—52no—
299C23—102no—
300C23—104no—
301C23C2×D4×D511yescharacteristic
302Q8—108no—
303Q8—108no—
304Q8—208no—
305C2×C4—24no—
306C2×C4—28no—
307C2×C4—48no—
308C2×C4—54no—
309C2×C4—52no—
310C2×C4—102no—
311C2×C4—104no—
312C2×C4—104no—
313C2×C4—102no—
314C2×C4—102no—
315C2×C4—108no—
316C2×C4—208no—
317C2×C4C2×D4×D514yes—
318C2×C4C2×D4×D511yescharacteristic
319C2×C4C2×#71312yes—
320C2×C4C2×#71312yes—
321C2×C4C24×D511yescharacteristic
322C8—102no—
323C8—102no—
324C8C2×#71314yes—
325C8C2×#71314yes—
326C5C2×#317711yescharacteristic, complemented, Sylow
327C22—104no—
328C22—102no—
329C22—204no—
330C22#6605912yes—
331C22#6610514yes—
332C22C22×D4×D511yescharacteristic
333C4—24no—
334C4—48no—
335C4—104no—
336C4—102no—
337C4—208no—
338C4#6605912yes—
339C4C22×#71311yescharacteristic
340C4C22×#71311yescharacteristic
341C2—202no—
342C2#1061364114yesdirect product factor
343C2C2×#6605911yescharacteristic
344C2C2×#6610512yes—
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#499C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
hypercenterC2×#499D5
hypocenterC5C2×#3177
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#499

Complements

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

NH ≅ G/Ntype
2. C2×C5×#499C2semidirect
3. C2×#65358C2semidirect
4. #10613641C2direct (N × H)
6. C2×#65162C2semidirect
8. C2×#65142C2semidirect
9. C2×#64988C2semidirect
24. C5×#499C22semidirect
30. #65358C22semidirect
35. #65162C22semidirect
37. #65142C22semidirect
38. #64988C22semidirect
88. C2×#499D5semidirect
150. #499C2×D5semidirect
294. C2×C5#3177semidirect
326. C5C2×#3177semidirect
342. C2#10613641direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660312
C2×C5×#4992
C2×#653582
#106136412
C2×#651762
C2×#651622
C2×#651572
C2×#651422
C2×#649882
C2×#649782
C2×#31775