Finite Group Databasebeta

← C2×#10613523 #12969042

Subgroups — C2×#10613523 #12969042

Order 1280.

2006 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66062C212yesmaximal
2C2×C5×#494C211yesmaximal, characteristic, complemented
3C2×#65477C214yesmaximal
4C2×Q16×Dic5C214yesmaximal, complemented
5C2×#65370C212yesmaximal, complemented
6#10613523C2116yesmaximal, direct product factor
7C2×C4×C8×D5C211yesmaximal, characteristic
8C2×#64971C211yesmaximal, characteristic, complemented
9C22×C5×Q16C2214yes—
10C2×C5×C4⋊Q8C2212yes—
11C2×#4092C2214yes—
12C2×Q8×Dic5C2214yes—
13C22×C8×D5C2212yes—
14#66062—28no—
15#66062C22116yes—
16C2×#4043—22no—
17C2×#4038—22no—
18C2×#4036—22no—
19C2×#4033—22no—
20C2×C42×D5C2211yescharacteristic
21C2×#4015C2212yes—
22C5×#494C2218yescomplemented
23C2×C4×C5×C8C2211yescharacteristic
24C2×#3967C2218yes—
25#65477C22132yes—
26Q16×Dic5C22132yescomplemented
27C2×#3950C2214yes—
28C2×C8×Dic5C2212yes—
29#65370C22116yescomplemented
30C2×C4×#168C2211yescharacteristic
31C4×C8×D5C2218yes—
32#64971C2218yescomplemented
33C2×#3170—51nomaximal, Sylow
34C22×C5×Q8C2314yes—
35C22×C4×D5D411yescharacteristic
36C22×C4×D5D411yescharacteristic
37C22×C4×D5C2311yescharacteristic
38C22×Dic10—22no—
39C2×C5×Q16—216no—
40C2×C5×Q16C23116yes—
41C22×C5×C8C2312yes—
42C5×C4⋊Q8—24no—
43C5×C4⋊Q8C2318yes—
44C2×C5×C4⋊C4—22no—
45C2×C5×C4⋊C4—22no—
46C2×C42×C5C2311yescharacteristic
47#4092—28no—
48#4092C23116yes—
49Q8×Dic5—28no—
50Q8×Dic5C23116yes—
51C2×#685—24no—
52C2×C4⋊Dic5—22no—
53C2×C4⋊Dic5—24no—
54C2×C4⋊Dic5C2314yes—
55C2×#683—24no—
56C2×C4×Dic5—24no—
57C2×C4×Dic5D411yescharacteristic
58C2×C4×Dic5D411yescharacteristic
59C2×C4×Dic5C2311yescharacteristic
60C22×#168C2312yes—
61C2×C8×D5—28no—
62C2×C8×D5C2318yes—
63#4043—216no—
64#4038—216no—
65#4036—216no—
66#4033—216no—
67C42×D5D414yes—
68C42×D5C2314yes—
69#4015—24no—
70#4015C2318yes—
71C4×C5×C8C2314yes—
72#3967C23132yes—
73#3950C23116yes—
74C8×Dic5C2318yes—
75C4×#168C2314yes—
76C2×#533—52no—
77#3170—516no—
78C2×#500—51no—
79C2×#494D511yescharacteristic, complemented
80C2×#487—52no—
81C2×#467—54no—
82C2×C4×Q16—54no—
83C22×C4×C8—51no—
84C23×D5C2×D411yescharacteristic
85C2×C5×Q8—24no—
86C2×C5×Q8—216no—
87C2×C5×Q8C2418yes—
88C22×C4×C5—24no—
89C22×C4×C5C2×D411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C22×C4×C5C2411yescharacteristic
92C22×Dic5—24no—
93C22×Dic5C2×D411yescharacteristic
94C22×Dic5C2×D411yescharacteristic
95C22×Dic5C2×D411yescharacteristic
96C2×C4×D5—24no—
97C2×C4×D5—24no—
98C2×C4×D5Q1618yescomplemented
99C2×C4×D5C2×D414yes—
100C2×C4×D5C2×D412yes—
101C2×C4×D5C2×D414yes—
102C2×C4×D5C2412yes—
103C2×Dic10—28no—
104C2×Dic10—48no—
105C5×Q16—232no—
106C2×C5×C8#4118yes—
107C2×C5×C8C2414yes—
108C5×C4⋊C4—28no—
109C5×C4⋊C4—28no—
110C42×C5C2×D412yes—
111C42×C5C2412yes—
112#685—216no—
113C4⋊Dic5—24no—
114C4⋊Dic5—28no—
115C4⋊Dic5—216no—
116C4⋊Dic5C2418yes—
117#683—216no—
118C4×Dic5—216no—
119C4×Dic5C2×D412yes—
120C4×Dic5C2×D414yes—
121C4×Dic5C2×D414yes—
122C4×Dic5C2412yes—
123C2×#168—24no—
124C2×#168C2414yes—
125C8×D5—216no—
126C22×Q16C2×D514yes—
127C23×C8—52no—
128#533—516no—
129#533—108no—
130C2×C4⋊Q8—52no—
131C2×C4⋊Q8C2×D512yes—
132C2×#125—102no—
133C2×C22⋊Q8—54no—
134C2×C22⋊Q8—102no—
135C2×C4×Q8—54no—
136C2×C4×Q8—102no—
137C2×#117—102no—
138C22×C42—51no—
139#500—58no—
140#494C2×D518yescomplemented
141#487—516no—
142#467—532no—
143C4×Q16—532no—
144C2×#107—54no—
145C2×#103—58no—
146C2×C4×C8—52no—
147C2×C4×C8—51no—
148C2×C4×C8—58no—
149C2×C4×C8C2×D511yescharacteristic
150C23×C5C22×D411yescharacteristic
151C22×D5—22no—
152C22×D5—22no—
153C22×D5C2×Q1614yes—
154C22×D5C22×D412yes—
155C5×Q8—216no—
156C5×Q8—48no—
157C2×C4×C5—28no—
158C2×C4×C5—48no—
159C2×C4×C5C2×Q1614yes—
160C2×C4×C5#13514yes—
161C2×C4×C5C22×D411yescharacteristic
162C2×C4×C5C22×D412yes—
163C2×C4×C5C22×D412yes—
164C2×C4×C5C2×#4114yes—
165C2×C4×C5C2511yescharacteristic
166C2×Dic5—22no—
167C2×Dic5—22no—
168C2×Dic5—28no—
169C2×Dic5—48no—
170C2×Dic5C2×Q1614yes—
171C2×Dic5C22×D412yes—
172C2×Dic5C22×D412yes—
173C2×Dic5C22×D412yes—
174C4×D5—24no—
175C4×D5—28no—
176C4×D5—24no—
177C4×D5C2×Q16116yescomplemented
178Dic10—416no—
179C5×C8C2×#4118yes—
180#168—24no—
181C22×Q8—102no—
182C22×Q8C22×D514yes—
183C23×C4—51no—
184C23×C4—51no—
185C23×C4—51no—
186C2×Q16—216no—
187C2×Q16C22×D5116yes—
188C22×C8—52no—
189C22×C8—58no—
190C22×C8—108no—
191C22×C8C22×D512yes—
192C4⋊Q8—24no—
193C4⋊Q8—58no—
194C4⋊Q8—104no—
195C4⋊Q8C22×D518yes—
196#125—1016no—
197C22⋊Q8—516no—
198C22⋊Q8—1016no—
199C22⋊Q8—108no—
200C4×Q8—516no—
201C4×Q8—1016no—
202C4×Q8—108no—
203#117—1016no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—54no—
207C2×C4⋊C4—104no—
208C2×C4⋊C4—104no—
209C2×C4⋊C4—102no—
210C2×C22⋊C4—104no—
211C2×C42—51no—
212C2×C42—51no—
213C2×C42—51no—
214C2×C42—54no—
215C2×C42—54no—
216C2×C42—104no—
217C2×C42C22×D511yescharacteristic
218#107—516no—
219#103—532no—
220C4×C8—58no—
221C4×C8—54no—
222C4×C8C22×D514yes—
223C22×C5#53212yes—
224C22×C5C22×Q1612yes—
225C22×C5C2×#13512yes—
226C22×C5C23×D411yescharacteristic
227C2×D5—28no—
228C2×D5—22no—
229C2×D5—22no—
230C2×D5C22×Q1614yes—
231C4×C5—48no—
232C4×C5#53212yes—
233C4×C5C22×Q1614yes—
234C4×C5C2×#13514yes—
235C4×C5C22×#4112yes—
236Dic5—22no—
237Dic5—22no—
238Dic5—48no—
239Dic5C22×Q1614yes—
240C24—51no—
241C2×Q8—24no—
242C2×Q8—216no—
243C2×Q8—108no—
244C2×Q8—208no—
245C2×Q8C23×D518yes—
246C22×C4—24no—
247C22×C4—51no—
248C22×C4—54no—
249C22×C4—58no—
250C22×C4—51no—
251C22×C4—51no—
252C22×C4—52no—
253C22×C4—54no—
254C22×C4—52no—
255C22×C4—104no—
256C22×C4—104no—
257C22×C4—104no—
258C22×C4D4×D511yescharacteristic
259C22×C4D4×D511yescharacteristic
260C22×C4C23×D511yescharacteristic
261Q16—232no—
262C2×C8—54no—
263C2×C8—104no—
264C2×C8—1016no—
265C2×C8#71118yes—
266C2×C8C23×D514yes—
267C4⋊C4—28no—
268C4⋊C4—28no—
269C4⋊C4—58no—
270C4⋊C4—1016no—
271C4⋊C4—1016no—
272C4⋊C4—104no—
273C4⋊C4—108no—
274C22⋊C4—1016no—
275C42—52no—
276C42—54no—
277C42—54no—
278C42—52no—
279C42—1016no—
280C42D4×D512yes—
281C42C23×D512yes—
282C2×C5#317014yescomplemented
283C2×C5C2×#53211yescharacteristic
284C2×C5C23×Q1611yescharacteristic
285C2×C5C22×#13511yescharacteristic
286D5—24no—
287C23—54no—
288C23—52no—
289C23—102no—
290C23—102no—
291C23C2×D4×D511yescharacteristic
292Q8—216no—
293Q8—48no—
294Q8—2016no—
295C2×C4—28no—
296C2×C4—48no—
297C2×C4—54no—
298C2×C4—52no—
299C2×C4—516no—
300C2×C4—52no—
301C2×C4—52no—
302C2×C4—102no—
303C2×C4—102no—
304C2×C4—104no—
305C2×C4—108no—
306C2×C4—104no—
307C2×C4—108no—
308C2×C4—208no—
309C2×C4D5×Q1614yes—
310C2×C4#406514yes—
311C2×C4C2×D4×D511yescharacteristic
312C2×C4C2×D4×D512yes—
313C2×C4C2×D4×D512yes—
314C2×C4C2×#71114yes—
315C2×C4C24×D511yescharacteristic
316C8—104no—
317C8C2×#71118yes—
318C5C2×#317011yescharacteristic, complemented, Sylow
319C22—54no—
320C22—108no—
321C22—102no—
322C22—102no—
323C22#6605012yes—
324C22C2×D5×Q1612yes—
325C22C2×#406512yes—
326C22C22×D4×D511yescharacteristic
327C4—48no—
328C4—54no—
329C4—102no—
330C4—102no—
331C4—208no—
332C4#6605012yes—
333C4C2×D5×Q1614yes—
334C4C2×#406514yes—
335C4C22×#71112yes—
336C2—104no—
337C2#1061352314yesdirect product factor
338C2C2×#6605011yescharacteristic
339C2C22×D5×Q1611yescharacteristic
340C2C22×#406511yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#494C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
hypercenterC2×#494D5
hypocenterC5C2×#3170
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
2. C2×C5×#494C2semidirect
4. C2×Q16×Dic5C2semidirect
5. C2×#65370C2semidirect
6. #10613523C2direct (N × H)
8. C2×#64971C2semidirect
22. C5×#494C22semidirect
26. Q16×Dic5C22semidirect
29. #65370C22semidirect
32. #64971C22semidirect
79. C2×#494D5semidirect
98. C2×C4×D5Q16semidirect
140. #494C2×D5semidirect
177. C4×D5C2×Q16semidirect
282. C2×C5#3170semidirect
318. C5C2×#3170semidirect
337. C2#10613523direct (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×#4942
C2×#654772
C2×Q16×Dic52
C2×#653702
#106135232
C2×C4×C8×D52
C2×#649712
C2×#31705