Finite Group Databasebeta

← C2×#10605879 #12257596

Subgroups — C2×#10605879 #12257596

Order 1280.

3854 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4038C212yesmaximal
2C22×C42×D5C211yesmaximal, characteristic
3C2×C5×#382C211yesmaximal, characteristic, complemented
4C2×#65265C212yesmaximal, complemented
5C2×#65225C211yesmaximal, characteristic, complemented
6#10605879C2116yesmaximal, direct product factor
7C2×#64956C214yesmaximal
8C2×#64938C214yesmaximal, complemented
9C23×C4×D5C2212yes—
10C23×C4×D5C2211yescharacteristic
11C22×C5×C4⋊C4C2212yes—
12C22×C42×C5C2211yescharacteristic
13C22×#685C2214yes—
14C22×C4⋊Dic5C2212yes—
15C22×#683C2218yes—
16C22×C4×Dic5C2214yes—
17C22×C4×Dic5C2211yescharacteristic
18C22×C4×Dic5C2212yes—
19C2×#4038—216no—
20C2×#4038C22116yes—
21C2×C42×D5C4116yescomplemented
22C2×C42×D5C2218yes—
23C5×#382C2218yescomplemented
24C2×C5×#95C2214yes—
25C2×#3963C2214yes—
26#65265C22116yescomplemented
27#65225C2218yescomplemented
28#64956C22132yes—
29#64938C22132yescomplemented
30C2×#2285—51nomaximal, Sylow
31C24×D5C2311yescharacteristic
32C23×C4×C5C2314yes—
33C23×C4×C5C2312yes—
34C23×C4×C5C2311yescharacteristic
35C23×Dic5C2314yes—
36C23×Dic5C2311yescharacteristic
37C23×Dic5C2312yes—
38C22×C4×D5—216no—
39C22×C4×D5C2×C4116yes—
40C22×C4×D5C2×C418yes—
41C22×C4×D5D418yes—
42C22×C4×D5Q818yes—
43C22×C4×D5C2318yes—
44C22×C4×D5C2314yes—
45C2×C5×C4⋊C4—28no—
46C2×C5×C4⋊C4C2318yes—
47C2×C42×C5C2×C418yes—
48C2×C42×C5C2314yes—
49C2×#685—216no—
50C2×#685C23116yes—
51C2×C4⋊Dic5—28no—
52C2×C4⋊Dic5C2318yes—
53C2×#683—232no—
54C2×#683C23132yes—
55C2×C4×Dic5—216no—
56C2×C4×Dic5C2×C4116yes—
57C2×C4×Dic5C2×C418yes—
58C2×C4×Dic5C23116yes—
59C2×C4×Dic5C2318yes—
60C2×C4×Dic5C2314yes—
61#4038—264no—
62C42×D5C2×C4164yescomplemented
63C5×#95C23116yes—
64#3963C23116yes—
65C22×#117—52no—
66C23×C42—51no—
67#2285—516no—
68C2×#384—52no—
69C2×#382—51no—
70C2×#382D511yescharacteristic, complemented
71C2×#380—54no—
72C2×C4×C4⋊C4—54no—
73C24×C5C2411yescharacteristic
74C23×D5—28no—
75C23×D5C22×C414yes—
76C23×D5C2×D414yes—
77C23×D5C2×Q814yes—
78C23×D5C2412yes—
79C22×C4×C5—28no—
80C22×C4×C5—28no—
81C22×C4×C5—216no—
82C22×C4×C5C22×C418yes—
83C22×C4×C5C22×C414yes—
84C22×C4×C5C2×D414yes—
85C22×C4×C5C2×Q814yes—
86C22×C4×C5C2418yes—
87C22×C4×C5C2414yes—
88C22×C4×C5C2412yes—
89C22×Dic5—28no—
90C22×Dic5—216no—
91C22×Dic5C22×C414yes—
92C22×Dic5C22×C418yes—
93C22×Dic5C2×D414yes—
94C22×Dic5C2×Q814yes—
95C22×Dic5#41116yes—
96C22×Dic5C2418yes—
97C22×Dic5C2412yes—
98C22×Dic5C2414yes—
99C2×C4×D5—264no—
100C2×C4×D5—232no—
101C2×C4×D5C4⋊C4164yescomplemented
102C2×C4×D5C22×C4132yes—
103C2×C4×D5C22×C4116yes—
104C2×C4×D5C2×D4116yes—
105C2×C4×D5C2×Q8116yes—
106C5×C4⋊C4—216no—
107C42×C5C22×C4116yes—
108#685—232no—
109C4⋊Dic5—216no—
110#683—264no—
111C4×Dic5—232no—
112C4×Dic5C22×C4132yes—
113C4×Dic5C22×C4116yes—
114C24×C4—51no—
115C24×C4—52no—
116C2×#117—516no—
117C2×#117—1016no—
118C22×C4⋊C4—58no—
119C22×C4⋊C4—52no—
120C22×C4⋊C4C2×D512yes—
121C22×C22⋊C4—54no—
122C22×C42—52no—
123C22×C42—51no—
124C22×C42—516no—
125C22×C42—58no—
126C22×C42—54no—
127C22×C42C2×D511yescharacteristic
128#384—516no—
129#382—58no—
130#382C2×D518yescomplemented
131#380—532no—
132C4×C4⋊C4—532no—
133C2×#95—54no—
134C2×#95C2×D514yes—
135C23×C5C23×C412yes—
136C23×C5C22×D412yes—
137C23×C5C22×Q812yes—
138C23×C5C2×#4118yes—
139C23×C5C2511yescharacteristic
140C22×D5—216no—
141C22×D5—216no—
142C22×D5—216no—
143C22×D5—28no—
144C22×D5C2×C4⋊C4116yes—
145C22×D5C23×C414yes—
146C22×D5C22×D414yes—
147C22×D5C22×Q814yes—
148C2×C4×C5—216no—
149C2×C4×C5—28no—
150C2×C4×C5—28no—
151C2×C4×C5—216no—
152C2×C4×C5—416no—
153C2×C4×C5C2×C4⋊C4116yes—
154C2×C4×C5C23×C418yes—
155C2×C4×C5C23×C414yes—
156C2×C4×C5C22×D414yes—
157C2×C4×C5C22×Q814yes—
158C2×Dic5—28no—
159C2×Dic5—216no—
160C2×Dic5—416no—
161C2×Dic5C2×C4⋊C4116yes—
162C2×Dic5#117132yescomplemented
163C2×Dic5C23×C414yes—
164C2×Dic5C23×C418yes—
165C2×Dic5C22×D414yes—
166C2×Dic5C22×Q814yes—
167C2×Dic5C2×#41116yes—
168C4×D5—264no—
169C4×D5C2×C4⋊C4164yescomplemented
170C25—51no—
171C23×C4—52no—
172C23×C4—51no—
173C23×C4—58no—
174C23×C4—58no—
175C23×C4—58no—
176C23×C4—54no—
177C23×C4—516no—
178C23×C4—58no—
179C23×C4—54no—
180C23×C4—1016no—
181C23×C4C22×D514yes—
182C23×C4C22×D512yes—
183C23×C4C22×D511yescharacteristic
184#117—1064no—
185C2×C4⋊C4—28no—
186C2×C4⋊C4—58no—
187C2×C4⋊C4—532no—
188C2×C4⋊C4—1032no—
189C2×C4⋊C4—108no—
190C2×C4⋊C4C22×D518yes—
191C2×C22⋊C4—516no—
192C2×C22⋊C4—1016no—
193C2×C42—516no—
194C2×C42—58no—
195C2×C42—58no—
196C2×C42—54no—
197C2×C42—564no—
198C2×C42—516no—
199C2×C42—1016no—
200C2×C42C4×D518yes—
201C2×C42C22×D514yes—
202#95—516no—
203#95C22×D5116yes—
204C22×C5C22×C4⋊C414yes—
205C22×C5C2×#11718yes—
206C22×C5#53218yes—
207C22×C5#53318yes—
208C22×C5C24×C411yescharacteristic
209C22×C5C23×D411yescharacteristic
210C22×C5C23×Q811yescharacteristic
211C22×C5C22×#4114yes—
212C2×D5—28no—
213C2×D5—28no—
214C2×D5—28no—
215C2×D5—232no—
216C2×D5C22×C4⋊C418yes—
217C4×C5—28no—
218C4×C5—48no—
219C4×C5C22×C4⋊C418yes—
220Dic5—48no—
221Dic5C22×C4⋊C418yes—
222Dic5C2×#117116yescomplemented
223C24—54no—
224C24—54no—
225C24—54no—
226C24—52no—
227C24—108no—
228C24C23×D511yescharacteristic
229C22×C4—28no—
230C22×C4—28no—
231C22×C4—216no—
232C22×C4—54no—
233C22×C4—58no—
234C22×C4—54no—
235C22×C4—54no—
236C22×C4—516no—
237C22×C4—52no—
238C22×C4—54no—
239C22×C4—516no—
240C22×C4—516no—
241C22×C4—516no—
242C22×C4—564no—
243C22×C4—532no—
244C22×C4—58no—
245C22×C4—1064no—
246C22×C4—1032no—
247C22×C4—108no—
248C22×C4—1016no—
249C22×C4C2×C4×D518yes—
250C22×C4C2×C4×D514yes—
251C22×C4D4×D514yes—
252C22×C4Q8×D514yes—
253C22×C4C23×D518yes—
254C22×C4C23×D514yes—
255C22×C4C23×D512yes—
256C4⋊C4—216no—
257C4⋊C4—1064no—
258C4⋊C4—1016no—
259C22⋊C4—1032no—
260C42—532no—
261C42—516no—
262C42—1032no—
263C42C2×C4×D5116yes—
264C2×C5#228518yescomplemented
265C2×C5C23×C4⋊C411yescharacteristic
266C2×C5C22×#11712yes—
267C2×C5C2×#53212yes—
268C2×C5C2×#53312yes—
269D5—28no—
270C23—516no—
271C23—54no—
272C23—54no—
273C23—54no—
274C23—1016no—
275C23—1016no—
276C23—1016no—
277C23—108no—
278C23C22×C4×D512yes—
279C23C2×D4×D512yes—
280C23C2×Q8×D512yes—
281C23D5×#4118yes—
282C23C24×D511yescharacteristic
283C2×C4—216no—
284C2×C4—28no—
285C2×C4—28no—
286C2×C4—216no—
287C2×C4—416no—
288C2×C4—516no—
289C2×C4—532no—
290C2×C4—54no—
291C2×C4—58no—
292C2×C4—54no—
293C2×C4—54no—
294C2×C4—516no—
295C2×C4—564no—
296C2×C4—1064no—
297C2×C4—108no—
298C2×C4—1016no—
299C2×C4—2016no—
300C2×C4D5×C4⋊C4116yes—
301C2×C4C22×C4×D518yes—
302C2×C4C22×C4×D514yes—
303C2×C4C2×D4×D514yes—
304C2×C4C2×Q8×D514yes—
305C5C2×#228511yescharacteristic, complemented, Sylow
306C22—58no—
307C22—108no—
308C22—1032no—
309C22—108no—
310C22—108no—
311C22C2×D5×C4⋊C414yes—
312C22D5×#11718yes—
313C22#6600218yes—
314C22#6602218yes—
315C22C23×C4×D511yescharacteristic
316C22C22×D4×D511yescharacteristic
317C22C22×Q8×D511yescharacteristic
318C22C2×D5×#4114yes—
319C4—28no—
320C4—48no—
321C4—58no—
322C4—516no—
323C4—208no—
324C4C2×D5×C4⋊C418yes—
325C2—108no—
326C2#1060587918yesdirect product factor
327C2C22×D5×C4⋊C411yescharacteristic
328C2C2×D5×#11712yes—
329C2C2×#6600212yes—
330C2C2×#6602212yes—
subgroupG/H
centerC24C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC2×C5×#382C2
socleC24×C5C24
prime radicalC24×D5C23
cosocleC23×C5C25
hypercenterC2×#382D5
hypocenterC5C2×#2285
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
3. C2×C5×#382C2semidirect
4. C2×#65265C2semidirect
5. C2×#65225C2semidirect
6. #10605879C2direct (N × H)
8. C2×#64938C2semidirect
21. C2×C42×D5C4semidirect
23. C5×#382C22semidirect
26. #65265C22semidirect
27. #65225C22semidirect
29. #64938C22semidirect
62. C42×D5C2×C4semidirect
70. C2×#382D5semidirect
101. C2×C4×D5C4⋊C4semidirect
130. #382C2×D5semidirect
162. C2×Dic5#117semidirect
169. C4×D5C2×C4⋊C4semidirect
222. Dic5C2×#117semidirect
264. C2×C5#2285semidirect
305. C5C2×#2285semidirect
326. C2#10605879direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40382
C22×C42×D52
C2×C5×#3822
C2×#652652
C2×#652252
#106058792
C2×#649562
C2×#649382
C2×#22855