Finite Group Databasebeta

← D5×#2982 #12964236

Subgroups — D5×#2982 #12964236

Order 1280.

2234 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
1C2×C4×Q8×D5C211yesmaximal, characteristic
2C5×#2982C211yesmaximal, characteristic, complemented
3#10614166C211yesmaximal, characteristic, complemented
4#10611651C218yesmaximal, complemented
5C8×Q8×D5C218yesmaximal, complemented
6D5×#431C216yesmaximal
7#10610994C216yesmaximal, complemented
8C22×Q8×D5C411yescharacteristic
9C2×C4×C5×Q8C2211yescharacteristic
10C2×Q8×Dic5C411yescharacteristic
11C4×Q8×D5C414yes—
12C4×Q8×D5C414yes—
13C4×Q8×D5C2214yes—
14C4×Q8×D5C2214yes—
15C2×D5×C4⋊C4C413yes—
16C2×#4033C413yes—
17C2×C42×D5C2213yes—
18C2×C4×Dic10C2213yes—
19C5×C8×Q8C2218yescomplemented
20C5×#431C2216yes—
21Q8×#168C2218yescomplemented
22#65214C2216yes—
23#65122C22112yes—
24D5×C4⋊C8C22112yes—
25#65119C22124yescomplemented
26D5×C22⋊C8C2214yes—
27#65007C22112yes—
28#64974C22112yes—
29C4×C8×D5C22112yes—
30C8×Dic10C22124yescomplemented
31C2×#2982—51nomaximal, Sylow
32C22×C5×Q8C2×C411yescharacteristic
33C2×Q8×D5C8116yescomplemented
34C2×Q8×D5C2×C414yes—
35C2×Q8×D5C2×C414yes—
36C22×C4×D5C2×C413yes—
37C22×C4×D5C2×C413yes—
38C22×C4×D5C2311yescharacteristic
39C22×Dic10C2×C413yes—
40C4×C5×Q8C2×C414yes—
41C4×C5×Q8C2314yes—
42C2×C5×C4⋊C4C2×C413yes—
43C2×C42×C5C2313yes—
44Q8×Dic5C2×C414yes—
45Q8×Dic5C2×C414yes—
46C2×C4⋊Dic5C2×C413yes—
47C2×#683C2×C416yes—
48C2×C4×Dic5C2×C413yes—
49C2×C4×Dic5C2×C413yes—
50C2×C4×Dic5C2313yes—
51C2×C8×D5C2318yes—
52D5×C4⋊C4C2×C4112yes—
53D5×C4⋊C4C2×C4112yes—
54#4033C2×C4112yes—
55#4033C2×C4112yes—
56C42×D5C2×C416yes—
57C42×D5C2×C416yes—
58C42×D5C2316yes—
59C42×D5C2316yes—
60C4×Dic10C2×C4112yes—
61C4×Dic10C23112yes—
62C5×C4⋊C8C23112yes—
63C5×C22⋊C8C2314yes—
64C4×C5×C8C23112yes—
65C22⋊#168C2314yes—
66#3952C2318yes—
67#3946C23124yes—
68C8×Dic5C23124yes—
69C4⋊#168C23112yes—
70C4×#168C23112yes—
71C22×C4×Q8—51no—
72#2982—58no—
73#2982—56no—
74#2982—51no—
75#2982D511yescharacteristic, direct product factor
76C2×C8×Q8—58no—
77C2×#431—56no—
78C23×D5C22×C411yescharacteristic
79C2×C5×Q8C2×C818yescomplemented
80C2×C5×Q8C22×C414yes—
81C22×C4×C5C22×C413yes—
82C22×C4×C5C22×C413yes—
83C22×C4×C5C2411yescharacteristic
84C22×Dic5C22×C411yescharacteristic
85C22×Dic5C22×C413yes—
86C22×Dic5C22×C413yes—
87Q8×D5C2×C8132yes—
88Q8×D5C2×C8132yescomplemented
89C2×C4×D5—24no—
90C2×C4×D5—46no—
91C2×C4×D5C2×C8124yes—
92C2×C4×D5C22×C416yes—
93C2×C4×D5C22×C411yescharacteristic
94C2×C4×D5C22×C411yescharacteristic
95C2×C4×D5C22×C416yes—
96C2×C4×D5C22×C416yes—
97C2×C4×D5C22×C416yes—
98C2×C4×D5C2411yescharacteristic
99C2×C4×D5C2411yescharacteristic
100C2×Dic10C2×C8124yescomplemented
101C2×Dic10C22×C4112yes—
102C2×C5×C8C2418yes—
103C5×C4⋊C4C22×C4112yes—
104C42×C5C22×C416yes—
105C42×C5C2416yes—
106C4⋊Dic5C22×C4112yes—
107#683C22×C4124yes—
108C4×Dic5C22×C416yes—
109C4×Dic5C22×C416yes—
110C4×Dic5C22×C416yes—
111C4×Dic5C22×C416yes—
112C4×Dic5C22×C416yes—
113C4×Dic5C2416yes—
114C2×#168C2418yes—
115C8×D5—216no—
116C23×Q8—51no—
117C2×C4×Q8—51no—
118C2×C4×Q8—54no—
119C2×C4×Q8—54no—
120C2×C4×Q8—54no—
121C2×C4×Q8—54no—
122C2×C4×Q8—53no—
123C2×C4×Q8—53no—
124C2×C4×Q8C2×D511yescharacteristic
125C22×C4⋊C4—53no—
126C22×C42—53no—
127C8×Q8—58no—
128C8×Q8—524no—
129C8×Q8—524no—
130C8×Q8C2×D518yescomplemented
131#431—56no—
132#431—512no—
133#431—512no—
134#431—512no—
135#431C2×D516yes—
136C2×C4⋊C8—512no—
137C2×C22⋊C8—54no—
138C2×C4×C8—512no—
139C23×C5C23×C411yescharacteristic
140C22×D5—22no—
141C22×D5—22no—
142C22×D5C22×C814yes—
143C22×D5C23×C411yescharacteristic
144C22×D5C23×C411yescharacteristic
145C5×Q8C22×C8116yes—
146C2×C4×C5—22no—
147C2×C4×C5—43no—
148C2×C4×C5C22×C8112yes—
149C2×C4×C5C23×C411yescharacteristic
150C2×C4×C5C23×C416yes—
151C2×C4×C5C23×C416yes—
152C2×C4×C5C2511yescharacteristic
153C2×Dic5—22no—
154C2×Dic5—43no—
155C2×Dic5C22×C8112yes—
156C2×Dic5C23×C411yescharacteristic
157C2×Dic5C23×C416yes—
158C2×Dic5C23×C411yescharacteristic
159C2×Dic5C23×C416yes—
160C4×D5—22no—
161C4×D5—212no—
162C4×D5—22no—
163C4×D5—22no—
164C4×D5—46no—
165C4×D5C22×C8124yes—
166C4×D5C22×C8124yes—
167C4×D52−1+414yes—
168Dic10C22×C8148yes—
169C5×C8—28no—
170#168—28no—
171C22×Q8—516no—
172C22×Q8—54no—
173C22×Q8—54no—
174C22×Q8—53no—
175C22×Q8C4×D511yescharacteristic
176C23×C4—53no—
177C23×C4—51no—
178C23×C4—53no—
179C22×C8—58no—
180C4×Q8—54no—
181C4×Q8—54no—
182C4×Q8—512no—
183C4×Q8—512no—
184C4×Q8—512no—
185C4×Q8—512no—
186C4×Q8C4×D514yes—
187C4×Q8C22×D514yes—
188C2×C4⋊C4—56no—
189C2×C4⋊C4—53no—
190C2×C4⋊C4—512no—
191C2×C4⋊C4—512no—
192C2×C4⋊C4C4×D513yes—
193C2×C42—53no—
194C2×C42—53no—
195C2×C42—53no—
196C2×C42—56no—
197C2×C42—56no—
198C2×C42—56no—
199C2×C42—56no—
200C2×C42C22×D513yes—
201C4⋊C8—524no—
202C4⋊C8—512no—
203C4⋊C8C22×D5112yes—
204C22⋊C8—54no—
205C22⋊C8—58no—
206C22⋊C8C22×D514yes—
207C4×C8—524no—
208C4×C8—512no—
209C4×C8C22×D5112yes—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5C23×C812yes—
213C22×C5C24×C411yescharacteristic
214C2×D5—21no—
215C2×D5—21no—
216C2×D5—28no—
217C2×D5#51912yes—
218C2×D5C23×C812yes—
219C2×D5C23×C812yes—
220C2×D5#56812yes—
221C4×C5—21no—
222C4×C5—26no—
223C4×C5C23×C8112yes—
224C4×C5C2×2−1+412yes—
225Dic5—21no—
226Dic5—26no—
227Dic5#51912yes—
228Dic5C23×C8112yes—
229C24—51no—
230C2×Q8—532no—
231C2×Q8—532no—
232C2×Q8—512no—
233C2×Q8—524no—
234C2×Q8C8×D518yescomplemented
235C2×Q8C2×C4×D514yes—
236C22×C4—53no—
237C22×C4—56no—
238C22×C4—56no—
239C22×C4—51no—
240C22×C4—524no—
241C22×C4—51no—
242C22×C4—53no—
243C22×C4—51no—
244C22×C4—51no—
245C22×C4—56no—
246C22×C4—51no—
247C22×C4—56no—
248C22×C4—104no—
249C22×C4—206no—
250C22×C4C2×C4×D513yes—
251C22×C4C2×C4×D513yes—
252C22×C4C23×D511yescharacteristic
253C2×C8—58no—
254C2×C8—1016no—
255C2×C8C23×D518yes—
256C4⋊C4—524no—
257C4⋊C4—512no—
258C4⋊C4C2×C4×D5112yes—
259C42—56no—
260C42—56no—
261C42—56no—
262C42—56no—
263C42—56no—
264C42—56no—
265C42C2×C4×D516yes—
266C42C23×D516yes—
267C2×C5—22no—
268C2×C5C2×#51911yescharacteristic
269C2×C5C24×C811yescharacteristic
270C2×C5C2×#56811yescharacteristic
271D5—22no—
272D5#298214yesdirect product factor
273C23—51no—
274C23—54no—
275C23—51no—
276C23—102no—
277C23—102no—
278C23C22×C4×D511yescharacteristic
279Q8—548no—
280Q8C2×C8×D5116yes—
281C2×C4—22no—
282C2×C4—43no—
283C2×C4—512no—
284C2×C4—51no—
285C2×C4—56no—
286C2×C4—524no—
287C2×C4—524no—
288C2×C4—54no—
289C2×C4—51no—
290C2×C4—56no—
291C2×C4—102no—
292C2×C4—102no—
293C2×C4—1012no—
294C2×C4—102no—
295C2×C4—102no—
296C2×C4—206no—
297C2×C4—203no—
298C2×C4C2×C8×D5112yes—
299C2×C4C22×C4×D511yescharacteristic
300C2×C4C22×C4×D516yes—
301C2×C4C22×C4×D516yes—
302C2×C4C24×D511yescharacteristic
303C8—28no—
304C8—108no—
305C5C2×#298211yescharacteristic, complemented, Sylow
306C22—21no—
307C22—21no—
308C22—52no—
309C22—52no—
310C22—52no—
311C22—52no—
312C22—108no—
313C22—101no—
314C22—101no—
315C22C22×C8×D512yes—
316C22C23×C4×D511yescharacteristic
317C4—21no—
318C4—26no—
319C4—512no—
320C4—52no—
321C4—101no—
322C4—106no—
323C4C22×C8×D5112yes—
324C4D5×2−1+412yes—
325C2—22no—
326C2—54no—
327C2—102no—
328C2D5×#51911yescharacteristic
329C2C23×C8×D511yescharacteristic
330C2D5×#56811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D5
commutatorC2×C5C24×C8
FittingC5×#2982C2
socleC22×C5C24×C4
prime radicalC23×D5C22×C4
cosocleC2×C4×C5C25
hypercenter#2982D5
hypocenterC5C2×#2982
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. C5×#2982C2semidirect
3. #10614166C2semidirect
4. #10611651C2semidirect
5. C8×Q8×D5C2semidirect
7. #10610994C2semidirect
19. C5×C8×Q8C22semidirect
21. Q8×#168C22semidirect
25. #65119C22semidirect
30. C8×Dic10C22semidirect
33. C2×Q8×D5C8semidirect
75. #2982D5direct (N × H)
79. C2×C5×Q8C2×C8semidirect
88. Q8×D5C2×C8semidirect
100. C2×Dic10C2×C8semidirect
130. C8×Q8C2×D5semidirect
234. C2×Q8C8×D5semidirect
272. D5#2982direct (N × H)
305. C5C2×#2982semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D52
C5×#29822
#106141662
#106116512
C8×Q8×D52
D5×#4312
#106109942
C2×#29825