Finite Group Databasebeta

← C2×#10615758 #12257571

Subgroups — C2×#10615758 #12257571

Order 1280.

7630 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C4×C5C211yesmaximal, characteristic
2C22×#4072C212yesmaximal, complemented
3C2×#65536C212yesmaximal
4#10615758C2116yesmaximal, direct product factor
5C2×#65500C212yesmaximal, complemented
6C2×#65501C214yesmaximal, complemented
7C2×C4×C22⋊Dic5C214yesmaximal, complemented
8C26×C5C2211yescharacteristic
9C24×C4×C5—216no—
10C24×C4×C5C4116yescomplemented
11C24×C4×C5C2212yes—
12C24×C4×C5C2212yes—
13C24×C4×C5C2211yescharacteristic
14C24×C4×C5C2218yes—
15C24×C4×C5C2211yescharacteristic
16C22×C22⋊Dic5C2218yes—
17C22×C22⋊Dic5C2214yes—
18C2×#4072—216no—
19C2×#4072C22116yescomplemented
20C22×C4⋊Dic5C2214yescomplemented
21C22×C4×Dic5C2214yescomplemented
22#65536C22116yes—
23#65501C22132yescomplemented
24#65500C22116yescomplemented
25C4×C22⋊Dic5C22132yescomplemented
26C2×#3963C2218yescomplemented
27C2×#2280—51nomaximal, Sylow
28C25×C5—28no—
29C25×C5—216no—
30C25×C5C2×C418yes—
31C25×C5C2314yes—
32C25×C5C2311yescharacteristic
33C25×C5C2312yes—
34C23×C4×C5—28no—
35C23×C4×C5—2128no—
36C23×C4×C5—216no—
37C23×C4×C5—216no—
38C23×C4×C5—264no—
39C23×C4×C5C2×C418yes—
40C23×C4×C5C2×C4116yes—
41C23×C4×C5C2×C4116yes—
42C23×C4×C5C2×C418yes—
43C23×C4×C5C2×C4164yescomplemented
44C23×C4×C5D4116yes—
45C23×C4×C5C2312yes—
46C23×C4×C5C2318yes—
47C23×C4×C5C2314yes—
48C23×C4×C5C2318yes—
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2314yes—
51C23×C4×C5C2311yescharacteristic
52C23×Dic5C2318yes—
53C2×C22⋊Dic5—216no—
54C2×C22⋊Dic5—232no—
55C2×C22⋊Dic5C23116yes—
56C2×C22⋊Dic5C23132yes—
57#4072—264no—
58C2×C4⋊Dic5—216no—
59C2×C4⋊Dic5C23116yescomplemented
60C2×C4×Dic5—216no—
61C2×C4×Dic5C23116yescomplemented
62#3963C23132yescomplemented
63C25×C4D511yescharacteristic
64C22×#117—52no—
65#2280—516no—
66C2×#381—52no—
67C2×#380—54no—
68C2×#379—52no—
69C2×C4×C22⋊C4—54no—
70C24×C5—2128no—
71C24×C5—232no—
72C24×C5—264no—
73C24×C5—216no—
74C24×C5—28no—
75C24×C5—232no—
76C24×C5—28no—
77C24×C5—28no—
78C24×C5C22×C4116yes—
79C24×C5C22×C414yes—
80C24×C5C22×C418yes—
81C24×C5C2×D418yes—
82C24×C5#41116yes—
83C24×C5C2412yes—
84C24×C5C2414yes—
85C24×C5C2411yescharacteristic
86C22×C4×C5—232no—
87C22×C4×C5—216no—
88C22×C4×C5—28no—
89C22×C4×C5—264no—
90C22×C4×C5—264no—
91C22×C4×C5—2256no—
92C22×C4×C5—232no—
93C22×C4×C5—232no—
94C22×C4×C5C22⋊C4164yescomplemented
95C22×C4×C5C22×C418yes—
96C22×C4×C5C22×C4116yes—
97C22×C4×C5C22×C4132yes—
98C22×C4×C5C22×C4132yes—
99C22×C4×C5C22×C414yes—
100C22×C4×C5C22×C414yes—
101C22×C4×C5C22×C4116yes—
102C22×C4×C5C2×D418yes—
103C22×C4×C5C2×D418yes—
104C22×C4×C5C2×D4132yes—
105C22×C4×C5C2414yes—
106C22×C4×C5C2412yes—
107C22×C4×C5C2412yes—
108C22×Dic5—216no—
109C22×Dic5—232no—
110C22×Dic5C24116yes—
111C22⋊Dic5—232no—
112C22⋊Dic5—264no—
113C4⋊Dic5—232no—
114C4×Dic5—232no—
115C26C2×D511yescharacteristic
116C24×C4—216no—
117C24×C4Dic5116yescomplemented
118C24×C4C2×D512yes—
119C24×C4C2×D511yescharacteristic
120C24×C4C2×D512yes—
121C24×C4C2×D518yes—
122C24×C4C2×D511yescharacteristic
123C2×#117—516no—
124C2×#117—1016no—
125C22×C4⋊C4—54no—
126C22×C22⋊C4—54no—
127C22×C22⋊C4—58no—
128C22×C42—54no—
129#381—516no—
130#380—532no—
131#379—516no—
132C4×C22⋊C4—532no—
133C2×#95—58no—
134C23×C5—2128no—
135C23×C5—2256no—
136C23×C5—232no—
137C23×C5—216no—
138C23×C5—216no—
139C23×C5—216no—
140C23×C5—264no—
141C23×C5—232no—
142C23×C5—264no—
143C23×C5—28no—
144C23×C5—28no—
145C23×C5—28no—
146C23×C5C2×C22⋊C4116yes—
147C23×C5#117132yescomplemented
148C23×C5C23×C414yes—
149C23×C5C23×C418yes—
150C23×C5C23×C412yes—
151C23×C5C22×D418yes—
152C23×C5C22×D414yes—
153C23×C5C2×#41116yes—
154C23×C5C2×#4118yes—
155C23×C5C2511yescharacteristic
156C2×C4×C5—232no—
157C2×C4×C5—216no—
158C2×C4×C5—28no—
159C2×C4×C5—264no—
160C2×C4×C5—264no—
161C2×C4×C5C2×C22⋊C4116yes—
162C2×C4×C5C2×C22⋊C4116yes—
163C2×C4×C5C2×C22⋊C4164yescomplemented
164C2×C4×C5C23×C418yes—
165C2×C4×C5C23×C414yes—
166C2×C4×C5C23×C414yes—
167C2×C4×C5C22×D418yes—
168C2×C4×C5C22×D418yes—
169C2×Dic5—216no—
170C2×Dic5—232no—
171C2×Dic5—432no—
172C25—216no—
173C25—28no—
174C25C2×Dic518yes—
175C25C22×D514yes—
176C25C22×D512yes—
177C25C22×D511yescharacteristic
178C23×C4—28no—
179C23×C4—2128no—
180C23×C4—216no—
181C23×C4—216no—
182C23×C4—264no—
183C23×C4—58no—
184C23×C4C2×Dic518yes—
185C23×C4C2×Dic5116yes—
186C23×C4C2×Dic5116yes—
187C23×C4C2×Dic518yes—
188C23×C4C2×Dic5164yescomplemented
189C23×C4C22⋊D5116yes—
190C23×C4C22×D512yes—
191C23×C4C22×D518yes—
192C23×C4C22×D518yes—
193C23×C4C22×D514yes—
194C23×C4C22×D511yescharacteristic
195C23×C4C22×D514yes—
196C23×C4C22×D511yescharacteristic
197#117—1064no—
198C2×C4⋊C4—516no—
199C2×C4⋊C4—1016no—
200C2×C22⋊C4—516no—
201C2×C22⋊C4—532no—
202C2×C22⋊C4—1032no—
203C2×C22⋊C4—1016no—
204C2×C42—516no—
205C2×C42—1016no—
206#95—532no—
207C22×C5—2128no—
208C22×C5—28no—
209C22×C5—28no—
210C22×C5—28no—
211C22×C5—216no—
212C22×C5—232no—
213C22×C5—232no—
214C22×C5—264no—
215C22×C5C22×C22⋊C418yes—
216C22×C5C22×C22⋊C414yes—
217C22×C5C2×#11718yes—
218C22×C5C2×#117116yescomplemented
219C22×C5#525116yes—
220C22×C5C24×C411yescharacteristic
221C22×C5C23×D412yes—
222C22×C5C22×#4114yes—
223C4×C5—28no—
224C4×C5C22×C22⋊C418yes—
225C4×C5C22×C22⋊C418yes—
226Dic5—416no—
227C24—2128no—
228C24—232no—
229C24—232no—
230C24—28no—
231C24—28no—
232C24—216no—
233C24—28no—
234C24—264no—
235C24#709116yes—
236C24C22×Dic5116yes—
237C24C22×Dic514yes—
238C24C22×Dic518yes—
239C24C2×C22⋊D518yes—
240C24C23×D514yes—
241C24C23×D512yes—
242C24C23×D511yescharacteristic
243C22×C4—232no—
244C22×C4—216no—
245C22×C4—28no—
246C22×C4—264no—
247C22×C4—264no—
248C22×C4—2256no—
249C22×C4—232no—
250C22×C4—232no—
251C22×C4—516no—
252C22×C4—1032no—
253C22×C4—1016no—
254C22×C4C22⋊Dic5164yescomplemented
255C22×C4C22×Dic518yes—
256C22×C4C22×Dic5116yes—
257C22×C4C22×Dic5132yes—
258C22×C4C22×Dic5132yes—
259C22×C4C22×Dic514yes—
260C22×C4C22×Dic514yes—
261C22×C4C22×Dic5116yes—
262C22×C4C2×C22⋊D518yes—
263C22×C4C2×C22⋊D518yes—
264C22×C4C2×C22⋊D5132yes—
265C22×C4C23×D514yes—
266C22×C4C23×D512yes—
267C22×C4C23×D512yes—
268C4⋊C4—1032no—
269C22⋊C4—1064no—
270C22⋊C4—1032no—
271C42—1032no—
272C2×C5—28no—
273C2×C5—216no—
274C2×C5#228018yescomplemented
275C2×C5C23×C22⋊C411yescharacteristic
276C2×C5C22×#11712yes—
277C2×C5C2×#52514yes—
278C23—2256no—
279C23—2128no—
280C23—216no—
281C23—216no—
282C23—264no—
283C23—264no—
284C23—232no—
285C23—232no—
286C23—216no—
287C23—28no—
288C23—28no—
289C23—28no—
290C23#4072132yescomplemented
291C23C2×C22⋊Dic5116yes—
292C23C2×#709116yes—
293C23C2×#70918yes—
294C23C23×Dic518yes—
295C23C23×Dic514yes—
296C23C23×Dic512yes—
297C23C22×C22⋊D518yes—
298C23C22×C22⋊D514yes—
299C23C24×D511yescharacteristic
300C2×C4—232no—
301C2×C4—216no—
302C2×C4—28no—
303C2×C4—264no—
304C2×C4—264no—
305C2×C4—1032no—
306C2×C4—1016no—
307C2×C4—2032no—
308C2×C4C2×C22⋊Dic5116yes—
309C2×C4C2×C22⋊Dic5116yes—
310C2×C4C2×C22⋊Dic5164yescomplemented
311C2×C4C23×Dic518yes—
312C2×C4C23×Dic514yes—
313C2×C4C23×Dic514yes—
314C2×C4C22×C22⋊D518yes—
315C2×C4C22×C22⋊D518yes—
316C5C2×#228011yescharacteristic, complemented, Sylow
317C22—2128no—
318C22—28no—
319C22—232no—
320C22—264no—
321C22—28no—
322C22—28no—
323C22—232no—
324C22—216no—
325C22C2×#407218yes—
326C22C2×#4072116yescomplemented
327C22#66125116yes—
328C22C22×C22⋊Dic518yes—
329C22C22×C22⋊Dic514yes—
330C22C22×#70914yes—
331C22C24×Dic511yescharacteristic
332C22C23×C22⋊D512yes—
333C4—28no—
334C4—2016no—
335C4C22×C22⋊Dic518yes—
336C4C22×C22⋊Dic518yes—
337C2—216no—
338C2—28no—
339C2#1061575818yesdirect product factor
340C2C22×#407212yes—
341C2C2×#6612514yes—
342C2C23×C22⋊Dic511yescharacteristic
subgroupG/H
centerC23×C4C22×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC25×C4×C5C2
socleC24×C5C24
prime radicalC26×C5C22
cosocleC23×C5C25
hypercenterC25×C4D5
hypocenterC5C2×#2280
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C25×C4

Complements

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

NH ≅ G/Ntype
2. C22×#4072C2semidirect
4. #10615758C2direct (N × H)
5. C2×#65500C2semidirect
6. C2×#65501C2semidirect
7. C2×C4×C22⋊Dic5C2semidirect
10. C24×C4×C5C4semidirect
19. C2×#4072C22semidirect
20. C22×C4⋊Dic5C22semidirect
21. C22×C4×Dic5C22semidirect
23. #65501C22semidirect
24. #65500C22semidirect
25. C4×C22⋊Dic5C22semidirect
26. C2×#3963C22semidirect
43. C23×C4×C5C2×C4semidirect
59. C2×C4⋊Dic5C23semidirect
61. C2×C4×Dic5C23semidirect
62. #3963C23semidirect
94. C22×C4×C5C22⋊C4semidirect
117. C24×C4Dic5semidirect
147. C23×C5#117semidirect
163. C2×C4×C5C2×C22⋊C4semidirect
188. C23×C4C2×Dic5semidirect
218. C22×C5C2×#117semidirect
254. C22×C4C22⋊Dic5semidirect
274. C2×C5#2280semidirect
290. C23#4072semidirect
310. C2×C4C2×C22⋊Dic5semidirect
316. C5C2×#2280semidirect
326. C22C2×#4072semidirect
339. C2#10615758direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C4×C52
C22×#40722
C2×#655362
#106157582
C2×#655002
C2×#655012
C2×C4×C22⋊Dic52
C2×#22805