Finite Group Databasebeta

← C2×#10610250 #12963039

Subgroups — C2×#10610250 #12963039

Order 1280.

2222 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
1C2×C4×#709C211yesmaximal, characteristic
2C2×C4×C5×M16C211yesmaximal, characteristic, complemented
3C2×#65418C212yesmaximal
4C2×#65408C212yesmaximal, complemented
5C22×C4×#168C211yesmaximal, characteristic, complemented
6#10610250C2116yesmaximal, direct product factor
7C2×#64998C214yesmaximal, complemented
8C2×#64974C214yesmaximal, complemented
9C22×#709C2211yescharacteristic
10C22×C5×M16C2212yes—
11C22×C42×C5C2211yescharacteristic
12C2×C4×C22⋊D5C414yes—
13C2×#4072C2211yescharacteristic
14C23×#168C2212yes—
15C4×#709C418yes—
16C4×#709C2218yes—
17C2×C4×D20C412yes—
18C2×#4018C2212yes—
19C2×C42×D5C2212yes—
20C2×C4×Dic10C412yes—
21C4×C5×M16C2218yescomplemented
22C2×C5×#97C2212yes—
23C2×C4×C5×C8C2212yes—
24#65418C22116yes—
25#65408C22116yescomplemented
26C2×#3952C2218yes—
27C2×#3946C2218yes—
28C2×C4×#168C2212yes—
29C2×C4×#168C2212yes—
30C2×C4×#168C2218yescomplemented
31#64998C22132yescomplemented
32#64974C22132yescomplemented
33C2×#2922—51nomaximal, Sylow
34C23×C4×C5C2×C412yes—
35C23×C4×C5C2311yescharacteristic
36C22×C22⋊D5C2×C412yes—
37C2×#709—28no—
38C2×#709C2×C414yes—
39C2×#709C2314yes—
40C22×D20C2×C411yescharacteristic
41C22×C4×D5C2×C414yes—
42C22×C4×D5C2312yes—
43C22×Dic10C2×C411yescharacteristic
44C2×C5×M16—28no—
45C2×C5×M16C2318yes—
46C22×C5×C8C2314yes—
47C2×C42×C5C2×C412yes—
48C2×C42×C5C2×C414yes—
49C2×C42×C5C2311yescharacteristic
50C2×C42×C5C2314yes—
51C2×C42×C5C2311yescharacteristic
52C2×C22⋊Dic5C2×C412yes—
53C4×C22⋊D5C2×C4132yes—
54C2×#685C2×C414yes—
55#4072C2×C414yes—
56#4072C2314yes—
57C2×C4⋊Dic5C2×C412yes—
58C2×#683C2×C414yes—
59C2×C4×Dic5C2×C414yes—
60C2×C4×Dic5C2312yes—
61C22×#168—28no—
62C22×#168C2314yes—
63C22×#168C2318yes—
64C4×D20C2×C4116yes—
65#4018C2×C418yes—
66#4018C2318yes—
67C42×D5C2×C418yes—
68C42×D5C2318yes—
69C4×Dic10C2×C4116yes—
70C5×#97C2318yes—
71C4×C5×C8C2318yes—
72#3952C23132yes—
73#3946C23132yes—
74C4×#168C2318yes—
75C4×#168C2318yes—
76C2×C4×#41—51no—
77#2922—516no—
78C2×#433—54no—
79C2×#431—54no—
80C2×#424—52no—
81C2×#408—52no—
82C2×C4×M16D511yescharacteristic, complemented
83C22×C4×C8—51no—
84C24×C5C22×C411yescharacteristic
85C23×D5C22×C412yes—
86C22×C4×C5—28no—
87C22×C4×C5C22×C412yes—
88C22×C4×C5C22×C418yes—
89C22×C4×C5C22×C411yescharacteristic
90C22×C4×C5C22×C412yes—
91C22×C4×C5C22×C412yes—
92C22×C4×C5#4118yes—
93C22×C4×C5C2411yescharacteristic
94C22×C4×C5C2412yes—
95C2×C22⋊D5—28no—
96C2×C22⋊D5C22×C418yes—
97C22×Dic5C22×C414yes—
98C22×Dic5C22×C412yes—
99#709—216no—
100#709—216no—
101C2×D20—24no—
102C2×D20C22×C414yes—
103C2×C4×D5—216no—
104C2×C4×D5—28no—
105C2×C4×D5C22×C4116yes—
106C2×C4×D5C22×C414yes—
107C2×C4×D5C2414yes—
108C2×Dic10—24no—
109C2×Dic10C22×C414yes—
110C5×M16—216no—
111C2×C5×C8—28no—
112C2×C5×C8C2418yes—
113C42×C5C22×C418yes—
114C42×C5C22×C412yes—
115C42×C5C22×C412yes—
116C42×C5C2412yes—
117C42×C5C2412yes—
118C22⋊Dic5C22×C418yes—
119#685C22×C4116yes—
120C4⋊Dic5C22×C418yes—
121#683C22×C4116yes—
122C4×Dic5C22×C4116yes—
123C4×Dic5C22×C414yes—
124C4×Dic5C2414yes—
125C2×#168—28no—
126C2×#168—216no—
127C2×#168C2418yes—
128C22×#41—51no—
129C22×M16C2×D512yes—
130C23×C8—52no—
131C4×#41—58no—
132C4×#41—58no—
133C2×C4×Q8—52no—
134C2×C4×D4—54no—
135C2×C4×D4—52no—
136C2×#117—51no—
137C2×#117—52no—
138C22×C42—52no—
139C22×C42C2×D511yescharacteristic
140#433—532no—
141#431—532no—
142#424—516no—
143C2×C4⋊C8—58no—
144#408—516no—
145C2×C22⋊C8—58no—
146C4×M16C2×D518yescomplemented
147C2×#97C2×D512yes—
148C2×C4×C8—52no—
149C2×C4×C8—58no—
150C2×C4×C8—52no—
151C2×C4×C8C2×D512yes—
152C23×C5—24no—
153C23×C5#11714yes—
154C23×C5C23×C412yes—
155C23×C5C23×C411yescharacteristic
156C22×D5—24no—
157C22×D5—28no—
158C22×D5C23×C414yes—
159C2×C4×C5—24no—
160C2×C4×C5—216no—
161C2×C4×C5#11714yes—
162C2×C4×C5#11718yes—
163C2×C4×C5#13118yes—
164C2×C4×C5C23×C414yes—
165C2×C4×C5C23×C411yescharacteristic
166C2×C4×C5C23×C412yes—
167C2×C4×C5C23×C414yes—
168C2×C4×C5C2×#4114yes—
169C2×C4×C5C2×#4118yes—
170C2×C4×C5C2511yescharacteristic
171C22⋊D5—216no—
172C2×Dic5—24no—
173C2×Dic5—28no—
174C2×Dic5C23×C414yes—
175C2×Dic5C23×C418yes—
176D20—28no—
177C4×D5—28no—
178C4×D5—232no—
179C4×D5—28no—
180Dic10—28no—
181C5×C8—28no—
182#168—28no—
183C2×#41—54no—
184C2×#41—54no—
185C2×#41—108no—
186C22×Q8—51no—
187C22×D4—52no—
188C22×D4—51no—
189C23×C4—54no—
190C23×C4—52no—
191C23×C4C4×D512yes—
192C23×C4C22×D511yescharacteristic
193C2×M16—28no—
194C2×M16C22×D518yes—
195C22×C8—54no—
196C22×C8—58no—
197C22×C8—108no—
198C22×C8C22×D514yes—
199C4×Q8—516no—
200C4×D4—532no—
201C4×D4—516no—
202#117—54no—
203#117—54no—
204#117—58no—
205#117—58no—
206C2×C4⋊C4—54no—
207C2×C4⋊C4—52no—
208C2×C22⋊C4—52no—
209C2×C22⋊C4—54no—
210C2×C42—54no—
211C2×C42—52no—
212C2×C42—58no—
213C2×C42—58no—
214C2×C42C4×D512yes—
215C2×C42C4×D514yes—
216C2×C42C22×D511yescharacteristic
217C2×C42C22×D514yes—
218C2×C42C22×D511yescharacteristic
219C4⋊C8—532no—
220C22⋊C8—532no—
221#97C22×D518yes—
222C4×C8—58no—
223C4×C8—58no—
224C4×C8C22×D518yes—
225C22×C5—28no—
226C22×C5—24no—
227C22×C5C2×#11714yes—
228C22×C5C2×#11712yes—
229C22×C5C2×#13114yes—
230C22×C5C24×C411yescharacteristic
231C2×D5—24no—
232C2×D5—28no—
233C2×D5—48no—
234C4×C5—24no—
235C4×C5C2×#11714yes—
236C4×C5C2×#11712yes—
237C4×C5C2×#13118yes—
238C4×C5C22×#4112yes—
239Dic5—24no—
240Dic5—28no—
241C24—52no—
242C24C2×C4×D511yescharacteristic
243#41—1016no—
244#41—1016no—
245C2×Q8—54no—
246C2×Q8—104no—
247C2×D4—58no—
248C2×D4—54no—
249C2×D4—108no—
250C2×D4—104no—
251C22×C4—28no—
252C22×C4—54no—
253C22×C4—52no—
254C22×C4—54no—
255C22×C4—516no—
256C22×C4—54no—
257C22×C4—108no—
258C22×C4—1016no—
259C22×C4C2×C4×D512yes—
260C22×C4C2×C4×D518yes—
261C22×C4C2×C4×D511yescharacteristic
262C22×C4C2×C4×D512yes—
263C22×C4C2×C4×D512yes—
264C22×C4#70918yes—
265C22×C4C23×D511yescharacteristic
266C22×C4C23×D512yes—
267M16—216no—
268C2×C8—28no—
269C2×C8—58no—
270C2×C8—108no—
271C2×C8—1016no—
272C2×C8C23×D518yes—
273C4⋊C4—516no—
274C4⋊C4—58no—
275C22⋊C4—58no—
276C22⋊C4—516no—
277C42—54no—
278C42—516no—
279C42—54no—
280C42C2×C4×D512yes—
281C42C2×C4×D512yes—
282C42C2×C4×D518yes—
283C42C23×D512yes—
284C42C23×D512yes—
285C2×C5—24no—
286C2×C5#292214yescomplemented
287C2×C5C22×#11711yescharacteristic
288C2×C5C22×#13112yes—
289D5—44no—
290C23—24no—
291C23—54no—
292C23—104no—
293C23—108no—
294C23#401814yes—
295C23C22×C4×D512yes—
296C23C22×C4×D511yescharacteristic
297Q8—108no—
298D4—1016no—
299D4—108no—
300C2×C4—24no—
301C2×C4—216no—
302C2×C4—58no—
303C2×C4—54no—
304C2×C4—104no—
305C2×C4—108no—
306C2×C4—108no—
307C2×C4—1032no—
308C2×C4—108no—
309C2×C4#401814yes—
310C2×C4#401818yes—
311C2×C4#405318yes—
312C2×C4C22×C4×D514yes—
313C2×C4C22×C4×D511yescharacteristic
314C2×C4C22×C4×D512yes—
315C2×C4C22×C4×D514yes—
316C2×C4C2×#70914yes—
317C2×C4C2×#70918yes—
318C2×C4C24×D511yescharacteristic
319C8—28no—
320C8—108no—
321C5C2×#292211yescharacteristic, complemented, Sylow
322C22—28no—
323C22—24no—
324C22—108no—
325C22—104no—
326C22—208no—
327C22C2×#401814yes—
328C22C2×#401812yes—
329C22C2×#405314yes—
330C22C23×C4×D511yescharacteristic
331C4—24no—
332C4—108no—
333C4—104no—
334C4C2×#401812yes—
335C4C2×#401814yes—
336C4C2×#405318yes—
337C4C22×#70912yes—
338C2—24no—
339C2—204no—
340C2#1061025014yesdirect product factor
341C2C22×#401811yescharacteristic
342C2C22×#405312yes—
subgroupG/H
centerC2×C42C22×D5
commutatorC22×C5C24×C4
FrattiniC2×C4C24×D5
FittingC2×C4×C5×M16C2
socleC23×C5C23×C4
prime radicalC22×#709C22
cosocleC2×C4×C5C25
hypercenterC2×C4×M16D5
hypocenterC5C2×#2922
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
2. C2×C4×C5×M16C2semidirect
4. C2×#65408C2semidirect
5. C22×C4×#168C2semidirect
6. #10610250C2direct (N × H)
7. C2×#64998C2semidirect
8. C2×#64974C2semidirect
21. C4×C5×M16C22semidirect
25. #65408C22semidirect
30. C2×C4×#168C22semidirect
31. #64998C22semidirect
32. #64974C22semidirect
82. C2×C4×M16D5semidirect
146. C4×M16C2×D5semidirect
286. C2×C5#2922semidirect
321. C5C2×#2922semidirect
340. C2#10610250direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#7092
C2×C4×C5×M162
C2×#654182
C2×#654082
C22×C4×#1682
#106102502
C2×#649982
C2×#649742
C2×#29225