Finite Group Databasebeta

← C2×#10615416 #12980197

Subgroups — C2×#10615416 #12980197

Order 1280.

2238 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#557C211yesmaximal, characteristic, complemented
2C2×#65911C211yesmaximal, characteristic
3#10615416C2116yesmaximal, direct product factor
4C2×#65372C213yesmaximal, complemented
5C2×#65374C213yesmaximal, complemented
6C2×#65316C213yesmaximal, complemented
7C2×Q8×#168C211yesmaximal, characteristic, complemented
8C2×C4×#688C213yesmaximal, complemented
9C22×#713—21no—
10C5×#557—24no—
11C5×#557C2218yescomplemented
12C2×C5×C4⋊Q8C2213yes—
13C2×C5×#125—23no—
14C2×C4×C5×Q8—21no—
15C2×C4×C5×Q8C2213yes—
16C2×C4×C5×Q8C2211yescharacteristic
17C22×#688C2213yes—
18C22×#688C2216yes—
19#65911—24no—
20#65911C2218yes—
21C2×#4041—23no—
22C2×#4020C2213yes—
23C2×C4×D20C2213yes—
24C2×#3967C2213yes—
25#65374C22124yescomplemented
26#65372C22124yescomplemented
27#65316C22124yescomplemented
28C4×#688C22124yescomplemented
29Q8×#168C2218yescomplemented
30C2×#3941C2213yes—
31C2×#3940C2211yescharacteristic
32C2×C4⋊#168C2213yes—
33C2×C4×#168C2213yes—
34C2×#3392—51nomaximal, Sylow
35C22×C5×Q8D411yescharacteristic
36C22×C5×Q8C2313yes—
37C2×#713—28no—
38C2×#713—48no—
39C22×D20—23no—
40C22×D20—23no—
41C22×D20C2313yes—
42C22×C4×D5—23no—
43C5×C4⋊Q8—26no—
44C5×C4⋊Q8C23112yes—
45C5×#125—224no—
46C4×C5×Q8—28no—
47C4×C5×Q8—26no—
48C4×C5×Q8D414yes—
49C4×C5×Q8C23112yes—
50C4×C5×Q8C2314yes—
51C2×C5×C4⋊C4—23no—
52C2×C5×C4⋊C4—23no—
53C2×C5×C4⋊C4—23no—
54C2×C5×C4⋊C4D413yes—
55C2×C5×C4⋊C4C2311yescharacteristic
56C2×C42×C5—23no—
57C2×C42×C5C2313yes—
58C2×#688—212no—
59C2×#688—412no—
60C2×#688C23112yes—
61C2×#688C23124yes—
62C2×#685—23no—
63C2×C4⋊Dic5C2311yescharacteristic
64C22×#168C2313yes—
65C22×#168C2311yescharacteristic
66#4041—224no—
67#4020—26no—
68#4020C23112yes—
69C4×D20—26no—
70C4×D20C23112yes—
71#3967C23112yes—
72#3941C23112yes—
73#3940C2314yes—
74C4⋊#168C23112yes—
75C4×#168C23112yes—
76C2×#557D511yescharacteristic, complemented
77C2×#550—51no—
78#3392—516no—
79C2×#492—53no—
80C2×#460—53no—
81C2×#461—53no—
82C2×C8×Q8—51no—
83C2×C4×SD16—53no—
84C23×D5—23no—
85C2×C5×Q8—23no—
86C2×C5×Q8—26no—
87C2×C5×Q8—26no—
88C2×C5×Q8SD1618yescomplemented
89C2×C5×Q8C2×D414yes—
90C2×C5×Q8C2416yes—
91C22×C4×C5—21no—
92C22×C4×C5—23no—
93C22×C4×C5C2×D413yes—
94C22×C4×C5C2×D413yes—
95C22×C4×C5C2411yescharacteristic
96C22×Dic5—21no—
97#713—432no—
98C2×D20—26no—
99C2×D20—26no—
100C2×D20—212no—
101C2×D20—23no—
102C2×D20—212no—
103C2×D20—412no—
104C2×D20—86no—
105C2×D20C2416yes—
106C2×C4×D5—212no—
107C2×C4×D5—412no—
108C5×C4⋊C4—212no—
109C5×C4⋊C4—212no—
110C5×C4⋊C4—212no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4C2×D4112yes—
113C5×C4⋊C4C2412yes—
114C42×C5—212no—
115C42×C5C2×D416yes—
116C42×C5C2416yes—
117#688—224no—
118#688—424no—
119#685—212no—
120C4⋊Dic5—21no—
121C4⋊Dic5C2412yes—
122C2×#168—26no—
123C2×#168#4114yescomplemented
124C2×#168C2416yes—
125C2×#168C2412yes—
126C22×#41—101no—
127C22×SD16—53no—
128C22×SD16—56no—
129#557—24no—
130#557C2×D518yescomplemented
131#550—58no—
132#550—104no—
133C2×C4⋊Q8C2×D513yes—
134C2×#127—53no—
135C2×#125—23no—
136C2×#121—103no—
137C2×C4×Q8—21no—
138C2×C4×Q8C2×D513yes—
139C2×C4×Q8C2×D511yescharacteristic
140C2×C4×D4—53no—
141#492—524no—
142#461—524no—
143#460—524no—
144C8×Q8—58no—
145C4×SD16—524no—
146C2×#106—51no—
147C2×C4⋊C8—53no—
148C2×#103—53no—
149C2×#102—53no—
150C2×C4×C8—53no—
151C23×C5C22×D411yescharacteristic
152C22×D5—26no—
153C22×D5—46no—
154C22×D5—46no—
155C22×D5—46no—
156C5×Q8—26no—
157C5×Q8—26no—
158C5×Q8—46no—
159C5×Q8C2×SD16116yescomplemented
160C2×C4×C5—26no—
161C2×C4×C5—22no—
162C2×C4×C5—26no—
163C2×C4×C5—46no—
164C2×C4×C5—42no—
165C2×C4×C5C2×SD16112yes—
166C2×C4×C5C22×D416yes—
167C2×C4×C5C22×D411yescharacteristic
168C2×C4×C5C22×D416yes—
169C2×C4×C5C2×#4112yes—
170C2×C4×C5H(5,𝔽2)12yes—
171C2×C4×C5C2511yescharacteristic
172C2×Dic5—22no—
173C2×Dic5—42no—
174D20—26no—
175D20—26no—
176D20—46no—
177D20—424no—
178D20—812no—
179C4×D5—424no—
180#168—26no—
181#168C2×#4114yescomplemented
182C2×#41—108no—
183C2×#41—208no—
184C22×Q8C22⋊D511yescharacteristic
185C22×Q8C22×D513yes—
186C22×D4—53no—
187C22×D4—103no—
188C22×D4—103no—
189C23×C4—103no—
190C2×SD16—512no—
191C2×SD16—524no—
192C2×SD16—1012no—
193C2×SD16—2012no—
194C22×C8—51no—
195C22×C8—53no—
196C4⋊Q8—26no—
197C4⋊Q8C22×D5112yes—
198#127—512no—
199#127—106no—
200#125—224no—
201#121—1024no—
202C4×Q8—28no—
203C4×Q8—26no—
204C4×Q8C22⋊D514yes—
205C4×Q8C22×D5112yes—
206C4×Q8C22×D514yes—
207C4×D4—512no—
208C4×D4—106no—
209C2×C4⋊C4—23no—
210C2×C4⋊C4—23no—
211C2×C4⋊C4—23no—
212C2×C4⋊C4—51no—
213C2×C4⋊C4C22⋊D513yes—
214C2×C4⋊C4C22×D511yescharacteristic
215C2×C22⋊C4—103no—
216C2×C42—23no—
217C2×C42C22×D513yes—
218#106—54no—
219C4⋊C8—512no—
220#103—512no—
221#102—512no—
222C4×C8—512no—
223C22×C5#55012yes—
224C22×C5C22×SD1612yes—
225C22×C5#57712yes—
226C22×C5C23×D411yescharacteristic
227C2×D5—46no—
228C2×D5—46no—
229C2×D5—46no—
230C2×D5—812no—
231C4×C5—26no—
232C4×C5—46no—
233C4×C5—42no—
234C4×C5#55012yes—
235C4×C5C22×SD16112yes—
236C4×C5C22×#4111yescharacteristic
237C4×C5C2×H(5,𝔽2)11yescharacteristic
238Dic5—42no—
239C24—103no—
240#41—2032no—
241C2×Q8—23no—
242C2×Q8—26no—
243C2×Q8—26no—
244C2×Q8#68818yescomplemented
245C2×Q8C2×C22⋊D514yes—
246C2×Q8C23×D516yes—
247C2×D4—56no—
248C2×D4—106no—
249C2×D4—106no—
250C2×D4—103no—
251C2×D4—1012no—
252C2×D4—1012no—
253C2×D4—2012no—
254C2×D4—406no—
255C22×C4—21no—
256C22×C4—23no—
257C22×C4—101no—
258C22×C4—1012no—
259C22×C4—2012no—
260C22×C4C2×C22⋊D513yes—
261C22×C4C2×C22⋊D513yes—
262C22×C4C23×D511yescharacteristic
263SD16—1024no—
264SD16—2024no—
265C2×C8—54no—
266C2×C8—52no—
267C2×C8—56no—
268C2×C8—106no—
269C4⋊C4—212no—
270C4⋊C4—212no—
271C4⋊C4—212no—
272C4⋊C4—21no—
273C4⋊C4—52no—
274C4⋊C4—101no—
275C4⋊C4C2×C22⋊D5112yes—
276C4⋊C4C23×D512yes—
277C22⋊C4—1012no—
278C42—212no—
279C42C2×C22⋊D516yes—
280C42C23×D516yes—
281C2×C5#339214yescomplemented
282C2×C5C2×#55011yescharacteristic
283C2×C5C23×SD1611yescharacteristic
284C2×C5C2×#57711yescharacteristic
285D5—86no—
286C23—106no—
287C23—206no—
288C23—206no—
289C23—206no—
290C23C22×C22⋊D511yescharacteristic
291Q8—26no—
292Q8—26no—
293Q8—46no—
294Q8C2×#688116yescomplemented
295D4—106no—
296D4—106no—
297D4—2024no—
298D4—206no—
299D4—4012no—
300C2×C4—26no—
301C2×C4—22no—
302C2×C4—26no—
303C2×C4—46no—
304C2×C4—42no—
305C2×C4—102no—
306C2×C4—202no—
307C2×C4—2024no—
308C2×C4C2×#688112yes—
309C2×C4D5×#4112yes—
310C2×C4#414912yes—
311C2×C4C22×C22⋊D516yes—
312C2×C4C22×C22⋊D516yes—
313C2×C4C22×C22⋊D511yescharacteristic
314C2×C4C24×D511yescharacteristic
315C8—54no—
316C8—106no—
317C5C2×#339211yescharacteristic, complemented, Sylow
318C22—206no—
319C22—206no—
320C22—206no—
321C22—4012no—
322C22C22×#68812yes—
323C22#6616812yes—
324C22#6617112yes—
325C22C23×C22⋊D511yescharacteristic
326C4—26no—
327C4—46no—
328C4—42no—
329C4—202no—
330C4C22×#688112yes—
331C4#6616812yes—
332C4C2×D5×#4111yescharacteristic
333C4C2×#414911yescharacteristic
334C2—406no—
335C2#1061541614yesdirect product factor
336C2C23×#68811yescharacteristic
337C2C2×#6616811yescharacteristic
338C2C2×#6617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#557C2
socleC23×C5C22×D4
prime radicalC2×#65911C2
hypercenterC2×#557D5
hypocenterC5C2×#3392
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. C2×C5×#557C2semidirect
3. #10615416C2direct (N × H)
4. C2×#65372C2semidirect
5. C2×#65374C2semidirect
6. C2×#65316C2semidirect
7. C2×Q8×#168C2semidirect
8. C2×C4×#688C2semidirect
11. C5×#557C22semidirect
25. #65374C22semidirect
26. #65372C22semidirect
27. #65316C22semidirect
28. C4×#688C22semidirect
29. Q8×#168C22semidirect
76. C2×#557D5semidirect
88. C2×C5×Q8SD16semidirect
123. C2×#168#41semidirect
130. #557C2×D5semidirect
159. C5×Q8C2×SD16semidirect
181. #168C2×#41semidirect
244. C2×Q8#688semidirect
281. C2×C5#3392semidirect
294. Q8C2×#688semidirect
317. C5C2×#3392semidirect
335. C2#10615416direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5572
C2×#659112
#106154162
C2×#653722
C2×#653742
C2×#653162
C2×Q8×#1682
C2×C4×#6882
C2×#33925