Finite Group Databasebeta

← C2×#10610773 #12963180

Subgroups — C2×#10610773 #12963180

Order 1280.

2806 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
1C22×#4053C212yesmaximal, complemented
2C2×#65811C211yesmaximal, characteristic
3C2×C5×#423C211yesmaximal, characteristic, complemented
4C2×#65418C212yesmaximal, complemented
5C22×#3935C211yesmaximal, characteristic, complemented
6#10610773C2116yesmaximal, direct product factor
7C2×#65125C218yesmaximal, complemented
8C22×#709C2212yes—
9C22×C5×M16C2212yes—
10C22×C42×C5C2211yescharacteristic
11C2×#4076C414yes—
12C23×#168C2211yescharacteristic
13C23×#168C2211yescharacteristic
14C2×#4053—216no—
15C2×#4053C22116yescomplemented
16C22×#676C2214yes—
17C22×C8×D5C2214yes—
18#65811C418yes—
19#65811C2218yes—
20C2×#4021C412yes—
21C2×#4020C411yescharacteristic
22C2×C4×D20C2214yes—
23C2×#4015C411yescharacteristic
24C5×#423C2218yescomplemented
25C2×C5×C4⋊C8C2214yes—
26#65418C22116yescomplemented
27C2×#3952C2218yes—
28C2×#3935C2214yes—
29C2×#3935C2218yescomplemented
30#65125C22164yescomplemented
31C2×#2932—51nomaximal, Sylow
32C23×C4×C5C2×C412yes—
33C23×C4×C5C2311yescharacteristic
34C22×C22⋊D5C2×C414yes—
35C2×#709—28no—
36C2×#709—28no—
37C2×#709C2×C418yes—
38C2×#709C2318yes—
39C22×D20C2×C412yes—
40C22×D20C2×C414yes—
41C22×C4×D5C2314yes—
42C22×Dic10C2×C412yes—
43C2×C5×M16—28no—
44C2×C5×M16C2318yes—
45C22×C5×C8C2314yes—
46C2×C42×C5C2×C411yescharacteristic
47C2×C42×C5C2×C411yescharacteristic
48C2×C42×C5C2×C414yes—
49C2×C42×C5C2312yes—
50C2×C42×C5C2314yes—
51#4076C2×C4132yes—
52C2×#685C2×C418yes—
53C2×C4⋊Dic5C2×C414yes—
54C22×#168—24no—
55C22×#168D418yescomplemented
56C22×#168C2312yes—
57C22×#168C2314yes—
58C22×#168C2312yes—
59C22×#168C2314yes—
60#4053—264no—
61C2×#676—216no—
62C2×#676C23116yes—
63C2×C8×D5—216no—
64C2×C8×D5C23116yes—
65#4021C2×C4116yes—
66#4020C2×C418yes—
67C4×D20C2×C4116yes—
68C4×D20C23116yes—
69#4015C2×C418yes—
70C5×C4⋊C8C23116yes—
71#3952C23132yes—
72#3935C23116yes—
73C22×#131—52no—
74C2×#532—51no—
75#2932—516no—
76C2×#435—58no—
77C2×#423D511yescharacteristic, complemented
78C2×#408—52no—
79C22×#97—51no—
80C24×C5C22×C411yescharacteristic
81C23×D5C22×C414yes—
82C22×C4×C5—44no—
83C22×C4×C5C22×C412yes—
84C22×C4×C5C22×C412yes—
85C22×C4×C5C22×C418yes—
86C22×C4×C5C22×C411yescharacteristic
87C22×C4×C5C22×C412yes—
88C22×C4×C5C2×D414yes—
89C22×C4×C5#4114yes—
90C22×C4×C5C2412yes—
91C22×C4×C5C2411yescharacteristic
92C2×C22⋊D5—216no—
93C2×C22⋊D5C22×C4116yes—
94C22×Dic5C22×C414yes—
95#709—232no—
96#709—216no—
97#709—216no—
98C2×D20—28no—
99C2×D20—48no—
100C2×D20C22×C418yes—
101C2×D20C22×C4116yes—
102C2×C4×D5—28no—
103C2×C4×D5—28no—
104C2×C4×D5C22×C418yes—
105C2×C4×D5C2418yes—
106C2×Dic10—28no—
107C2×Dic10C22×C418yes—
108C5×M16—216no—
109C2×C5×C8—28no—
110C2×C5×C8C2418yes—
111C42×C5C22×C414yes—
112C42×C5C22×C414yes—
113C42×C5C22×C414yes—
114C42×C5C2414yes—
115#685C22×C4132yes—
116C4⋊Dic5C22×C4116yes—
117C2×#168—24no—
118C2×#168—28no—
119C2×#168C2×D418yes—
120C2×#168C2×D4116yescomplemented
121C2×#168C2414yes—
122C2×#168C2414yes—
123#676—232no—
124C8×D5—232no—
125C22×#41—52no—
126C2×#131—516no—
127C2×#131—1016no—
128C22×M16—54no—
129C22×M16C2×D512yes—
130C23×C8—51no—
131C23×C8—51no—
132C23×C8—54no—
133#532—58no—
134#532—58no—
135C2×C4⋊Q8—51no—
136C2×#127—51no—
137C2×#124—52no—
138C2×#121—54no—
139C2×C4×D4—54no—
140C22×C42C2×D511yescharacteristic
141#435—564no—
142#423C2×D518yescomplemented
143C2×C4⋊C8C2×D514yes—
144#408—516no—
145C2×C22⋊C8—58no—
146C2×#97—54no—
147C2×#97—58no—
148C23×C5—24no—
149C23×C5C4×D414yes—
150C23×C5C23×C412yes—
151C23×C5C23×C411yescharacteristic
152C22×D5—28no—
153C22×D5—216no—
154C22×D5C23×C418yes—
155C2×C4×C5—24no—
156C2×C4×C5—24no—
157C2×C4×C5—48no—
158C2×C4×C5C4×D414yes—
159C2×C4×C5C4×D418yes—
160C2×C4×C5C23×C414yes—
161C2×C4×C5C23×C414yes—
162C2×C4×C5C23×C412yes—
163C2×C4×C5C23×C411yescharacteristic
164C2×C4×C5C22×D412yes—
165C2×C4×C5C22×D414yes—
166C2×C4×C5C2×#4112yes—
167C2×C4×C5C2×#4114yes—
168C2×C4×C5C2511yescharacteristic
169C22⋊D5—232no—
170C2×Dic5—28no—
171C2×Dic5C23×C418yes—
172D20—216no—
173D20—416no—
174C4×D5—216no—
175C4×D5—28no—
176C4×D5—28no—
177Dic10—216no—
178C5×C8—28no—
179#168—24no—
180#168C22×D418yes—
181C2×#41—58no—
182C2×#41—58no—
183C2×#41—108no—
184C2×#41—108no—
185C22×Q8—52no—
186C22×D4—54no—
187C22×D4—52no—
188C22×D4—54no—
189C23×C4—54no—
190C23×C4C4×D512yes—
191C23×C4C22×D511yescharacteristic
192#131—1064no—
193C2×M16—28no—
194C2×M16—516no—
195C2×M16—1016no—
196C2×M16C22×D518yes—
197C22×C8—58no—
198C22×C8—54no—
199C22×C8—52no—
200C22×C8—54no—
201C22×C8—52no—
202C22×C8—516no—
203C22×C8—1016no—
204C22×C8—104no—
205C22×C8C22×D514yes—
206C4⋊Q8—58no—
207#127—58no—
208#124—516no—
209#121—532no—
210C4×D4—516no—
211C4×D4—516no—
212C2×C4⋊C4—54no—
213C2×C22⋊C4—58no—
214C2×C42C4×D511yescharacteristic
215C2×C42C4×D511yescharacteristic
216C2×C42C4×D514yes—
217C2×C42C22×D514yes—
218C2×C42C22×D512yes—
219C4⋊C8C22×D5116yes—
220C22⋊C8—532no—
221#97—516no—
222C22×C5—28no—
223C22×C5—24no—
224C22×C5C2×C4×D414yes—
225C22×C5C2×C4×D412yes—
226C22×C5#56814yes—
227C22×C5C24×C411yescharacteristic
228C2×D5—28no—
229C2×D5—216no—
230C2×D5—416no—
231C4×C5—24no—
232C4×C5—24no—
233C4×C5C2×C4×D414yes—
234C4×C5C2×C4×D412yes—
235C4×C5C23×D411yescharacteristic
236C4×C5C22×#4111yescharacteristic
237Dic5—28no—
238C24—54no—
239C24C2×C4×D511yescharacteristic
240#41—1016no—
241#41—1016no—
242#41—1032no—
243C2×Q8—58no—
244C2×Q8—108no—
245C2×D4—516no—
246C2×D4—58no—
247C2×D4—516no—
248C2×D4—1016no—
249C2×D4—108no—
250C2×D4—208no—
251C22×C4—44no—
252C22×C4—54no—
253C22×C4—58no—
254C22×C4—58no—
255C22×C4—108no—
256C22×C4—108no—
257C22×C4C2×C4×D512yes—
258C22×C4C2×C4×D512yes—
259C22×C4C2×C4×D518yes—
260C22×C4C2×C4×D511yescharacteristic
261C22×C4C2×C4×D512yes—
262C22×C4D4×D514yes—
263C22×C4#71314yes—
264C22×C4C23×D512yes—
265C22×C4C23×D511yescharacteristic
266M16—216no—
267M16—1032no—
268C2×C8—28no—
269C2×C8—58no—
270C2×C8—516no—
271C2×C8—54no—
272C2×C8—54no—
273C2×C8—1032no—
274C2×C8—104no—
275C2×C8—108no—
276C2×C8C23×D518yes—
277C4⋊C4—516no—
278C22⋊C4—532no—
279C42C2×C4×D514yes—
280C42C2×C4×D514yes—
281C42C2×C4×D514yes—
282C42C23×D514yes—
283C2×C5—24no—
284C2×C5#293214yescomplemented
285C2×C5C22×C4×D411yescharacteristic
286C2×C5C2×#56812yes—
287D5—48no—
288C23—24no—
289C23—58no—
290C23—1016no—
291C23—108no—
292C23#403914yes—
293C23C22×C4×D512yes—
294C23C22×C4×D511yescharacteristic
295Q8—1016no—
296D4—1032no—
297D4—1016no—
298D4—2016no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—48no—
302C2×C4—58no—
303C2×C4—108no—
304C2×C4—1016no—
305C2×C4—108no—
306C2×C4—108no—
307C2×C4#403914yes—
308C2×C4#403918yes—
309C2×C4C22×C4×D514yes—
310C2×C4C22×C4×D514yes—
311C2×C4C22×C4×D511yescharacteristic
312C2×C4C22×C4×D512yes—
313C2×C4C2×D4×D512yes—
314C2×C4C2×D4×D514yes—
315C2×C4C2×#71312yes—
316C2×C4C2×#71314yes—
317C2×C4C24×D511yescharacteristic
318C8—28no—
319C8—58no—
320C8—104no—
321C5C2×#293211yescharacteristic, complemented, Sylow
322C22—28no—
323C22—24no—
324C22—108no—
325C22—1016no—
326C22—2016no—
327C22C2×#403914yes—
328C22C2×#403912yes—
329C22#6607914yes—
330C22C23×C4×D511yescharacteristic
331C4—24no—
332C4—24no—
333C4—108no—
334C4C2×#403912yes—
335C4C2×#403914yes—
336C4C22×D4×D511yescharacteristic
337C4C22×#71311yescharacteristic
338C2—24no—
339C2—208no—
340C2#1061077314yesdirect product factor
341C2C22×#403911yescharacteristic
342C2C2×#6607912yes—
subgroupG/H
centerC22×C4C23×D5
commutatorC22×C5C24×C4
FrattiniC2×C4C24×D5
FittingC2×C5×#423C2
socleC23×C5C23×C4
prime radicalC2×#65811C2
cosocleC2×C4×C5C25
hypercenterC2×#423D5
hypocenterC5C2×#2932
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
1. C22×#4053C2semidirect
3. C2×C5×#423C2semidirect
4. C2×#65418C2semidirect
5. C22×#3935C2semidirect
6. #10610773C2direct (N × H)
7. C2×#65125C2semidirect
15. C2×#4053C22semidirect
24. C5×#423C22semidirect
26. #65418C22semidirect
29. C2×#3935C22semidirect
30. #65125C22semidirect
55. C22×#168D4semidirect
77. C2×#423D5semidirect
120. C2×#168C2×D4semidirect
142. #423C2×D5semidirect
284. C2×C5#2932semidirect
321. C5C2×#2932semidirect
340. C2#10610773direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40532
C2×#658112
C2×C5×#4232
C2×#654182
C22×#39352
#106107732
C2×#651252
C2×#29325