Finite Group Databasebeta

← C22×#65483 #13005785

Subgroups — C22×#65483 #13005785

Order 1280.

2118 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#135C211yesmaximal, characteristic, complemented
2C22×#4050C211yesmaximal, characteristic, complemented
3C2×#65483C2124yesmaximal, direct product factor
4C22×#3961C211yesmaximal, characteristic, complemented
5C22×#3960C211yesmaximal, characteristic, complemented
6C22×#3959C211yesmaximal, characteristic, complemented
7C22×#3958C211yesmaximal, characteristic, complemented
8C23×#672C211yesmaximal, characteristic, complemented
9C22×C5×#41—21no—
10C22×#709—21no—
11C2×C5×#135—26no—
12C2×C5×#135C22112yescomplemented
13C22×C5×Q16C2211yescharacteristic
14C22×C5×SD16—21no—
15C22×C5×D8C2211yescharacteristic
16C23×C5×C8C2211yescharacteristic
17C22×Dic20C2211yescharacteristic
18C2×#4050—26no—
19C2×#4050C22112yescomplemented
20C22×D40C2211yescharacteristic
21C22×#677—21no—
22#65483C22164yesdirect product factor
23C2×#3961C22112yescomplemented
24C2×#3960C22112yescomplemented
25C2×#3959C22112yescomplemented
26C2×#3958C22112yescomplemented
27C22×#672C2211yescharacteristic
28C22×#672C2211yescharacteristic
29C22×#672C22112yescomplemented
30C22×#508—51nomaximal, Sylow
31C2×C5×#41—212no—
32C2×C5×#41—46no—
33C22×C5×Q8—21no—
34C22×C5×D4—21no—
35C22×C5×D4—41no—
36C23×C4×C5—41no—
37C23×C4×C5D411yescharacteristic
38C22×C22⋊D5—41no—
39C2×#709—212no—
40C2×#709—46no—
41C22×D20—21no—
42C22×C4×D5—41no—
43C22×Dic10—21no—
44C5×#135—224no—
45C5×#135C23116yescomplemented
46C2×C5×Q16—23no—
47C2×C5×Q16C2316yes—
48C2×C5×SD16—212no—
49C2×C5×D8—23no—
50C2×C5×D8C2316yes—
51C22×C5×C8D411yescharacteristic
52C22×C5×C8D416yes—
53C22×C5×C8C2311yescharacteristic
54C22×C5×C8C2316yes—
55C2×Dic20—23no—
56C2×Dic20C2316yes—
57#4050—224no—
58#4050C23116yescomplemented
59C2×D40—23no—
60C2×D40C2316yes—
61C2×#677—212no—
62#3961C23116yescomplemented
63#3960C23116yescomplemented
64#3959C23116yescomplemented
65#3958C23116yescomplemented
66C2×#672C2316yes—
67C2×#672C2316yes—
68C2×#672C23116yescomplemented
69C22×#135—51no—
70C22×#135D511yescharacteristic, complemented
71C2×#508—524no—
72C22×Q32—51no—
73C22×SD32—51no—
74C22×SD32—51no—
75C22×D16—51no—
76C23×C16—51no—
77C24×C5—41no—
78C24×C5D811yescharacteristic
79C23×D5—41no—
80C5×#41—216no—
81C5×#41—424no—
82C2×C5×Q8—26no—
83C2×C5×Q8—43no—
84C2×C5×D4—26no—
85C2×C5×D4—412no—
86C2×C5×D4—43no—
87C22×C4×C5—41no—
88C22×C4×C5—412no—
89C22×C4×C5D816yes—
90C22×C4×C5D811yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5C2×D416yes—
93C2×C22⋊D5—412no—
94C22×Dic5—41no—
95#709—216no—
96#709—424no—
97C2×D20—26no—
98C2×D20—43no—
99C2×C4×D5—412no—
100C2×Dic10—26no—
101C2×Dic10—43no—
102C5×Q16—26no—
103C5×Q16C2414yes—
104C5×SD16—216no—
105C5×D8—26no—
106C5×D8C2414yes—
107C2×C5×C8C2×D413yes—
108C2×C5×C8C2×D416yes—
109C2×C5×C8C2×D4112yes—
110C2×C5×C8C2413yes—
111C2×C5×C8C2414yes—
112Dic20—26no—
113Dic20C2414yes—
114D40—26no—
115D40C2414yes—
116#677—216no—
117#672C2414yes—
118#672C2414yes—
119C22×#41—21no—
120C22×#41—101no—
121C2×#135—26no—
122C2×#135—512no—
123C2×#135—106no—
124C2×#135C2×D5112yescomplemented
125C22×Q16—51no—
126C22×Q16C2×D511yescharacteristic
127C22×SD16—21no—
128C22×SD16—101no—
129C22×D8—51no—
130C22×D8C2×D511yescharacteristic
131C23×C8C2×D511yescharacteristic
132#508—564no—
133C2×Q32—512no—
134C2×SD32—512no—
135C2×SD32—512no—
136C2×D16—512no—
137C22×C16—51no—
138C22×C16—51no—
139C22×C16—512no—
140C23×C5—24no—
141C23×C5—46no—
142C23×C5—84no—
143C23×C5C2×D816yes—
144C23×C5C2×D811yescharacteristic
145C22×D5—46no—
146C22×D5—84no—
147C5×Q8—24no—
148C5×Q8—46no—
149C5×D4—24no—
150C5×D4—416no—
151C5×D4—46no—
152C2×C4×C5—46no—
153C2×C4×C5—416no—
154C2×C4×C5C2×D813yes—
155C2×C4×C5C2×D816yes—
156C2×C4×C5C2×D8112yes—
157C2×C4×C5C22×D413yes—
158C2×C4×C5C22×D414yes—
159C22⋊D5—416no—
160C2×Dic5—46no—
161D20—24no—
162D20—46no—
163C4×D5—416no—
164Dic10—24no—
165Dic10—46no—
166C5×C8C22×D414yes—
167C5×C8C22×D413yes—
168C5×C8C2511yescharacteristic
169C2×#41—212no—
170C2×#41—46no—
171C2×#41—1012no—
172C2×#41—206no—
173C22×Q8—21no—
174C22×Q8—101no—
175C22×D4—21no—
176C22×D4—41no—
177C22×D4—101no—
178C22×D4—201no—
179C23×C4—41no—
180C23×C4—201no—
181C23×C4C22⋊D511yescharacteristic
182#135—224no—
183#135—516no—
184#135—1024no—
185#135C22×D5116yescomplemented
186C2×Q16—23no—
187C2×Q16—56no—
188C2×Q16—103no—
189C2×Q16C22×D516yes—
190C2×SD16—212no—
191C2×SD16—1012no—
192C2×D8—23no—
193C2×D8—56no—
194C2×D8—103no—
195C2×D8C22×D516yes—
196C22×C8C22⋊D511yescharacteristic
197C22×C8C22⋊D516yes—
198C22×C8C22×D511yescharacteristic
199C22×C8C22×D516yes—
200Q32—516no—
201SD32—516no—
202SD32—516no—
203D16—516no—
204C2×C16—56no—
205C2×C16—56no—
206C2×C16—516no—
207C22×C5—212no—
208C22×C5—44no—
209C22×C5—812no—
210C22×C5#50814yescomplemented
211C22×C5C22×D814yes—
212C22×C5C22×D813yes—
213C2×D5—44no—
214C2×D5—812no—
215C4×C5—44no—
216C4×C5C22×D813yes—
217C4×C5C22×D814yes—
218C4×C5C23×D411yescharacteristic
219Dic5—44no—
220C24—41no—
221C24—201no—
222C24#68611yescharacteristic
223#41—216no—
224#41—424no—
225#41—1016no—
226#41—2024no—
227C2×Q8—26no—
228C2×Q8—43no—
229C2×Q8—106no—
230C2×Q8—203no—
231C2×D4—26no—
232C2×D4—412no—
233C2×D4—43no—
234C2×D4—106no—
235C2×D4—2012no—
236C2×D4—203no—
237C22×C4—41no—
238C22×C4—412no—
239C22×C4—201no—
240C22×C4—2012no—
241C22×C4#68616yes—
242C22×C4#68611yescharacteristic
243C22×C4C2×C22⋊D511yescharacteristic
244C22×C4C2×C22⋊D516yes—
245Q16—26no—
246Q16—54no—
247Q16—106no—
248Q16C23×D514yes—
249SD16—216no—
250SD16—1016no—
251D8—26no—
252D8—54no—
253D8—106no—
254D8C23×D514yes—
255C2×C8C2×C22⋊D513yes—
256C2×C8C2×C22⋊D516yes—
257C2×C8C2×C22⋊D5112yes—
258C2×C8C23×D513yes—
259C2×C8C23×D514yes—
260C16—54no—
261C16—54no—
262C2×C5—24no—
263C2×C5—84no—
264C2×C5C2×#50816yescomplemented
265C2×C5C23×D811yescharacteristic
266D5—84no—
267C23—24no—
268C23—46no—
269C23—84no—
270C23—206no—
271C23—404no—
272C23C2×#68616yes—
273C23C2×#68611yescharacteristic
274Q8—24no—
275Q8—46no—
276Q8—104no—
277Q8—206no—
278D4—24no—
279D4—416no—
280D4—46no—
281D4—104no—
282D4—2016no—
283D4—206no—
284C2×C4—46no—
285C2×C4—416no—
286C2×C4—206no—
287C2×C4—2016no—
288C2×C4C2×#68616yes—
289C2×C4C2×#68613yes—
290C2×C4C2×#686112yes—
291C2×C4C22×C22⋊D513yes—
292C2×C4C22×C22⋊D514yes—
293C8C22×C22⋊D513yes—
294C8C22×C22⋊D514yes—
295C8C24×D511yescharacteristic
296C5C22×#50811yescharacteristic, complemented, Sylow
297C22—212no—
298C22—44no—
299C22—812no—
300C22—204no—
301C22—4012no—
302C22#6548314yesdirect product factor
303C22C22×#68614yes—
304C22C22×#68613yes—
305C4—44no—
306C4—204no—
307C4C22×#68614yes—
308C4C22×#68613yes—
309C4C23×C22⋊D511yescharacteristic
310C2—24no—
311C2—84no—
312C2—404no—
313C2C2×#6548316yesdirect product factor
314C2C23×#68611yescharacteristic
subgroupG/H
centerC22×C4#686
commutator, cosocleC5×C8C25
FrattiniC8C24×D5
FittingC22×C5×#135C2
socleC23×C5C2×D8
hypercenterC22×#135D5
hypocenterC5C22×#508
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C22×C5×#135C2semidirect
2. C22×#4050C2semidirect
3. C2×#65483C2direct (N × H)
4. C22×#3961C2semidirect
5. C22×#3960C2semidirect
6. C22×#3959C2semidirect
7. C22×#3958C2semidirect
8. C23×#672C2semidirect
12. C2×C5×#135C22semidirect
19. C2×#4050C22semidirect
22. #65483C22direct (N × H)
23. C2×#3961C22semidirect
24. C2×#3960C22semidirect
25. C2×#3959C22semidirect
26. C2×#3958C22semidirect
29. C22×#672C22semidirect
45. C5×#135C23semidirect
58. #4050C23semidirect
62. #3961C23semidirect
63. #3960C23semidirect
64. #3959C23semidirect
65. #3958C23semidirect
68. C2×#672C23semidirect
70. C22×#135D5semidirect
124. C2×#135C2×D5semidirect
185. #135C22×D5semidirect
210. C22×C5#508semidirect
264. C2×C5C2×#508semidirect
296. C5C22×#508semidirect
302. C22#65483direct (N × H)
313. C2C2×#65483direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1352
C22×#40502
C2×#654832
C22×#39612
C22×#39602
C22×#39592
C22×#39582
C23×#6722
C22×#5085