Finite Group Databasebeta

← C22×#65481 #12966684

Subgroups — C22×#65481 #12966684

Order 1280.

2630 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
1C23×C5×Q16C211yesmaximal, characteristic, complemented
2C22×#4088C212yesmaximal
3C22×#4047C211yesmaximal, characteristic
4C22×#3968C212yesmaximal, complemented
5C2×#65481C2124yesmaximal, direct product factor
6C22×#3951C211yesmaximal, characteristic, complemented
7C23×C5×Q8C2212yes—
8C22×#709C2211yescharacteristic
9C22×C5×Q16—21no—
10C22×C5×Q16—21no—
11C22×C5×Q16—26no—
12C22×C5×Q16C22112yescomplemented
13C23×C5×C8C2211yescharacteristic
14C22×#689—22no—
15C2×#4088—212no—
16C2×#4088C22124yes—
17C22×#688—22no—
18C22×#681C2212yes—
19C22×#681C2211yescharacteristic
20C2×#4047—26no—
21C2×#4047C22112yes—
22C22×#676—21no—
23C22×C8×D5—21no—
24C2×#3968C22124yescomplemented
25#65481C22164yesdirect product factor
26C2×#3951C22112yescomplemented
27C22×#473—51nomaximal, Sylow
28C22×C5×Q8—26no—
29C22×C5×Q8—22no—
30C22×C5×Q8—26no—
31C22×C5×Q8—22no—
32C22×C5×Q8—26no—
33C22×C5×Q8C23112yes—
34C23×C4×C5—22no—
35C23×C4×C5C2311yescharacteristic
36C22×C22⋊D5—21no—
37C2×#709—23no—
38C2×#709—23no—
39C2×#709D416yes—
40C2×#709C2316yes—
41C22×D20D411yescharacteristic
42C22×C4×D5—21no—
43C22×Dic10D411yescharacteristic
44C2×C5×Q16—212no—
45C2×C5×Q16—212no—
46C2×C5×Q16—224no—
47C2×C5×Q16C23116yescomplemented
48C22×C5×C8D411yescharacteristic
49C22×C5×C8D411yescharacteristic
50C22×C5×C8D416yes—
51C22×C5×C8C2316yes—
52C2×#689—224no—
53#4088—248no—
54#4088C23132yes—
55C2×#688—224no—
56C2×#681—23no—
57C2×#681—26no—
58C2×#681C2316yes—
59C2×#681C23112yes—
60C22×#168—21no—
61C22×#168—22no—
62#4047—224no—
63#4047C23116yes—
64C2×#676—212no—
65C2×C8×D5—212no—
66#3968C23132yescomplemented
67#3951C23116yescomplemented
68C22×#137—52no—
69C23×Q16D511yescharacteristic, complemented
70C22×#131—51no—
71C2×#473—524no—
72C22×#108—51no—
73C22×#101—52no—
74C24×C5#4111yescharacteristic
75C23×D5—21no—
76C2×C5×Q8—212no—
77C2×C5×Q8—212no—
78C2×C5×Q8—212no—
79C2×C5×Q8—212no—
80C2×C5×Q8—212no—
81C2×C5×Q8—46no—
82C2×C5×Q8—46no—
83C2×C5×Q8—412no—
84C2×C5×Q8C2418yes—
85C22×C4×C5—212no—
86C22×C4×C5—46no—
87C22×C4×C5—42no—
88C22×C4×C5C2×D411yescharacteristic
89C22×C4×C5C2×D413yes—
90C22×C4×C5C2×D411yescharacteristic
91C22×C4×C5C2×D413yes—
92C22×C4×C5#4113yes—
93C22×C4×C5C2413yes—
94C2×C22⋊D5—26no—
95C2×C22⋊D5—26no—
96C22×Dic5—21no—
97#709—212no—
98#709—26no—
99#709—26no—
100#709C2×D4112yes—
101#709C2414yes—
102C2×D20—23no—
103C2×D20C2×D416yes—
104C2×C4×D5—26no—
105C2×C4×D5—26no—
106C2×Dic10—23no—
107C2×Dic10C2×D416yes—
108C5×Q16—216no—
109C5×Q16—216no—
110C2×C5×C8C2×D416yes—
111C2×C5×C8C2×D416yes—
112C2×C5×C8C2×D4112yes—
113C2×C5×C8C2414yes—
114#689—232no—
115#688—232no—
116#681—26no—
117#681—212no—
118#681C2418yes—
119#681C2414yes—
120C2×#168—26no—
121C2×#168—212no—
122#676—216no—
123C8×D5—216no—
124C22×#41—51no—
125C23×Q8C2×D512yes—
126C2×#137—524no—
127C2×#137—1012no—
128C22×Q16—21no—
129C22×Q16—21no—
130C22×Q16—26no—
131C22×Q16—102no—
132C22×Q16C2×D5112yescomplemented
133C22×SD16—102no—
134C2×#131—512no—
135C2×#131—106no—
136C22×M16—51no—
137C22×M16—52no—
138C22×M16—101no—
139C23×C8—101no—
140C23×C8C2×D511yescharacteristic
141#473—564no—
142C2×#108—512no—
143C2×#101—524no—
144C23×C5—24no—
145C23×C5#12113yes—
146C23×C5#12111yescharacteristic
147C23×C5C2×#4113yes—
148C22×D5—26no—
149C22×D5—44no—
150C5×Q8—28no—
151C5×Q8—28no—
152C5×Q8—412no—
153C5×Q8—412no—
154C2×C4×C5—28no—
155C2×C4×C5—412no—
156C2×C4×C5—412no—
157C2×C4×C5#12113yes—
158C2×C4×C5#12113yes—
159C2×C4×C5#12116yes—
160C2×C4×C5C22×D413yes—
161C2×C4×C5C22×D413yes—
162C2×C4×C5C22×D413yes—
163C2×C4×C5C22×D413yes—
164C2×C4×C5C2×#4113yes—
165C2×C4×C5C2511yescharacteristic
166C22⋊D5—212no—
167C22⋊D5—24no—
168C2×Dic5—26no—
169D20—26no—
170D20C22×D414yes—
171C4×D5—212no—
172C4×D5—24no—
173Dic10—26no—
174Dic10C22×D414yes—
175C5×C8C22×D414yes—
176C5×C8C22×D414yes—
177#168—24no—
178#168—28no—
179C2×#41—56no—
180C2×#41—56no—
181C2×#41—103no—
182C2×#41—103no—
183C22×Q8—26no—
184C22×Q8—22no—
185C22×Q8—26no—
186C22×Q8—26no—
187C22×Q8—22no—
188C22×Q8—51no—
189C22×Q8C22×D5112yes—
190C22×D4—51no—
191C22×D4—101no—
192C23×C4—22no—
193C23×C4—101no—
194C23×C4C22×D511yescharacteristic
195#137—532no—
196#137—1048no—
197C2×Q16—212no—
198C2×Q16—212no—
199C2×Q16—224no—
200C2×Q16—1024no—
201C2×Q16C22×D5116yescomplemented
202C2×SD16—1024no—
203#131—516no—
204#131—1024no—
205C2×M16—56no—
206C2×M16—512no—
207C2×M16—106no—
208C2×M16—103no—
209C2×M16—1012no—
210C22×C8—102no—
211C22×C8—101no—
212C22×C8—1012no—
213C22×C8C22⋊D511yescharacteristic
214C22×C8C22⋊D511yescharacteristic
215C22×C8C22⋊D516yes—
216C22×C8C22×D516yes—
217#108—516no—
218#101—532no—
219C22×C5—26no—
220C22×C5—26no—
221C22×C5#47314yescomplemented
222C22×C5C2×#12113yes—
223C22×C5C2×#12113yes—
224C22×C5C22×#4111yescharacteristic
225C2×D5—24no—
226C2×D5—412no—
227C4×C5—48no—
228C4×C5C2×#12113yes—
229C4×C5C2×#12113yes—
230C4×C5C23×D411yescharacteristic
231C4×C5C23×D411yescharacteristic
232Dic5—24no—
233C24—101no—
234C24#71111yescharacteristic
235#41—512no—
236#41—54no—
237#41—106no—
238#41—106no—
239#41—1012no—
240C2×Q8—212no—
241C2×Q8—212no—
242C2×Q8—212no—
243C2×Q8—212no—
244C2×Q8—212no—
245C2×Q8—46no—
246C2×Q8—46no—
247C2×Q8—412no—
248C2×Q8—56no—
249C2×Q8—103no—
250C2×Q8C23×D518yes—
251C2×D4—56no—
252C2×D4—106no—
253C2×D4—106no—
254C2×D4—103no—
255C22×C4—212no—
256C22×C4—46no—
257C22×C4—42no—
258C22×C4—101no—
259C22×C4—106no—
260C22×C4—106no—
261C22×C4D4×D513yes—
262C22×C4D4×D511yescharacteristic
263C22×C4#71113yes—
264C22×C4C2×C22⋊D513yes—
265C22×C4C2×C22⋊D511yescharacteristic
266C22×C4C23×D513yes—
267Q16—216no—
268Q16—216no—
269Q16—1032no—
270SD16—1032no—
271M16—54no—
272M16—58no—
273M16—1012no—
274M16—106no—
275M16—1016no—
276C2×C8—1012no—
277C2×C8—106no—
278C2×C8—1016no—
279C2×C8C2×C22⋊D516yes—
280C2×C8C2×C22⋊D516yes—
281C2×C8C2×C22⋊D5112yes—
282C2×C8C23×D514yes—
283C2×C5—23no—
284C2×C5—21no—
285C2×C5C2×#47316yescomplemented
286C2×C5C22×#12111yescharacteristic
287D5—44no—
288C23—24no—
289C23—106no—
290C23—204no—
291C23#408413yes—
292C23#408411yescharacteristic
293C23C2×#71113yes—
294Q8—28no—
295Q8—28no—
296Q8—412no—
297Q8—412no—
298Q8—54no—
299Q8—106no—
300D4—54no—
301D4—1012no—
302D4—104no—
303D4—106no—
304C2×C4—28no—
305C2×C4—412no—
306C2×C4—412no—
307C2×C4—106no—
308C2×C4—1012no—
309C2×C4—104no—
310C2×C4#408413yes—
311C2×C4#408413yes—
312C2×C4#408416yes—
313C2×C4C2×D4×D513yes—
314C2×C4C2×D4×D513yes—
315C2×C4C2×#71113yes—
316C2×C4C22×C22⋊D513yes—
317C2×C4C22×C22⋊D513yes—
318C2×C4C24×D511yescharacteristic
319C8—108no—
320C8—104no—
321C8C22×C22⋊D514yes—
322C8C22×C22⋊D514yes—
323C5C22×#47311yescharacteristic, complemented, Sylow
324C22—26no—
325C22—26no—
326C22—104no—
327C22—2012no—
328C22#6548114yesdirect product factor
329C22C2×#408413yes—
330C22C2×#408413yes—
331C22C22×#71111yescharacteristic
332C4—48no—
333C4—104no—
334C4C2×#408413yes—
335C4C2×#408413yes—
336C4C22×D4×D511yescharacteristic
337C4C23×C22⋊D511yescharacteristic
338C2—23no—
339C2—21no—
340C2—204no—
341C2C2×#6548116yesdirect product factor
342C2C22×#408411yescharacteristic
subgroupG/H
centerC23#4084
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC23×C5×Q16C2
socleC23×C5#121
prime radicalC22×#709C22
hypercenterC23×Q16D5
hypocenterC5C22×#473
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

Complements

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

NH ≅ G/Ntype
1. C23×C5×Q16C2semidirect
4. C22×#3968C2semidirect
5. C2×#65481C2direct (N × H)
6. C22×#3951C2semidirect
12. C22×C5×Q16C22semidirect
24. C2×#3968C22semidirect
25. #65481C22direct (N × H)
26. C2×#3951C22semidirect
47. C2×C5×Q16C23semidirect
66. #3968C23semidirect
67. #3951C23semidirect
69. C23×Q16D5semidirect
132. C22×Q16C2×D5semidirect
201. C2×Q16C22×D5semidirect
221. C22×C5#473semidirect
285. C2×C5C2×#473semidirect
323. C5C22×#473semidirect
328. C22#65481direct (N × H)
341. C2C2×#65481direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×Q162
C22×#40882
C22×#40472
C22×#39682
C2×#654812
C22×#39512
C22×#4735