Finite Group Databasebeta

← C4×C13⋊#564 #16025640

Subgroups — C4×C13⋊#564 #16025640

Order 3328.

1800 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13⋊#564C211yesmaximal, characteristic
2#13118022C211yesmaximal, characteristic
3#13118021C212yesmaximal
4#13118020C214yesmaximal
5#13118019C214yesmaximal
6#13118018C214yesmaximal
7C4×#88124C212yesmaximal
8C4×#88144C214yesmaximal
9C4×#88143C214yesmaximal
10C4×#88143C214yesmaximal
11C4×C13×#125C211yesmaximal, characteristic
12C2×C13×#125C2211yescharacteristic
13C13⋊#564C4116yesdirect product factor
14C2×#88144C2214yes—
15C2×#88143C2214yes—
16C2×#88143C2214yes—
17C2×#88124C2212yes—
18C13×#389C2212yes—
19C13×#387C2214yes—
20C13×#382C2211yescharacteristic
21C4×C13×C4⋊C4C2212yes—
22C4×C13×C4⋊C4C2214yes—
23C43×C13C2211yescharacteristic
24#11718646C2214yes—
25#11718642C2214yes—
26#11718642C2214yes—
27#11718639C2214yes—
28#11718639C2214yes—
29#11718638C2214yes—
30#11718634C2214yes—
31#11718633C2214yes—
32#11718633C2214yes—
33#11718597C2212yes—
34C4×C4⋊Dic13C2212yes—
35C4×C4⋊Dic13C2214yes—
36C4×C4⋊Dic13C2212yes—
37#11718594C2214yes—
38#11718594C2214yes—
39C4×#6101C2214yes—
40C4×#6101C2214yes—
41C4×#6101C2214yes—
42C4×#6101C2214yes—
43C42×Dic13C2214yes—
44#11718589C2212yes—
45#11718589C2212yes—
46#11718316C2214yes—
47#11718316C2214yes—
48#11718315C2214yes—
49#11718315C2214yes—
50#11718314C2214yes—
51#11718314C2214yes—
52#11718313C2214yes—
53#11718313C2214yes—
54#11718311C2214yes—
55#11718311C2214yes—
56#11718308C2214yes—
57#11718308C2214yes—
58C13×#125C2×C418yes—
59C2×C13×C4⋊C4C2312yes—
60C2×C13×C4⋊C4C2314yes—
61C2×C13×C4⋊C4C2314yes—
62C2×C13×C4⋊C4C2312yes—
63C2×C42×C13C2314yes—
64C2×C42×C13C2311yescharacteristic
65C2×C42×C13C2312yes—
66C2×C42×C13C2312yes—
67C2×C42×C13C2311yescharacteristic
68C2×C42×C13C2311yescharacteristic
69C2×C4⋊Dic13C2312yes—
70C2×C4⋊Dic13C2314yes—
71C2×C4⋊Dic13C2312yes—
72C2×C4⋊Dic13C2312yes—
73C2×C4⋊Dic13C2312yes—
74C2×C4⋊Dic13C2314yes—
75C2×#6101C2314yes—
76C2×#6101C2314yes—
77C2×#6101C2314yes—
78C2×#6101C2314yes—
79C2×#6101C2314yes—
80C2×#6101C2314yes—
81C2×#6101C2314yes—
82C2×#6101C2314yes—
83C2×C4×Dic13C2314yes—
84C2×C4×Dic13C2314yes—
85C2×C4×Dic13C2314yes—
86C2×C4×Dic13C2314yes—
87C2×C4×Dic13C2314yes—
88C2×C4×Dic13C2314yes—
89#88144C2×C4132yes—
90#88143C2×C4132yes—
91#88143C2×C4132yes—
92#88124C2×C4116yes—
93C13×#95C2314yes—
94C13×#95C2314yes—
95C13×#95C2314yes—
96#88071C2314yes—
97#88071C2314yes—
98#88071C2314yes—
99#88071C2314yes—
100#88071C2314yes—
101#88071C2314yes—
102#88071C2314yes—
103#88071C2314yes—
104#88071C2314yes—
105#88071C2314yes—
106#88071C2314yes—
107#88071C2314yes—
108C4×#564—131nomaximal, Sylow
109C22×C4×C13C2412yes—
110C22×C4×C13C2414yes—
111C22×C4×C13C2411yescharacteristic
112C22×C4×C13C2411yescharacteristic
113C22×C4×C13C2414yes—
114C22×C4×C13C2412yes—
115C22×C4×C13C2411yescharacteristic
116C22×Dic13C2414yes—
117C22×Dic13C2414yes—
118C22×Dic13C2414yes—
119C22×Dic13C2414yes—
120C13×C4⋊C4—44no—
121C13×C4⋊C4—42no—
122C13×C4⋊C4C22×C418yes—
123C13×C4⋊C4C22×C4116yes—
124C42×C13—22no—
125C42×C13—28no—
126C42×C13—24no—
127C42×C13—42no—
128C42×C13—41no—
129C42×C13C22×C414yes—
130C4⋊Dic13—42no—
131C4⋊Dic13—44no—
132C4⋊Dic13—42no—
133C4⋊Dic13C22×C418yes—
134C4⋊Dic13C22×C418yes—
135C4⋊Dic13C22×C4116yes—
136#6101—44no—
137#6101—44no—
138#6101—44no—
139#6101—44no—
140#6101C22×C4116yes—
141#6101C22×C4116yes—
142#6101C22×C4116yes—
143#6101C22×C4116yes—
144C4×Dic13—28no—
145C4×Dic13—28no—
146C4×Dic13—44no—
147C4×Dic13—44no—
148C4×Dic13—44no—
149C4×Dic13C22×C4116yes—
150C2×#564—131no—
151#2382—134no—
152#2382—134no—
153#2382—134no—
154#2382—132no—
155#2382—131no—
156C4×#125—134no—
157C4×#125—134no—
158C4×#125—134no—
159C4×#125—132no—
160C4×#125D1311yescharacteristic
161C23×C13C2511yescharacteristic
162C2×C4×C13—21no—
163C2×C4×C13—24no—
164C2×C4×C13—22no—
165C2×C4×C13—24no—
166C2×C4×C13—22no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—22no—
170C2×C4×C13—24no—
171C2×C4×C13—24no—
172C2×C4×C13—24no—
173C2×C4×C13—22no—
174C2×C4×C13—22no—
175C2×C4×C13—22no—
176C2×C4×C13C23×C418yes—
177C2×C4×C13C23×C412yes—
178C2×C4×C13C23×C414yes—
179C2×C4×C132−1+412yes—
180C2×C4×C132−1+414yes—
181C2×Dic13—24no—
182C2×Dic13—24no—
183C2×Dic13—24no—
184C2×Dic13—24no—
185C2×Dic13—24no—
186C2×Dic13—24no—
187C2×Dic13—24no—
188C2×Dic13—24no—
189C2×Dic13—24no—
190C2×Dic13—24no—
191C2×Dic13C23×C418yes—
192C2×Dic13C23×C418yes—
193#564—1316no—
194C2×#125—134no—
195C2×#125—134no—
196C2×#125—134no—
197C2×#125—132no—
198C2×#125C2×D1311yescharacteristic
199#389—134no—
200#389—134no—
201#389—134no—
202#389—134no—
203#389—132no—
204#389—132no—
205#389—134no—
206#389—134no—
207#389C2×D1312yes—
208#387—134no—
209#387—134no—
210#387—134no—
211#387—134no—
212#387—134no—
213#387—134no—
214#387—134no—
215#387—134no—
216#387—134no—
217#387—134no—
218#387—134no—
219#387—134no—
220#387—134no—
221#387—134no—
222#387C2×D1314yes—
223#382—134no—
224#382—132no—
225#382—134no—
226#382—134no—
227#382C2×D1311yescharacteristic
228C4×C4⋊C4—134no—
229C4×C4⋊C4—134no—
230C4×C4⋊C4—134no—
231C4×C4⋊C4—134no—
232C4×C4⋊C4—134no—
233C4×C4⋊C4—132no—
234C4×C4⋊C4—132no—
235C4×C4⋊C4C2×D1314yes—
236C4×C4⋊C4C2×D1312yes—
237C43—134no—
238C43C2×D1311yescharacteristic
239C22×C13C24×C411yescharacteristic
240C22×C13C2×2−1+411yescharacteristic
241C22×C13C2×2−1+412yes—
242C22×C13#58511yescharacteristic
243C22×C13#58512yes—
244C4×C13—28no—
245C4×C13—24no—
246C4×C13—22no—
247C4×C13—44no—
248C4×C13—42no—
249C4×C13—41no—
250C4×C13#56414yescomplemented
251Dic13—28no—
252Dic13—28no—
253Dic13—44no—
254Dic13—44no—
255#125—1332no—
256#125—1332no—
257#125—1332no—
258#125—1316no—
259#125C4×D1318yes—
260C2×C4⋊C4—134no—
261C2×C4⋊C4—134no—
262C2×C4⋊C4—134no—
263C2×C4⋊C4—134no—
264C2×C4⋊C4—134no—
265C2×C4⋊C4—132no—
266C2×C4⋊C4—132no—
267C2×C4⋊C4—134no—
268C2×C4⋊C4—134no—
269C2×C4⋊C4—134no—
270C2×C4⋊C4—134no—
271C2×C4⋊C4—134no—
272C2×C4⋊C4—132no—
273C2×C4⋊C4—132no—
274C2×C4⋊C4C22×D1314yes—
275C2×C4⋊C4C22×D1312yes—
276C2×C4⋊C4C22×D1312yes—
277C2×C4⋊C4C22×D1314yes—
278C2×C42—134no—
279C2×C42—134no—
280C2×C42—134no—
281C2×C42—134no—
282C2×C42—134no—
283C2×C42—134no—
284C2×C42C22×D1314yes—
285C2×C42C22×D1311yescharacteristic
286C2×C42C22×D1312yes—
287C2×C42C22×D1311yescharacteristic
288C2×C42C22×D1312yes—
289C2×C42C22×D1311yescharacteristic
290#95—134no—
291#95—134no—
292#95—134no—
293#95—134no—
294#95—134no—
295#95—134no—
296#95—134no—
297#95—134no—
298#95—134no—
299#95—134no—
300#95—134no—
301#95—134no—
302#95C22×D1314yes—
303#95C22×D1314yes—
304#95C22×D1314yes—
305C2×C13C4×2−1+412yes—
306C2×C13C4×2−1+411yescharacteristic
307C2×C13C2×#56411yescharacteristic
308C2×C13#353112yes—
309C2×C13#353111yescharacteristic
310C22×C4—134no—
311C22×C4—134no—
312C22×C4—134no—
313C22×C4—134no—
314C22×C4C23×D1312yes—
315C22×C4C23×D1314yes—
316C22×C4C23×D1311yescharacteristic
317C22×C4C23×D1311yescharacteristic
318C22×C4C23×D1314yes—
319C22×C4C23×D1312yes—
320C22×C4C23×D1311yescharacteristic
321C4⋊C4—42no—
322C4⋊C4—44no—
323C4⋊C4—1316no—
324C4⋊C4—1316no—
325C4⋊C4—1316no—
326C4⋊C4—1316no—
327C4⋊C4—1316no—
328C4⋊C4—138no—
329C4⋊C4—138no—
330C4⋊C4—524no—
331C4⋊C4—524no—
332C4⋊C4—524no—
333C4⋊C4—524no—
334C4⋊C4—522no—
335C4⋊C4—522no—
336C4⋊C4—524no—
337C4⋊C4C2×C4×D1318yes—
338C4⋊C4C2×C4×D13116yes—
339C42—22no—
340C42—28no—
341C42—24no—
342C42—41no—
343C42—42no—
344C42—1316no—
345C42—268no—
346C42—268no—
347C42—524no—
348C42—524no—
349C42—524no—
350C42C2×C4×D1314yes—
351C13C4×#56411yescharacteristic, complemented, Sylow
352C23C24×D1311yescharacteristic
353C2×C4—21no—
354C2×C4—24no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—138no—
368C2×C4—138no—
369C2×C4—264no—
370C2×C4—264no—
371C2×C4—264no—
372C2×C4—264no—
373C2×C4—264no—
374C2×C4—264no—
375C2×C4—264no—
376C2×C4—264no—
377C2×C4—264no—
378C2×C4—264no—
379C2×C4C22×C4×D1318yes—
380C2×C4C22×C4×D1314yes—
381C2×C4C22×C4×D1312yes—
382C2×C4#8825412yes—
383C2×C4#8825714yes—
384C22C23×C4×D1311yescharacteristic
385C22C2×#8825411yescharacteristic
386C22C2×#8825712yes—
387C22#1171964811yescharacteristic
388C22#1171964812yes—
389C4—24no—
390C4—28no—
391C4—22no—
392C4—42no—
393C4—44no—
394C4—41no—
395C4—268no—
396C4—268no—
397C4—524no—
398C4—524no—
399C4C13⋊#56414yesdirect product factor
400C2C4×#8825712yes—
401C2C4×#8825411yescharacteristic
402C2C2×C13⋊#56411yescharacteristic
403C2#1312898112yes—
404C2#1312898311yescharacteristic
subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC4×C13×#125C2
socle, prime radical, cosocleC23×C13C25
hypercenterC4×#125D13
hypocenterC13C4×#564
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
13. C13⋊#564C4direct (N × H)
250. C4×C13#564semidirect
351. C13C4×#564semidirect
399. C4C13⋊#564direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13⋊#5642
#131180222
#131180212
#131180202
#131180192
#131180182
C4×#881242
C4×#881442
C4×#881432
C4×C13×#1252
C4×#56413