Finite Group Databasebeta

← D13×#1960 #15866565

Subgroups — D13×#1960 #15866565

Order 3328.

1598 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C4⋊Q8C211yesmaximal, characteristic
2C2×D13×#103C214yesmaximal
3C2×D13×#97C211yesmaximal, characteristic
4D13×#382C211yesmaximal, characteristic
5#13115657C211yesmaximal, characteristic, complemented
6#13115656C211yesmaximal, characteristic, complemented
7#13115655C211yesmaximal, characteristic, complemented
8#13115654C214yesmaximal, complemented
9C13×#1960C211yesmaximal, characteristic, complemented
10C22×Q8×D13C2212yes—
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×#88198C2212yes—
13C22×C8×D13C2212yes—
14D13×C4⋊Q8—24no—
15D13×C4⋊Q8C418yescomplemented
16C2×C4⋊C4×D13—22no—
17C2×C4⋊C4×D13C2212yes—
18C2×#88142—22no—
19C2×C42×D13C2211yescharacteristic
20C2×#88123C2211yescharacteristic
21C2×C13×#103C2214yes—
22C2×C13×#97C2211yescharacteristic
23C13×#382C2211yescharacteristic
24C2×#88075C2214yes—
25C2×#88056C2214yes—
26C2×#88055C2212yes—
27#11718638C2212yes—
28C2×#88050C2214yes—
29#11718597C2211yescharacteristic
30C2×#88043C2211yescharacteristic
31D13×#103—216no—
32D13×#97—24no—
33D13×#95—22no—
34#11718311—22no—
35C22×Q8×C13C2312yes—
36C2×Q8×D13—24no—
37C2×Q8×D13—28no—
38C2×Q8×D13—28no—
39C2×Q8×D13C2×C418yes—
40C22×C4×D13—22no—
41C22×C4×D13—22no—
42C22×C4×D13D412yes—
43C22×C4×D13C2311yescharacteristic
44C22×Dic26—22no—
45C22×Dic26C2312yes—
46C22×C8×C13C2312yes—
47C13×C4⋊Q8—22no—
48C13×C4⋊Q8C2×C414yescomplemented
49C2×C13×C4⋊C4—22no—
50C2×C13×C4⋊C4C2312yes—
51C2×C42×C13C2311yescharacteristic
52#88198—24no—
53#88198C2×C418yescomplemented
54C2×C4⋊Dic13—22no—
55C2×C4⋊Dic13C2312yes—
56C2×#6101—24no—
57C2×#6101—22no—
58C2×C4×Dic13D412yes—
59C2×C4×Dic13C2311yescharacteristic
60C22×#1055C2312yes—
61C2×C8×D13—24no—
62C2×C8×D13—24no—
63C2×C8×D13D418yes—
64C4⋊C4×D13—216no—
65C4⋊C4×D13—28no—
66#88142—216no—
67C42×D13C2×C414yes—
68C42×D13D414yes—
69#88123—22no—
70#88123C2×C414yescomplemented
71C13×#103—28no—
72C13×#97—22no—
73C13×#95—22no—
74#88075—28no—
75#88071—22no—
76#88071—24no—
77#88056—28no—
78#88055—24no—
79#88050—28no—
80#88043—22no—
81C2×#1960—131nomaximal, Sylow
82C23×D13C2×D411yescharacteristic
83C2×Q8×C13—22no—
84C2×Q8×C13—24no—
85C2×Q8×C13—24no—
86C2×Q8×C13C22×C414yes—
87C22×C4×C13—22no—
88C22×C4×C13—22no—
89C22×C4×C13C2×D412yes—
90C22×C4×C13C2411yescharacteristic
91C22×Dic13—22no—
92C22×Dic13—22no—
93C22×Dic13C2×D412yes—
94C22×Dic13C2×D411yescharacteristic
95Q8×D13—232no—
96Q8×D13—416no—
97C2×C4×D13—28no—
98C2×C4×D13—28no—
99C2×C4×D13—44no—
100C2×C4×D13—44no—
101C2×C4×D13—44no—
102C2×C4×D13—48no—
103C2×C4×D13C22⋊C418yes—
104C2×C4×D13C22×C412yes—
105C2×C4×D13C2×D414yes—
106C2×C4×D13C2×D412yes—
107C2×C4×D13#4114yes—
108C2×Dic26—24no—
109C2×Dic26—24no—
110C2×Dic26—22no—
111C2×Dic26—28no—
112C2×Dic26—44no—
113C2×Dic26—44no—
114C2×Dic26C22×C414yes—
115C2×C8×C13—22no—
116C2×C8×C13—22no—
117C2×C8×C13C2×D414yes—
118C13×C4⋊C4—28no—
119C13×C4⋊C4—24no—
120C42×C13C22×C412yes—
121C42×C13C2×D412yes—
122C4⋊Dic13—28no—
123C4⋊Dic13—24no—
124#6101—216no—
125#6101—44no—
126C4×Dic13C22⋊C418yes—
127C4×Dic13C22×C412yes—
128C4×Dic13C2×D412yes—
129C2×#1055—22no—
130C2×#1055—22no—
131C2×#1055C2×D414yes—
132C8×D13—216no—
133C22×C4⋊Q8—131no—
134C22×#103—134no—
135C22×#97—131no—
136C2×#382—131no—
137#1960—134no—
138#1960—131no—
139#1960—131no—
140#1960—131no—
141#1960D1311yescharacteristic, direct product factor
142C23×C13C22×D411yescharacteristic
143C22×D13C2×C22⋊C412yes—
144C22×D13#12412yes—
145C22×D13#12712yes—
146C22×D13#13718yes—
147Q8×C13—28no—
148Q8×C13—44no—
149C2×C4×C13—24no—
150C2×C4×C13—24no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—44no—
155C2×C4×C13C2×C22⋊C414yes—
156C2×C4×C13C23×C411yescharacteristic
157C2×C4×C13C22×D412yes—
158C2×C4×C13C22×D411yescharacteristic
159C2×C4×C13C2×#4112yes—
160C2×Dic13—24no—
161C2×Dic13—24no—
162C2×Dic13—42no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C2×Dic13—44no—
166C2×Dic13C2×C22⋊C414yes—
167C2×Dic13C2×C22⋊C412yes—
168C2×Dic13#12412yes—
169C2×Dic13#12712yes—
170C4×D13—216no—
171C4×D13—416no—
172C4×D13—88no—
173C4×D13C4×D418yes—
174C4×D13#12118yes—
175Dic26—28no—
176Dic26—44no—
177Dic26—416no—
178C8×C13—24no—
179#1055—24no—
180C23×Q8—132no—
181C23×C8—132no—
182C2×C4⋊Q8—132no—
183C2×C4⋊Q8—138no—
184C2×C4⋊Q8—131no—
185C2×C4⋊Q8—262no—
186C2×C4⋊Q8—264no—
187C2×C4⋊Q8C2×D1311yescharacteristic
188C22×C4⋊C4—132no—
189C22×C4⋊C4—262no—
190C22×C42—131no—
191C2×#103—134no—
192C2×#103—134no—
193C2×#103—134no—
194C2×#103—2616no—
195C2×#103C2×D1314yes—
196C2×#97—132no—
197C2×#97—131no—
198C2×#97—264no—
199C2×#97C2×D1311yescharacteristic
200#382—132no—
201#382—131no—
202#382—262no—
203#382C2×D1311yescharacteristic
204C2×#95—262no—
205C22×C13C22×C22⋊C411yescharacteristic
206C22×C13C2×#12411yescharacteristic
207C22×C13C2×#12711yescharacteristic
208C22×C13C2×#13714yes—
209C2×D13#39014yes—
210C2×D13#41918yes—
211C2×D13#49118yes—
212C2×D13#49718yes—
213C4×C13—24no—
214C4×C13—44no—
215C4×C13—82no—
216C4×C13C2×C4×D412yes—
217C4×C13C2×#12112yes—
218Dic13—24no—
219Dic13—44no—
220Dic13—82no—
221Dic13#39014yes—
222C22×Q8—138no—
223C22×Q8—132no—
224C22×Q8—262no—
225C22×Q8—264no—
226C22×Q8—268no—
227C22×Q8—268no—
228C22×Q8C22×D1312yes—
229C23×C4—131no—
230C23×C4—132no—
231C23×C4—262no—
232C23×C4—262no—
233C22×C8—132no—
234C22×C8—138no—
235C22×C8—264no—
236C22×C8—264no—
237C22×C8C22×D1312yes—
238C4⋊Q8—22no—
239C4⋊Q8—138no—
240C4⋊Q8—134no—
241C4⋊Q8—2616no—
242C4⋊Q8—264no—
243C4⋊Q8—262no—
244C4⋊Q8C4×D1314yescomplemented
245C2×C4⋊C4—22no—
246C2×C4⋊C4—132no—
247C2×C4⋊C4—2616no—
248C2×C4⋊C4—268no—
249C2×C4⋊C4—264no—
250C2×C4⋊C4—262no—
251C2×C4⋊C4—262no—
252C2×C4⋊C4C22×D1312yes—
253C2×C42—132no—
254C2×C42—131no—
255C2×C42—134no—
256C2×C42—134no—
257C2×C42C22×D1311yescharacteristic
258#103—28no—
259#103—268no—
260#103—268no—
261#103—268no—
262#97—22no—
263#97—264no—
264#97—262no—
265#95—22no—
266#95—264no—
267#95—262no—
268C2×C13C2×#39011yescharacteristic
269C2×C13C2×#41912yes—
270C2×C13C2×#49112yes—
271C2×C13C2×#49712yes—
272D13#196018yesdirect product factor
273C24—131no—
274C2×Q8—22no—
275C2×Q8—24no—
276C2×Q8—24no—
277C2×Q8—134no—
278C2×Q8—268no—
279C2×Q8—2632no—
280C2×Q8—262no—
281C2×Q8—264no—
282C2×Q8—264no—
283C2×Q8—524no—
284C2×Q8—524no—
285C2×Q8—5216no—
286C2×Q8C2×C4×D1314yes—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—131no—
290C22×C4—132no—
291C22×C4—132no—
292C22×C4—134no—
293C22×C4—134no—
294C22×C4—132no—
295C22×C4—138no—
296C22×C4—268no—
297C22×C4—268no—
298C22×C4—262no—
299C22×C4—262no—
300C22×C4—524no—
301C22×C4—524no—
302C22×C4—524no—
303C22×C4—528no—
304C22×C4D4×D1312yes—
305C22×C4C23×D1311yescharacteristic
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—134no—
309C2×C8—2616no—
310C2×C8—262no—
311C2×C8—262no—
312C2×C8D4×D1314yes—
313C4⋊C4—28no—
314C4⋊C4—24no—
315C4⋊C4—2616no—
316C4⋊C4—268no—
317C4⋊C4—264no—
318C4⋊C4—524no—
319C42—138no—
320C42—132no—
321C42—132no—
322C42C2×C4×D1312yes—
323C42D4×D1312yes—
324C13C2×#196011yescharacteristic, complemented, Sylow
325C23—132no—
326C23—138no—
327C23—132no—
328C23—132no—
329C23C2×D4×D1311yescharacteristic
330Q8—28no—
331Q8—44no—
332Q8—268no—
333Q8—5216no—
334Q8—524no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—132no—
342C2×C4—132no—
343C2×C4—132no—
344C2×C4—138no—
345C2×C4—138no—
346C2×C4—134no—
347C2×C4—2616no—
348C2×C4—264no—
349C2×C4—264no—
350C2×C4—5216no—
351C2×C4—522no—
352C2×C4—522no—
353C2×C4—524no—
354C2×C4—522no—
355C2×C4—1048no—
356C2×C4C22⋊C4×D1314yes—
357C2×C4C22×C4×D1311yescharacteristic
358C2×C4C2×D4×D1312yes—
359C2×C4C2×D4×D1311yescharacteristic
360C2×C4#41×D1312yes—
361C8—24no—
362C8—264no—
363C22—138no—
364C22—138no—
365C22—134no—
366C22—138no—
367C22C2×C22⋊C4×D1311yescharacteristic
368C22D13×#12411yescharacteristic
369C22D13×#12711yescharacteristic
370C22D13×#13714yes—
371C4—24no—
372C4—44no—
373C4—82no—
374C4—134no—
375C4—264no—
376C4—524no—
377C4—1042no—
378C4C4×D4×D1312yes—
379C4D13×#12112yes—
380C2—138no—
381C2D13×#39011yescharacteristic
382C2D13×#41912yes—
383C2D13×#49112yes—
384C2D13×#49712yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1960C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1960D13
hypocenterC13C2×#1960
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
5. #13115657C2semidirect
6. #13115656C2semidirect
7. #13115655C2semidirect
8. #13115654C2semidirect
9. C13×#1960C2semidirect
15. D13×C4⋊Q8C4semidirect
48. C13×C4⋊Q8C2×C4semidirect
53. #88198C2×C4semidirect
70. #88123C2×C4semidirect
141. #1960D13direct (N × H)
244. C4⋊Q8C4×D13semidirect
272. D13#1960direct (N × H)
324. C13C2×#1960semidirect

Maximal subgroups

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

subgroupindex
C2×D13×C4⋊Q82
C2×D13×#1032
C2×D13×#972
D13×#3822
#131156572
#131156562
#131156552
#131156542
C13×#19602
C2×#196013