Finite Group Databasebeta

← C13×#18407 #15704746

Subgroups — C13×#18407 #15704746

Order 3328.

904 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3493C211yesmaximal, characteristic
2C13×#3232C212yesmaximal, complemented
3C13×#2611C211yesmaximal, characteristic, complemented
4C13×#1618C212yesmaximal, complemented
5C13×#1617C211yesmaximal, characteristic, complemented
6C13×#1616C211yesmaximal, characteristic, complemented
7C13×#1612C212yesmaximal, complemented
8C13×#1611C211yesmaximal, characteristic, complemented
9C13×#1610C211yesmaximal, characteristic, complemented
10C13×#1500C212yesmaximal, complemented
11C13×#1458C211yesmaximal, characteristic, complemented
12C13×#556—22no—
13C13×#555—22no—
14C13×#553—22no—
15C13×#552—22no—
16C13×#544C2211yescharacteristic
17C13×#538—21no—
18C13×#538C2212yes—
19C13×#537C2211yescharacteristic
20C13×#529—21no—
21C13×#529C2212yes—
22C2×C13×#125C2211yescharacteristic
23C13×#525—21no—
24C13×#520—21no—
25C2×C13×#117C2211yescharacteristic
26C13×#499—22no—
27C13×#488—22no—
28C13×#484C2212yes—
29C13×#483C2212yes—
30C13×#481C2212yes—
31C13×#480C2212yes—
32C13×#479—22no—
33C13×#478—22no—
34C13×#431C2212yes—
35C13×#400C2211yescharacteristic
36C13×#399C2211yescharacteristic
37C13×#398C2211yescharacteristic
38C13×#397C2211yescharacteristic
39C13×#389—21no—
40C13×#388—21no—
41C13×#387—21no—
42C13×#385—21no—
43C13×#376C2211yescharacteristic
44C13×#328C2212yes—
45C13×#328C2212yes—
46C13×#327C2212yes—
47C13×#327C2212yes—
48C13×#324C2211yescharacteristic
49C13×#324C2211yescharacteristic
50C13×#323C2212yes—
51C2×C13×#41—21no—
52C23×C4×C13D411yescharacteristic
53C13×C4⋊Q8—22no—
54C13×#126—22no—
55C13×#126—22no—
56C13×#126—22no—
57C13×#126—22no—
58C13×#125—21no—
59C13×#125—22no—
60C13×#125—22no—
61C13×#125—22no—
62C13×#125D412yes—
63C13×#124—21no—
64C13×#124—22no—
65C13×#124—22no—
66C13×#124D412yes—
67C13×#123—22no—
68C13×#123—22no—
69C13×#123—22no—
70C13×C22⋊Q8—21no—
71C13×C22⋊Q8—21no—
72C13×C22⋊Q8—21no—
73C13×C22⋊Q8—22no—
74C13×C22⋊Q8C2312yes—
75C13×#121—21no—
76C13×#121—21no—
77C13×#121—22no—
78C13×#121—22no—
79C13×#121—22no—
80C13×#121—21no—
81C13×#121C2312yes—
82C13×#120—22no—
83C4×Q8×C13—22no—
84C4×Q8×C13—21no—
85C4×Q8×C13D412yes—
86C4×D4×C13—22no—
87C4×D4×C13—22no—
88C4×D4×C13—22no—
89C4×D4×C13—21no—
90C4×D4×C13—22no—
91C4×D4×C13—22no—
92C4×D4×C13D412yes—
93C13×#117—22no—
94C13×#117—22no—
95C13×#117—21no—
96C13×#117—22no—
97C13×#117—22no—
98C13×#117—22no—
99C2×C13×C4⋊C4—22no—
100C2×C13×C4⋊C4—21no—
101C2×C13×C4⋊C4—21no—
102C2×C13×C4⋊C4—21no—
103C2×C13×C4⋊C4—21no—
104C2×C13×C4⋊C4D411yescharacteristic
105C2×C13×C4⋊C4C2311yescharacteristic
106C2×C13×C4⋊C4C2311yescharacteristic
107C2×C13×C4⋊C4C2311yescharacteristic
108C2×C13×C22⋊C4—21no—
109C2×C13×C22⋊C4—21no—
110C2×C13×C22⋊C4D411yescharacteristic
111C2×C13×C22⋊C4C2311yescharacteristic
112C2×C42×C13—21no—
113C2×C42×C13D411yescharacteristic
114C2×C42×C13C2311yescharacteristic
115C13×#107—22no—
116C13×#107—22no—
117C13×#106—22no—
118C13×#106—22no—
119C13×C4⋊C8—22no—
120C13×#103—22no—
121C13×#103—22no—
122C13×#102—22no—
123C13×#102—22no—
124C13×C22⋊C8C2312yes—
125C13×C22⋊C8C2312yes—
126C4×C8×C13—22no—
127C13×#95—21no—
128C13×#95—21no—
129C13×#95—21no—
130C13×#95—21no—
131C13×#95—21no—
132C13×#95C2311yescharacteristic
133C13×#95C2311yescharacteristic
134#18407C1311yesmaximal, characteristic, direct product factor, Sylow
135C24×C13C2×D411yescharacteristic
136C13×#41—42no—
137C13×#41—42no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13C2×D412yes—
141C2×D4×C13—21no—
142C2×D4×C13—22no—
143C2×D4×C13—22no—
144C2×D4×C13—22no—
145C2×D4×C13—21no—
146C2×D4×C13C2×D412yes—
147C22×C4×C13—22no—
148C22×C4×C13—21no—
149C22×C4×C13—22no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—41no—
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2411yescharacteristic
164C2×C8×C13—22no—
165C2×C8×C13—22no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—42no—
181C13×C4⋊C4—41no—
182C13×C4⋊C4—41no—
183C13×C4⋊C4—42no—
184C13×C4⋊C4—42no—
185C13×C4⋊C4C2×D412yes—
186C13×C4⋊C4C2×D412yes—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—22no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—42no—
199C13×C22⋊C4—42no—
200C42×C13—22no—
201C42×C13—22no—
202C42×C13—21no—
203C42×C13—21no—
204C42×C13—22no—
205C42×C13—42no—
206C42×C13C2×D412yes—
207C42×C13C2×D412yes—
208#3493C2×C1311yescharacteristic
209#3232C2×C1312yescomplemented
210#2611C2×C1311yescharacteristic, complemented
211#1618C2×C1312yescomplemented
212#1617C2×C1311yescharacteristic, complemented
213#1616C2×C1311yescharacteristic, complemented
214#1612C2×C1312yescomplemented
215#1611C2×C1311yescharacteristic, complemented
216#1610C2×C1311yescharacteristic, complemented
217#1500C2×C1312yescomplemented
218#1458C2×C1311yescharacteristic, complemented
219C23×C13—21no—
220C23×C13—22no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13C22×D411yescharacteristic
226Q8×C13—42no—
227Q8×C13—42no—
228Q8×C13—81no—
229D4×C13—42no—
230D4×C13—42no—
231D4×C13—42no—
232D4×C13—42no—
233D4×C13—82no—
234D4×C13—81no—
235D4×C13—82no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—22no—
241C2×C4×C13—21no—
242C2×C4×C13—22no—
243C2×C4×C13—21no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—44no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—82no—
265C2×C4×C13—82no—
266C2×C4×C13#12011yescharacteristic
267C2×C4×C13#12011yescharacteristic
268C2×C4×C13#12012yes—
269C2×C4×C13#13512yes—
270C2×C4×C13C22×D412yes—
271C8×C13—42no—
272C8×C13—42no—
273#556—22no—
274#555—22no—
275#553—22no—
276#552—22no—
277#544C22×C1311yescharacteristic
278#538—21no—
279#538C22×C1312yes—
280#537C22×C1311yescharacteristic
281#529—21no—
282#529C22×C1312yes—
283C2×#125C22×C1311yescharacteristic
284#525—21no—
285#520—21no—
286C2×#117C22×C1311yescharacteristic
287#499—22no—
288#488—22no—
289#484C22×C1312yes—
290#483C22×C1312yes—
291#481C22×C1312yes—
292#480C22×C1312yes—
293#479—22no—
294#478—22no—
295#431C22×C1312yes—
296#400C22×C1311yescharacteristic
297#399C22×C1311yescharacteristic
298#398C22×C1311yescharacteristic
299#397C22×C1311yescharacteristic
300#389—21no—
301#388—21no—
302#387—21no—
303#385—21no—
304#376C22×C1311yescharacteristic
305#328C22×C1312yes—
306#328C22×C1312yes—
307#327C22×C1312yes—
308#327C22×C1312yes—
309#324C22×C1311yescharacteristic
310#324C22×C1311yescharacteristic
311#323C22×C1312yes—
312C22×C13—21no—
313C22×C13—21no—
314C22×C13—42no—
315C22×C13—41no—
316C22×C13—42no—
317C22×C13—42no—
318C22×C13—41no—
319C22×C13—42no—
320C22×C13—41no—
321C22×C13—81no—
322C22×C13C2×#12011yescharacteristic
323C22×C13C2×#13511yescharacteristic
324C22×C13#57511yescharacteristic
325C4×C13—22no—
326C4×C13—21no—
327C4×C13—21no—
328C4×C13—22no—
329C4×C13—22no—
330C4×C13—42no—
331C4×C13—42no—
332C4×C13—41no—
333C4×C13—42no—
334C4×C13—41no—
335C4×C13—42no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13—81no—
339C2×#41—21no—
340C23×C4D4×C1311yescharacteristic
341C4⋊Q8—22no—
342#126—22no—
343#126—22no—
344#126—22no—
345#126—22no—
346#125—21no—
347#125—22no—
348#125—22no—
349#125—22no—
350#125D4×C1312yes—
351#124—21no—
352#124—22no—
353#124—22no—
354#124D4×C1312yes—
355#123—22no—
356#123—22no—
357#123—22no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—22no—
362C22⋊Q8C23×C1312yes—
363#121—21no—
364#121—21no—
365#121—22no—
366#121—22no—
367#121—22no—
368#121—21no—
369#121C23×C1312yes—
370#120—22no—
371C4×Q8—22no—
372C4×Q8—21no—
373C4×Q8D4×C1312yes—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—21no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4D4×C1312yes—
381#117—22no—
382#117—22no—
383#117—21no—
384#117—22no—
385#117—22no—
386#117—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4D4×C1311yescharacteristic
393C2×C4⋊C4C23×C1311yescharacteristic
394C2×C4⋊C4C23×C1311yescharacteristic
395C2×C4⋊C4C23×C1311yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4D4×C1311yescharacteristic
399C2×C22⋊C4C23×C1311yescharacteristic
400C2×C42—21no—
401C2×C42D4×C1311yescharacteristic
402C2×C42C23×C1311yescharacteristic
403#107—22no—
404#107—22no—
405#106—22no—
406#106—22no—
407C4⋊C8—22no—
408#103—22no—
409#103—22no—
410#102—22no—
411#102—22no—
412C22⋊C8C23×C1312yes—
413C22⋊C8C23×C1312yes—
414C4×C8—22no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95C23×C1311yescharacteristic
421#95C23×C1311yescharacteristic
422C2×C13—21no—
423C2×C13—21no—
424C2×C13—82no—
425C2×C13—81no—
426C2×C13#300211yescharacteristic
427C2×C13#301811yescharacteristic
428C2×C13#302811yescharacteristic
429C24C2×D4×C1311yescharacteristic
430#41—42no—
431#41—42no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8C2×D4×C1312yes—
435C2×D4—21no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—21no—
440C2×D4C2×D4×C1312yes—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—41no—
452C22×C4C2×D4×C1311yescharacteristic
453C22×C4C2×D4×C1311yescharacteristic
454C22×C4C2×D4×C1311yescharacteristic
455C22×C4C2×D4×C1311yescharacteristic
456C22×C4C2×D4×C1311yescharacteristic
457C22×C4C24×C1311yescharacteristic
458C2×C8—22no—
459C2×C8—22no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—42no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4C2×D4×C1312yes—
480C4⋊C4C2×D4×C1312yes—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C42—22no—
495C42—22no—
496C42—21no—
497C42—21no—
498C42—22no—
499C42—42no—
500C42C2×D4×C1312yes—
501C42C2×D4×C1312yes—
502C13#1840711yescharacteristic, direct product factor, Sylow
503C23—21no—
504C23—22no—
505C23—21no—
506C23—21no—
507C23—41no—
508C23—41no—
509C23C22×D4×C1311yescharacteristic
510Q8—42no—
511Q8—42no—
512Q8—81no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—82no—
518D4—81no—
519D4—82no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4C13×#12012yes—
551C2×C4C13×#12011yescharacteristic
552C2×C4C13×#12011yescharacteristic
553C2×C4C13×#13512yes—
554C2×C4C22×D4×C1312yes—
555C8—42no—
556C8—42no—
557C22—21no—
558C22—21no—
559C22—42no—
560C22—42no—
561C22—41no—
562C22—42no—
563C22—41no—
564C22—41no—
565C22—42no—
566C22—81no—
567C22C2×C13×#12011yescharacteristic
568C22C2×C13×#13511yescharacteristic
569C22C13×#57511yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—21no—
574C4—21no—
575C4—42no—
576C4—41no—
577C4—42no—
578C4—41no—
579C4—42no—
580C4—42no—
581C4—81no—
582C4—81no—
583C4—81no—
584C2—21no—
585C2—21no—
586C2—81no—
587C2—82no—
588C2C13×#300211yescharacteristic
589C2C13×#301811yescharacteristic
590C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3493C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3232C2semidirect
3. C13×#2611C2semidirect
4. C13×#1618C2semidirect
5. C13×#1617C2semidirect
6. C13×#1616C2semidirect
7. C13×#1612C2semidirect
8. C13×#1611C2semidirect
9. C13×#1610C2semidirect
10. C13×#1500C2semidirect
11. C13×#1458C2semidirect
134. #18407C13direct (N × H)
209. #3232C2×C13semidirect
210. #2611C2×C13semidirect
211. #1618C2×C13semidirect
212. #1617C2×C13semidirect
213. #1616C2×C13semidirect
214. #1612C2×C13semidirect
215. #1611C2×C13semidirect
216. #1610C2×C13semidirect
217. #1500C2×C13semidirect
218. #1458C2×C13semidirect
502. C13#18407direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34932
C13×#32322
C13×#26112
C13×#16182
C13×#16172
C13×#16162
C13×#16122
C13×#16112
C13×#16102
C13×#15002
C13×#14582
#1840713