Finite Group Databasebeta

← C13×#18261 #15704600

Subgroups — C13×#18261 #15704600

Order 3328.

1192 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3536C211yesmaximal, characteristic
2C13×#3004C211yesmaximal, characteristic, complemented
3C2×C13×#448C211yesmaximal, characteristic, complemented
4C13×#2434C211yesmaximal, characteristic, complemented
5C13×#1604C214yesmaximal, complemented
6C13×#1603C214yesmaximal, complemented
7C13×#1507C211yesmaximal, characteristic, complemented
8C13×#1501C211yesmaximal, characteristic, complemented
9C13×#1472C211yesmaximal, characteristic, complemented
10C23×Q8×C13C2211yescharacteristic
11C2×C13×#137—21no—
12C22×C13×SD16—21no—
13C13×#562—22no—
14C13×#554—21no—
15C13×#548—21no—
16C13×#547—21no—
17C13×#546—21no—
18C13×#546—22no—
19C13×#543—21no—
20C13×#542—21no—
21C13×#539C2212yes—
22C13×#538—21no—
23C13×#537—21no—
24C13×#537C2212yes—
25C2×C13×C4⋊Q8—21no—
26C13×#525C2211yescharacteristic
27C2×C13×C22⋊Q8C2211yescharacteristic
28C2×C13×#121C2211yescharacteristic
29C13×#451—21no—
30C13×#451C2212yescomplemented
31C13×#448—22no—
32C13×#448—21no—
33C13×#448C2214yes—
34C13×#448C2212yescomplemented
35C13×#419—21no—
36C2×C13×#103—21no—
37C13×#407C2211yescharacteristic
38C2×C13×C22⋊C8C2211yescharacteristic
39C13×#395C2214yescomplemented
40C13×#391—21no—
41C13×#385—22no—
42C4×C13×C22⋊C4C2211yescharacteristic
43C13×#328C2212yescomplemented
44C13×#327C2214yes—
45C13×#327C2212yescomplemented
46C13×#324C2214yescomplemented
47C2×C13×#41—21no—
48C2×C13×#41—22no—
49C2×C13×#41D411yescharacteristic
50C22×Q8×C13—21no—
51C22×Q8×C13—21no—
52C22×Q8×C13—21no—
53C22×Q8×C13—21no—
54C22×Q8×C13—21no—
55C22×Q8×C13—44no—
56C22×Q8×C13D411yescharacteristic
57C22×Q8×C13C2312yes—
58C22×D4×C13—21no—
59C22×D4×C13D411yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C13×#137—44no—
63C2×C13×Q16—22no—
64C2×C13×SD16—24no—
65C2×C13×SD16—22no—
66C2×C13×SD16—44no—
67C2×C13×M16—21no—
68C22×C8×C13—21no—
69C13×C4⋊Q8—21no—
70C13×C4⋊Q8—44no—
71C13×#126—22no—
72C13×#125—22no—
73C13×#124—22no—
74C13×#124—21no—
75C13×#124—22no—
76C13×#123—22no—
77C13×#123—22no—
78C13×#123—22no—
79C13×#123—21no—
80C13×#123—22no—
81C13×C22⋊Q8—21no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8D411yescharacteristic
93C13×C22⋊Q8C2311yescharacteristic
94C13×#121—21no—
95C13×#121—22no—
96C13×#121—22no—
97C13×#121—22no—
98C13×#121—22no—
99C13×#121—21no—
100C13×#121—21no—
101C13×#121—22no—
102C13×#121D412yes—
103C13×#121D411yescharacteristic
104C13×#121C2312yes—
105C13×#121C2311yescharacteristic
106C13×#120—22no—
107C13×#120—21no—
108C4×Q8×C13—21no—
109C4×D4×C13—22no—
110C4×D4×C13—21no—
111C4×D4×C13—21no—
112C4×D4×C13—21no—
113C4×D4×C13—22no—
114C13×#117D411yescharacteristic
115C2×C13×C4⋊C4—21no—
116C2×C13×C4⋊C4—24no—
117C2×C13×C4⋊C4D411yescharacteristic
118C2×C13×C4⋊C4D411yescharacteristic
119C2×C13×C4⋊C4C2312yes—
120C2×C13×C22⋊C4—22no—
121C2×C13×C22⋊C4—21no—
122C2×C13×C22⋊C4—21no—
123C2×C13×C22⋊C4D412yes—
124C2×C42×C13—21no—
125C13×#103—24no—
126C13×#103—22no—
127C13×#103—22no—
128C13×C22⋊C8—21no—
129C13×C22⋊C8—21no—
130C13×C22⋊C8C2312yes—
131C13×C22⋊C8C2312yes—
132C13×#95—24no—
133C13×#95C2312yes—
134#18261C1311yesmaximal, characteristic, direct product factor, Sylow
135C24×C13—21no—
136C24×C13C2×D411yescharacteristic
137C13×#41—42no—
138C13×#41—84no—
139C13×#41—82no—
140C2×Q8×C13—24no—
141C2×Q8×C13—22no—
142C2×Q8×C13—21no—
143C2×Q8×C13—21no—
144C2×Q8×C13—24no—
145C2×Q8×C13—24no—
146C2×Q8×C13—22no—
147C2×Q8×C13—22no—
148C2×Q8×C13—44no—
149C2×Q8×C13—42no—
150C2×Q8×C13—42no—
151C2×Q8×C13—42no—
152C2×Q8×C13—42no—
153C2×Q8×C13—44no—
154C2×Q8×C13—44no—
155C2×Q8×C13—41no—
156C2×Q8×C13—41no—
157C2×Q8×C13C2×D411yescharacteristic
158C2×D4×C13—21no—
159C2×D4×C13—21no—
160C2×D4×C13—22no—
161C2×D4×C13—22no—
162C2×D4×C13—22no—
163C2×D4×C13—21no—
164C2×D4×C13—22no—
165C2×D4×C13—21no—
166C2×D4×C13—42no—
167C2×D4×C13—82no—
168C2×D4×C13C2×D411yescharacteristic
169C2×D4×C13C2×D412yes—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—42no—
178C22×C4×C13—44no—
179C22×C4×C13—41no—
180C22×C4×C13—41no—
181C22×C4×C13C2×D412yes—
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2×D411yescharacteristic
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2×D412yes—
186C22×C4×C13C2×D411yescharacteristic
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2411yescharacteristic
189C13×Q16—44no—
190C13×SD16—48no—
191C13×SD16—44no—
192C13×M16—42no—
193C2×C8×C13—22no—
194C2×C8×C13—22no—
195C2×C8×C13—42no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—22no—
198C13×C4⋊C4—22no—
199C13×C4⋊C4—22no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—22no—
205C13×C4⋊C4—22no—
206C13×C4⋊C4—21no—
207C13×C4⋊C4—48no—
208C13×C4⋊C4C2×D412yes—
209C13×C4⋊C4C2×D411yescharacteristic
210C13×C4⋊C4C2×D411yescharacteristic
211C13×C22⋊C4—24no—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—22no—
214C13×C22⋊C4—22no—
215C13×C22⋊C4—22no—
216C13×C22⋊C4—22no—
217C13×C22⋊C4—21no—
218C13×C22⋊C4—22no—
219C13×C22⋊C4—22no—
220C13×C22⋊C4—21no—
221C13×C22⋊C4—21no—
222C13×C22⋊C4—22no—
223C13×C22⋊C4—21no—
224C13×C22⋊C4—22no—
225C13×C22⋊C4—21no—
226C42×C13—22no—
227C42×C13—21no—
228C42×C13—42no—
229#3536C2×C1311yescharacteristic
230#3004C2×C1311yescharacteristic, complemented
231C2×#448C2×C1311yescharacteristic, complemented
232#2434C2×C1311yescharacteristic, complemented
233#1604C2×C1314yescomplemented
234#1603C2×C1314yescomplemented
235#1507C2×C1311yescharacteristic, complemented
236#1501C2×C1311yescharacteristic, complemented
237#1472C2×C1311yescharacteristic, complemented
238C23×C13—22no—
239C23×C13—22no—
240C23×C13—22no—
241C23×C13—21no—
242C23×C13—41no—
243C23×C13—42no—
244C23×C13—81no—
245C23×C13—81no—
246C23×C13#12011yescharacteristic
247C23×C13#12011yescharacteristic
248C23×C13C22×D411yescharacteristic
249Q8×C13—24no—
250Q8×C13—24no—
251Q8×C13—42no—
252Q8×C13—42no—
253Q8×C13—44no—
254Q8×C13—41no—
255Q8×C13—44no—
256Q8×C13—42no—
257Q8×C13—81no—
258Q8×C13—82no—
259D4×C13—42no—
260D4×C13—41no—
261D4×C13—44no—
262D4×C13—42no—
263D4×C13—42no—
264D4×C13—42no—
265D4×C13—82no—
266D4×C13—81no—
267D4×C13—82no—
268D4×C13—82no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—22no—
272C2×C4×C13—24no—
273C2×C4×C13—24no—
274C2×C4×C13—21no—
275C2×C4×C13—22no—
276C2×C4×C13—21no—
277C2×C4×C13—22no—
278C2×C4×C13—21no—
279C2×C4×C13—22no—
280C2×C4×C13—24no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13—44no—
287C2×C4×C13—44no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—81no—
293C2×C4×C13—82no—
294C2×C4×C13—82no—
295C2×C4×C13—82no—
296C2×C4×C13#12011yescharacteristic
297C2×C4×C13#12011yescharacteristic
298C2×C4×C13C22×D411yescharacteristic
299C2×C4×C13C22×D411yescharacteristic
300C8×C13—42no—
301C8×C13—42no—
302C23×Q8C22×C1311yescharacteristic
303C2×#137—21no—
304C22×SD16—21no—
305#562—22no—
306#554—21no—
307#548—21no—
308#547—21no—
309#546—21no—
310#546—22no—
311#543—21no—
312#542—21no—
313#539C22×C1312yes—
314#538—21no—
315#537—21no—
316#537C22×C1312yes—
317C2×C4⋊Q8—21no—
318#525C22×C1311yescharacteristic
319C2×C22⋊Q8C22×C1311yescharacteristic
320C2×#121C22×C1311yescharacteristic
321#451—21no—
322#451C22×C1312yescomplemented
323#448—22no—
324#448—21no—
325#448C22×C1314yes—
326#448C22×C1312yescomplemented
327#419—21no—
328C2×#103—21no—
329#407C22×C1311yescharacteristic
330C2×C22⋊C8C22×C1311yescharacteristic
331#395C22×C1314yescomplemented
332#391—21no—
333#385—22no—
334C4×C22⋊C4C22×C1311yescharacteristic
335#328C22×C1312yescomplemented
336#327C22×C1314yes—
337#327C22×C1312yescomplemented
338#324C22×C1314yescomplemented
339C22×C13—21no—
340C22×C13—21no—
341C22×C13—21no—
342C22×C13—21no—
343C22×C13—21no—
344C22×C13—21no—
345C22×C13—21no—
346C22×C13—44no—
347C22×C13—41no—
348C22×C13—42no—
349C22×C13—41no—
350C22×C13—42no—
351C22×C13—41no—
352C22×C13—42no—
353C22×C13—162no—
354C22×C13#45612yes—
355C22×C13C2×#12011yescharacteristic
356C22×C13#57712yes—
357C4×C13—21no—
358C4×C13—21no—
359C4×C13—21no—
360C4×C13—44no—
361C4×C13—42no—
362C4×C13—42no—
363C4×C13—41no—
364C4×C13—41no—
365C4×C13—44no—
366C4×C13—41no—
367C4×C13—42no—
368C4×C13B(4,𝔽2)12yes—
369C2×#41—21no—
370C2×#41—22no—
371C2×#41D4×C1311yescharacteristic
372C22×Q8—21no—
373C22×Q8—21no—
374C22×Q8—21no—
375C22×Q8—21no—
376C22×Q8—21no—
377C22×Q8—44no—
378C22×Q8D4×C1311yescharacteristic
379C22×Q8C23×C1312yes—
380C22×D4—21no—
381C22×D4D4×C1311yescharacteristic
382C23×C4—21no—
383C23×C4C23×C1311yescharacteristic
384#137—44no—
385C2×Q16—22no—
386C2×SD16—24no—
387C2×SD16—22no—
388C2×SD16—44no—
389C2×M16—21no—
390C22×C8—21no—
391C4⋊Q8—21no—
392C4⋊Q8—44no—
393#126—22no—
394#125—22no—
395#124—22no—
396#124—21no—
397#124—22no—
398#123—22no—
399#123—22no—
400#123—22no—
401#123—21no—
402#123—22no—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8D4×C1311yescharacteristic
415C22⋊Q8C23×C1311yescharacteristic
416#121—21no—
417#121—22no—
418#121—22no—
419#121—22no—
420#121—22no—
421#121—21no—
422#121—21no—
423#121—22no—
424#121D4×C1312yes—
425#121D4×C1311yescharacteristic
426#121C23×C1312yes—
427#121C23×C1311yescharacteristic
428#120—22no—
429#120—21no—
430C4×Q8—21no—
431C4×D4—22no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—22no—
436#117D4×C1311yescharacteristic
437C2×C4⋊C4—21no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4D4×C1311yescharacteristic
440C2×C4⋊C4D4×C1311yescharacteristic
441C2×C4⋊C4C23×C1312yes—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4D4×C1312yes—
446C2×C42—21no—
447#103—24no—
448#103—22no—
449#103—22no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8C23×C1312yes—
453C22⋊C8C23×C1312yes—
454#95—24no—
455#95C23×C1312yes—
456C2×C13—22no—
457C2×C13—22no—
458C2×C13—41no—
459C2×C13—81no—
460C2×C13—82no—
461C2×C13#300911yescharacteristic
462C2×C13C2×#45611yescharacteristic
463C2×C13C2×B(4,𝔽2)11yescharacteristic
464C24—21no—
465C24C2×D4×C1311yescharacteristic
466#41—42no—
467#41—84no—
468#41—82no—
469C2×Q8—24no—
470C2×Q8—22no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—24no—
474C2×Q8—24no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—44no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—41no—
485C2×Q8—41no—
486C2×Q8C2×D4×C1311yescharacteristic
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—22no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—82no—
497C2×D4C2×D4×C1311yescharacteristic
498C2×D4C2×D4×C1312yes—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—42no—
507C22×C4—44no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4C2×D4×C1312yes—
511C22×C4C2×D4×C1311yescharacteristic
512C22×C4C2×D4×C1311yescharacteristic
513C22×C4C2×D4×C1311yescharacteristic
514C22×C4C2×D4×C1312yes—
515C22×C4C2×D4×C1311yescharacteristic
516C22×C4C2×D4×C1311yescharacteristic
517C22×C4C24×C1311yescharacteristic
518Q16—44no—
519SD16—48no—
520SD16—44no—
521M16—42no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—42no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—21no—
536C4⋊C4—48no—
537C4⋊C4C2×D4×C1312yes—
538C4⋊C4C2×D4×C1311yescharacteristic
539C4⋊C4C2×D4×C1311yescharacteristic
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—24no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—21no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—22no—
552C22⋊C4—21no—
553C22⋊C4—22no—
554C22⋊C4—21no—
555C42—22no—
556C42—21no—
557C42—42no—
558C13#1826111yescharacteristic, direct product factor, Sylow
559C23—22no—
560C23—22no—
561C23—22no—
562C23—21no—
563C23—41no—
564C23—42no—
565C23—81no—
566C23—81no—
567C23C13×#12011yescharacteristic
568C23C13×#12011yescharacteristic
569C23C22×D4×C1311yescharacteristic
570Q8—24no—
571Q8—24no—
572Q8—41no—
573Q8—42no—
574Q8—42no—
575Q8—44no—
576Q8—44no—
577Q8—42no—
578Q8—81no—
579Q8—82no—
580D4—42no—
581D4—41no—
582D4—42no—
583D4—44no—
584D4—42no—
585D4—42no—
586D4—82no—
587D4—81no—
588D4—82no—
589D4—82no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—44no—
608C2×C4—44no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—81no—
614C2×C4—82no—
615C2×C4—82no—
616C2×C4—82no—
617C2×C4C13×#12011yescharacteristic
618C2×C4C13×#12011yescharacteristic
619C2×C4C22×D4×C1311yescharacteristic
620C2×C4C22×D4×C1311yescharacteristic
621C8—42no—
622C8—42no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—44no—
631C22—41no—
632C22—42no—
633C22—41no—
634C22—42no—
635C22—41no—
636C22—42no—
637C22—162no—
638C22C13×#45612yes—
639C22C2×C13×#12011yescharacteristic
640C22C13×#57712yes—
641C4—21no—
642C4—21no—
643C4—21no—
644C4—44no—
645C4—42no—
646C4—42no—
647C4—41no—
648C4—41no—
649C4—44no—
650C4—41no—
651C4—42no—
652C4C13×B(4,𝔽2)12yes—
653C2—22no—
654C2—22no—
655C2—41no—
656C2—82no—
657C2—81no—
658C2C13×#300911yescharacteristic
659C2C2×C13×#45611yescharacteristic
660C2C2×C13×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3536C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3004C2semidirect
3. C2×C13×#448C2semidirect
4. C13×#2434C2semidirect
5. C13×#1604C2semidirect
6. C13×#1603C2semidirect
7. C13×#1507C2semidirect
8. C13×#1501C2semidirect
9. C13×#1472C2semidirect
30. C13×#451C22semidirect
34. C13×#448C22semidirect
39. C13×#395C22semidirect
43. C13×#328C22semidirect
45. C13×#327C22semidirect
46. C13×#324C22semidirect
134. #18261C13direct (N × H)
230. #3004C2×C13semidirect
231. C2×#448C2×C13semidirect
232. #2434C2×C13semidirect
233. #1604C2×C13semidirect
234. #1603C2×C13semidirect
235. #1507C2×C13semidirect
236. #1501C2×C13semidirect
237. #1472C2×C13semidirect
322. #451C22×C13semidirect
326. #448C22×C13semidirect
331. #395C22×C13semidirect
335. #328C22×C13semidirect
337. #327C22×C13semidirect
338. #324C22×C13semidirect
558. C13#18261direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35362
C13×#30042
C2×C13×#4482
C13×#24342
C13×#16042
C13×#16032
C13×#15072
C13×#15012
C13×#14722
#1826113