Finite Group Databasebeta

← C13×#18423 #15704762

Subgroups — C13×#18423 #15704762

Order 3328.

934 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3538C211yesmaximal, characteristic
2C13×#3195C211yesmaximal, characteristic, complemented
3C13×#3190C211yesmaximal, characteristic
4C13×#2659C211yesmaximal, characteristic, complemented
5C13×#1611C212yesmaximal, complemented
6C13×#1609C212yesmaximal, complemented
7C13×#1605C212yesmaximal, complemented
8C13×#1603C212yesmaximal, complemented
9C13×#1504C211yesmaximal, characteristic
10C2×C13×#328C211yesmaximal, characteristic, complemented
11C13×#1472C211yesmaximal, characteristic, complemented
12C13×#563—22no—
13C13×#552—21no—
14C13×#552—21no—
15C13×#551—22no—
16D4×Q8×C13—21no—
17D4×Q8×C13—21no—
18C13×#544—21no—
19C13×#544C2212yes—
20C13×#541—21no—
21C13×#539—21no—
22C13×#539C2212yes—
23C13×#536—21no—
24C13×#525C2211yescharacteristic
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C13×C22⋊Q8C2211yescharacteristic
27C2×C13×C22⋊Q8C2211yescharacteristic
28C13×#485—21no—
29C13×#483—21no—
30C13×#483C2212yes—
31C13×#483C2211yescharacteristic
32C13×#480C2211yescharacteristic
33C13×#470—22no—
34C13×#467—21no—
35C13×#465—21no—
36C13×#452—21no—
37C13×#451—21no—
38C13×#451C2212yes—
39C13×#451C2211yescharacteristic
40C13×#448C2211yescharacteristic
41C13×#407C2211yescharacteristic
42C2×C13×C22⋊C8C2211yescharacteristic
43C13×#398—21no—
44C13×#398C2212yes—
45C13×#395—21no—
46C13×#395C2212yes—
47C13×#380—22no—
48C2×C13×#95C2211yescharacteristic
49C13×#328C2212yes—
50C13×#328C2212yes—
51C13×#328C2212yes—
52C13×#327C2212yes—
53C13×#324C2212yes—
54C13×#324C2212yes—
55C2×C13×#41D411yescharacteristic
56C22×Q8×C13—21no—
57C22×Q8×C13D411yescharacteristic
58C22×Q8×C13D411yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C2×C13×Q16—22no—
63C2×C13×Q16—21no—
64C2×C13×SD16—21no—
65C2×C13×M16—21no—
66C22×C8×C13—21no—
67C13×C4⋊Q8—21no—
68C13×C4⋊Q8—22no—
69C13×C4⋊Q8—22no—
70C13×C4⋊Q8—22no—
71C13×#126—22no—
72C13×#126—22no—
73C13×#126—22no—
74C13×#126—22no—
75C13×#125—21no—
76C13×#125—22no—
77C13×#125—22no—
78C13×#125—22no—
79C13×#125—22no—
80C13×#124—22no—
81C13×#123—22no—
82C13×#123—22no—
83C13×#123—22no—
84C13×#123—21no—
85C13×#123—22no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—21no—
92C13×C22⋊Q8—21no—
93C13×C22⋊Q8—21no—
94C13×C22⋊Q8—21no—
95C13×C22⋊Q8—21no—
96C13×C22⋊Q8—21no—
97C13×C22⋊Q8—22no—
98C13×C22⋊Q8—21no—
99C13×C22⋊Q8—21no—
100C13×C22⋊Q8—21no—
101C13×C22⋊Q8—21no—
102C13×C22⋊Q8D411yescharacteristic
103C13×C22⋊Q8D412yes—
104C13×C22⋊Q8C2312yes—
105C13×C22⋊Q8C2311yescharacteristic
106C13×#121D411yescharacteristic
107C13×#121C2311yescharacteristic
108C13×#120—21no—
109C4×Q8×C13—21no—
110C4×Q8×C13—21no—
111C4×D4×C13—22no—
112C4×D4×C13—21no—
113C4×D4×C13—21no—
114C4×D4×C13—22no—
115C13×#117—21no—
116C13×#117—22no—
117C13×#117—22no—
118C13×#117D411yescharacteristic
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—21no—
121C2×C13×C4⋊C4—22no—
122C2×C13×C4⋊C4—22no—
123C2×C13×C4⋊C4D411yescharacteristic
124C2×C13×C4⋊C4D411yescharacteristic
125C2×C13×C4⋊C4C2311yescharacteristic
126C2×C13×C4⋊C4C2312yes—
127C2×C13×C22⋊C4—21no—
128C2×C13×C22⋊C4—21no—
129C2×C13×C22⋊C4D412yes—
130C13×#107—21no—
131C13×#106—21no—
132C13×#106—22no—
133C13×#103—22no—
134C13×#103—21no—
135C13×#103—21no—
136C13×#103—21no—
137C13×#103—22no—
138C13×#102—21no—
139C13×C22⋊C8—21no—
140C13×C22⋊C8—21no—
141C13×C22⋊C8C2312yes—
142C13×C22⋊C8C2311yescharacteristic
143C13×C22⋊C8C2311yescharacteristic
144C13×#95—22no—
145C13×#95—22no—
146C13×#95—21no—
147C13×#95C2312yes—
148#18423C1311yesmaximal, characteristic, direct product factor, Sylow
149C24×C13C2×D411yescharacteristic
150C13×#41—81no—
151C2×Q8×C13—22no—
152C2×Q8×C13—21no—
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13—21no—
157C2×Q8×C13—81no—
158C2×Q8×C13—81no—
159C2×Q8×C13—82no—
160C2×Q8×C13—81no—
161C2×Q8×C13C2×D412yes—
162C2×Q8×C13C2×D411yescharacteristic
163C2×D4×C13—21no—
164C2×D4×C13—21no—
165C2×D4×C13—21no—
166C2×D4×C13C2×D411yescharacteristic
167C22×C4×C13—21no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—24no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—81no—
176C22×C4×C13—81no—
177C22×C4×C13—81no—
178C22×C4×C13C2×D412yes—
179C22×C4×C13C2×D412yes—
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2×D411yescharacteristic
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2411yescharacteristic
186C13×Q16—81no—
187C13×Q16—82no—
188C13×SD16—81no—
189C13×M16—81no—
190C2×C8×C13—21no—
191C2×C8×C13—21no—
192C2×C8×C13—22no—
193C2×C8×C13—81no—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—22no—
198C13×C4⋊C4—22no—
199C13×C4⋊C4—22no—
200C13×C4⋊C4—22no—
201C13×C4⋊C4—22no—
202C13×C4⋊C4—22no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—21no—
207C13×C4⋊C4—22no—
208C13×C4⋊C4—22no—
209C13×C4⋊C4—22no—
210C13×C4⋊C4—21no—
211C13×C4⋊C4—21no—
212C13×C4⋊C4—21no—
213C13×C4⋊C4—41no—
214C13×C4⋊C4—41no—
215C13×C4⋊C4—82no—
216C13×C4⋊C4—82no—
217C13×C4⋊C4C2×D412yes—
218C13×C4⋊C4C2×D411yescharacteristic
219C13×C4⋊C4C2×D411yescharacteristic
220C13×C22⋊C4—22no—
221C13×C22⋊C4—22no—
222C13×C22⋊C4—22no—
223C13×C22⋊C4—22no—
224C13×C22⋊C4—22no—
225C13×C22⋊C4—22no—
226C13×C22⋊C4—21no—
227C13×C22⋊C4—21no—
228C13×C22⋊C4—22no—
229C13×C22⋊C4—21no—
230C13×C22⋊C4—21no—
231C13×C22⋊C4—21no—
232C13×C22⋊C4—41no—
233C13×C22⋊C4—41no—
234C42×C13—22no—
235C42×C13—22no—
236C42×C13—22no—
237C42×C13—21no—
238#3538C2×C1311yescharacteristic
239#3195C2×C1311yescharacteristic, complemented
240#3190C2×C1311yescharacteristic
241#2659C2×C1311yescharacteristic, complemented
242#1611C2×C1312yescomplemented
243#1609C2×C1312yescomplemented
244#1605C2×C1312yescomplemented
245#1603C2×C1312yescomplemented
246#1504C2×C1311yescharacteristic
247C2×#328C2×C1311yescharacteristic, complemented
248#1472C2×C1311yescharacteristic, complemented
249C23×C13—21no—
250C23×C13—21no—
251C23×C13—22no—
252C23×C13—21no—
253C23×C13—41no—
254C23×C13#12011yescharacteristic
255C23×C13#12011yescharacteristic
256C23×C13C22×D411yescharacteristic
257Q8×C13—42no—
258Q8×C13—42no—
259Q8×C13—42no—
260Q8×C13—41no—
261Q8×C13—41no—
262Q8×C13—41no—
263Q8×C13—42no—
264Q8×C13—81no—
265Q8×C13—82no—
266D4×C13—41no—
267D4×C13—41no—
268D4×C13—41no—
269D4×C13—42no—
270D4×C13—81no—
271C2×C4×C13—24no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—21no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—42no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—81no—
298C2×C4×C13—84no—
299C2×C4×C13—82no—
300C2×C4×C13#12011yescharacteristic
301C2×C4×C13#12011yescharacteristic
302C2×C4×C13C22×D411yescharacteristic
303C2×C4×C13C22×D411yescharacteristic
304C8×C13—41no—
305C8×C13—41no—
306C8×C13—42no—
307#563—22no—
308#552—21no—
309#552—21no—
310#551—22no—
311D4×Q8—21no—
312D4×Q8—21no—
313#544—21no—
314#544C22×C1312yes—
315#541—21no—
316#539—21no—
317#539C22×C1312yes—
318#536—21no—
319#525C22×C1311yescharacteristic
320C2×C22⋊Q8C22×C1311yescharacteristic
321C2×C22⋊Q8C22×C1311yescharacteristic
322C2×C22⋊Q8C22×C1311yescharacteristic
323#485—21no—
324#483—21no—
325#483C22×C1312yes—
326#483C22×C1311yescharacteristic
327#480C22×C1311yescharacteristic
328#470—22no—
329#467—21no—
330#465—21no—
331#452—21no—
332#451—21no—
333#451C22×C1312yes—
334#451C22×C1311yescharacteristic
335#448C22×C1311yescharacteristic
336#407C22×C1311yescharacteristic
337C2×C22⋊C8C22×C1311yescharacteristic
338#398—21no—
339#398C22×C1312yes—
340#395—21no—
341#395C22×C1312yes—
342#380—22no—
343C2×#95C22×C1311yescharacteristic
344#328C22×C1312yes—
345#328C22×C1312yes—
346#328C22×C1312yes—
347#327C22×C1312yes—
348#324C22×C1312yes—
349#324C22×C1312yes—
350C22×C13—21no—
351C22×C13—21no—
352C22×C13—21no—
353C22×C13—21no—
354C22×C13—21no—
355C22×C13—21no—
356C22×C13—21no—
357C22×C13—42no—
358C22×C13—42no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13#45612yes—
363C22×C13C2×#12011yescharacteristic
364C22×C13#57711yescharacteristic
365C22×C13#57811yescharacteristic
366C4×C13—21no—
367C4×C13—21no—
368C4×C13—21no—
369C4×C13—21no—
370C4×C13—44no—
371C4×C13—42no—
372C4×C13—41no—
373C4×C13—42no—
374C4×C13—41no—
375C4×C13—41no—
376C4×C13—42no—
377C4×C13—42no—
378C4×C13—81no—
379C4×C13—81no—
380C2×#41D4×C1311yescharacteristic
381C22×Q8—21no—
382C22×Q8D4×C1311yescharacteristic
383C22×Q8D4×C1311yescharacteristic
384C22×Q8C23×C1311yescharacteristic
385C23×C4—21no—
386C23×C4C23×C1311yescharacteristic
387C2×Q16—22no—
388C2×Q16—21no—
389C2×SD16—21no—
390C2×M16—21no—
391C22×C8—21no—
392C4⋊Q8—21no—
393C4⋊Q8—22no—
394C4⋊Q8—22no—
395C4⋊Q8—22no—
396#126—22no—
397#126—22no—
398#126—22no—
399#126—22no—
400#125—21no—
401#125—22no—
402#125—22no—
403#125—22no—
404#125—22no—
405#124—22no—
406#123—22no—
407#123—22no—
408#123—22no—
409#123—21no—
410#123—22no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—22no—
423C22⋊Q8—21no—
424C22⋊Q8—21no—
425C22⋊Q8—21no—
426C22⋊Q8—21no—
427C22⋊Q8D4×C1312yes—
428C22⋊Q8D4×C1311yescharacteristic
429C22⋊Q8C23×C1312yes—
430C22⋊Q8C23×C1311yescharacteristic
431#121D4×C1311yescharacteristic
432#121C23×C1311yescharacteristic
433#120—21no—
434C4×Q8—21no—
435C4×Q8—21no—
436C4×D4—22no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—22no—
440#117—21no—
441#117—22no—
442#117—22no—
443#117D4×C1311yescharacteristic
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4D4×C1311yescharacteristic
449C2×C4⋊C4D4×C1311yescharacteristic
450C2×C4⋊C4C23×C1311yescharacteristic
451C2×C4⋊C4C23×C1312yes—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4D4×C1312yes—
455#107—21no—
456#106—21no—
457#106—22no—
458#103—22no—
459#103—21no—
460#103—21no—
461#103—21no—
462#103—22no—
463#102—21no—
464C22⋊C8—21no—
465C22⋊C8—21no—
466C22⋊C8C23×C1312yes—
467C22⋊C8C23×C1311yescharacteristic
468C22⋊C8C23×C1311yescharacteristic
469#95—21no—
470#95—22no—
471#95—22no—
472#95C23×C1312yes—
473C2×C13—21no—
474C2×C13—21no—
475C2×C13—22no—
476C2×C13—41no—
477C2×C13—81no—
478C2×C13#301311yescharacteristic
479C2×C13C2×#45611yescharacteristic
480C2×C13#302611yescharacteristic
481C24C2×D4×C1311yescharacteristic
482#41—81no—
483C2×Q8—22no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—81no—
490C2×Q8—81no—
491C2×Q8—82no—
492C2×Q8—81no—
493C2×Q8C2×D4×C1312yes—
494C2×Q8C2×D4×C1311yescharacteristic
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4C2×D4×C1311yescharacteristic
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—81no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4C2×D4×C1312yes—
511C22×C4C2×D4×C1312yes—
512C22×C4C2×D4×C1311yescharacteristic
513C22×C4C2×D4×C1311yescharacteristic
514C22×C4C2×D4×C1311yescharacteristic
515C22×C4C2×D4×C1311yescharacteristic
516C22×C4C2×D4×C1311yescharacteristic
517C22×C4C24×C1311yescharacteristic
518Q16—81no—
519Q16—82no—
520SD16—81no—
521M16—81no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—22no—
525C2×C8—81no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—82no—
548C4⋊C4—82no—
549C4⋊C4C2×D4×C1312yes—
550C4⋊C4C2×D4×C1311yescharacteristic
551C4⋊C4C2×D4×C1311yescharacteristic
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—22no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C42—22no—
567C42—22no—
568C42—22no—
569C42—21no—
570C13#1842311yescharacteristic, direct product factor, Sylow
571C23—22no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—41no—
576C23C13×#12011yescharacteristic
577C23C13×#12011yescharacteristic
578C23C22×D4×C1311yescharacteristic
579Q8—42no—
580Q8—41no—
581Q8—42no—
582Q8—42no—
583Q8—41no—
584Q8—41no—
585Q8—42no—
586Q8—81no—
587Q8—82no—
588D4—41no—
589D4—42no—
590D4—41no—
591D4—41no—
592D4—81no—
593C2×C4—24no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—81no—
620C2×C4—84no—
621C2×C4—82no—
622C2×C4C13×#12011yescharacteristic
623C2×C4C13×#12011yescharacteristic
624C2×C4C22×D4×C1311yescharacteristic
625C2×C4C22×D4×C1311yescharacteristic
626C8—41no—
627C8—41no—
628C8—42no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—21no—
636C22—42no—
637C22—42no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C13×#45612yes—
642C22C2×C13×#12011yescharacteristic
643C22C13×#57711yescharacteristic
644C22C13×#57811yescharacteristic
645C4—21no—
646C4—21no—
647C4—21no—
648C4—21no—
649C4—44no—
650C4—42no—
651C4—41no—
652C4—42no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—42no—
657C4—81no—
658C4—81no—
659C2—21no—
660C2—22no—
661C2—21no—
662C2—41no—
663C2—81no—
664C2C13×#301311yescharacteristic
665C2C2×C13×#45611yescharacteristic
666C2C13×#302611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#525C22
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×#3195C2semidirect
4. C13×#2659C2semidirect
5. C13×#1611C2semidirect
6. C13×#1609C2semidirect
7. C13×#1605C2semidirect
8. C13×#1603C2semidirect
10. C2×C13×#328C2semidirect
11. C13×#1472C2semidirect
148. #18423C13direct (N × H)
239. #3195C2×C13semidirect
241. #2659C2×C13semidirect
242. #1611C2×C13semidirect
243. #1609C2×C13semidirect
244. #1605C2×C13semidirect
245. #1603C2×C13semidirect
247. C2×#328C2×C13semidirect
248. #1472C2×C13semidirect
570. C13#18423direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35382
C13×#31952
C13×#31902
C13×#26592
C13×#16112
C13×#16092
C13×#16052
C13×#16032
C13×#15042
C2×C13×#3282
C13×#14722
#1842313