Finite Group Databasebeta

← C13×#24085 #15710424

Subgroups — C13×#24085 #15710424

Order 3328.

998 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3495C211yesmaximal, characteristic
2C13×#3092C211yesmaximal, characteristic
3C2×C13×#428C211yesmaximal, characteristic, complemented
4C13×#2503C211yesmaximal, characteristic, complemented
5C13×#2061C212yesmaximal, complemented
6C13×#2038C212yesmaximal, complemented
7C13×#1901C211yesmaximal, characteristic, complemented
8C13×#1871C211yesmaximal, characteristic
9C13×#1860C212yesmaximal, complemented
10C13×#1857C212yesmaximal, complemented
11C13×#1826C211yesmaximal, characteristic, complemented
12C22×C13×M16C2211yescharacteristic
13C13×#556—21no—
14C13×#554—21no—
15C13×#552—21no—
16C13×#552—22no—
17C13×#552—21no—
18C13×#551—22no—
19C13×#544C2211yescharacteristic
20C13×#542—21no—
21C13×#541—21no—
22C13×#536C2211yescharacteristic
23C13×#533—21no—
24C13×#529—21no—
25C13×#525C2211yescharacteristic
26C2×C13×C22⋊Q8C2211yescharacteristic
27C13×#520C2211yescharacteristic
28C13×#519C2211yescharacteristic
29C2×C13×#117C2211yescharacteristic
30C22×C13×C4⋊C4C2211yescharacteristic
31C13×#484—21no—
32C13×#483—21no—
33C13×#481—21no—
34C13×#480—21no—
35C13×#428—21no—
36C13×#428—21no—
37C13×#428C2212yes—
38C13×#428C2212yes—
39C13×#428C2212yes—
40C2×C13×#107—21no—
41C2×C13×#106—21no—
42C2×C13×#104C2212yes—
43C13×#417C2212yes—
44C2×C13×#101C2212yes—
45C13×#407C2211yescharacteristic
46C13×#400—22no—
47C13×#391C2212yes—
48C13×#382C2212yes—
49C13×#381—22no—
50C4×C13×C22⋊C4C2211yescharacteristic
51C13×#343C2212yes—
52C13×#339C2212yes—
53C13×#339C2212yes—
54C13×#339C2212yes—
55C2×C13×#41C2311yescharacteristic
56C22×Q8×C13C2311yescharacteristic
57C23×C4×C13—21no—
58C23×C4×C13C2311yescharacteristic
59C2×C13×M16—21no—
60C2×C13×M16—24no—
61C2×C13×M16C2312yes—
62C2×C13×M16C2312yes—
63C22×C8×C13—21no—
64C13×C4⋊Q8—21no—
65C13×C4⋊Q8—21no—
66C13×C4⋊Q8—21no—
67C13×#126—22no—
68C13×#126—22no—
69C13×#126—22no—
70C13×#126—22no—
71C13×#125—22no—
72C13×#125—22no—
73C13×#125—22no—
74C13×#125—21no—
75C13×#125—21no—
76C13×#124—22no—
77C13×#124—21no—
78C13×#123—22no—
79C13×#123—22no—
80C13×#123—21no—
81C13×#123—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—21no—
85C13×C22⋊Q8—21no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—21no—
91C13×C22⋊Q8D411yescharacteristic
92C13×C22⋊Q8D411yescharacteristic
93C13×#121D411yescharacteristic
94C13×#121D411yescharacteristic
95C13×#120—21no—
96C4×Q8×C13—22no—
97C4×Q8×C13—21no—
98C4×Q8×C13—21no—
99C4×Q8×C13—21no—
100C4×Q8×C13—21no—
101C4×Q8×C13—21no—
102C4×D4×C13—22no—
103C4×D4×C13—21no—
104C4×D4×C13—22no—
105C4×D4×C13—21no—
106C4×D4×C13—21no—
107C13×#117—22no—
108C13×#117—22no—
109C13×#117—21no—
110C13×#117—21no—
111C13×#117—22no—
112C13×#117—21no—
113C13×#117D411yescharacteristic
114C13×#117D411yescharacteristic
115C13×#117C2311yescharacteristic
116C13×#117C2311yescharacteristic
117C13×#117C2311yescharacteristic
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—21no—
121C2×C13×C4⋊C4—21no—
122C2×C13×C4⋊C4—21no—
123C2×C13×C4⋊C4—21no—
124C2×C13×C4⋊C4D412yes—
125C2×C13×C4⋊C4D411yescharacteristic
126C2×C13×C4⋊C4D411yescharacteristic
127C2×C13×C4⋊C4C2312yes—
128C2×C13×C4⋊C4C2311yescharacteristic
129C2×C13×C22⋊C4—21no—
130C2×C13×C22⋊C4—21no—
131C2×C13×C22⋊C4D412yes—
132C2×C42×C13—21no—
133C2×C42×C13C2312yes—
134C13×#107—22no—
135C13×#107—22no—
136C13×#107—22no—
137C13×#106—22no—
138C13×#106—22no—
139C13×#106—22no—
140C13×#104—24no—
141C13×#103—22no—
142C13×#102—22no—
143C13×#101—24no—
144C13×C22⋊C8—21no—
145C13×C22⋊C8—21no—
146C13×#95—21no—
147C13×#95—24no—
148C13×#95—24no—
149#24085C1311yesmaximal, characteristic, direct product factor, Sylow
150C24×C13C2×D411yescharacteristic
151C13×#41—22no—
152C13×#41—22no—
153C2×Q8×C13—22no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13—22no—
157C2×Q8×C13—22no—
158C2×Q8×C13C2×D411yescharacteristic
159C2×D4×C13—21no—
160C2×D4×C13—21no—
161C2×D4×C13—21no—
162C2×D4×C13C2×D411yescharacteristic
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—21no—
166C22×C4×C13—22no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—44no—
172C22×C4×C13—41no—
173C22×C4×C13—41no—
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D412yes—
181C22×C4×C13C2411yescharacteristic
182C13×M16—24no—
183C13×M16—22no—
184C13×M16—22no—
185C13×M16—22no—
186C13×M16#4114yes—
187C2×C8×C13—24no—
188C2×C8×C13—22no—
189C2×C8×C13—22no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—22no—
198C13×C4⋊C4—21no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—22no—
201C13×C4⋊C4—22no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—22no—
207C13×C4⋊C4—22no—
208C13×C4⋊C4—41no—
209C13×C4⋊C4—41no—
210C13×C4⋊C4C2×D411yescharacteristic
211C13×C4⋊C4C2×D411yescharacteristic
212C13×C4⋊C4C2×D411yescharacteristic
213C13×C4⋊C4C2×D411yescharacteristic
214C13×C4⋊C4C2×D411yescharacteristic
215C13×C4⋊C4C2×D411yescharacteristic
216C13×C22⋊C4—22no—
217C13×C22⋊C4—22no—
218C13×C22⋊C4—22no—
219C13×C22⋊C4—21no—
220C13×C22⋊C4—21no—
221C13×C22⋊C4—22no—
222C13×C22⋊C4—22no—
223C13×C22⋊C4—21no—
224C13×C22⋊C4—21no—
225C13×C22⋊C4—21no—
226C13×C22⋊C4—21no—
227C13×C22⋊C4—21no—
228C13×C22⋊C4—21no—
229C13×C22⋊C4—21no—
230C13×C22⋊C4—42no—
231C42×C13—22no—
232C42×C13—22no—
233C42×C13—22no—
234C42×C13—21no—
235C42×C13—21no—
236C42×C13—21no—
237C42×C13—21no—
238C42×C13—21no—
239C42×C13—22no—
240C42×C13—22no—
241#3495C2×C1311yescharacteristic
242#3092C2×C1311yescharacteristic
243C2×#428C2×C1311yescharacteristic, complemented
244#2503C2×C1311yescharacteristic, complemented
245#2061C2×C1312yescomplemented
246#2038C2×C1312yescomplemented
247#1901C2×C1311yescharacteristic, complemented
248#1871C2×C1311yescharacteristic
249#1860C2×C1312yescomplemented
250#1857C2×C1312yescomplemented
251#1826C2×C1311yescharacteristic, complemented
252C23×C13—22no—
253C23×C13—22no—
254C23×C13—21no—
255C23×C13—41no—
256C23×C13#12011yescharacteristic
257C23×C13#12011yescharacteristic
258C23×C13C22×D411yescharacteristic
259Q8×C13—22no—
260Q8×C13—41no—
261Q8×C13—41no—
262Q8×C13—42no—
263Q8×C13—82no—
264D4×C13—22no—
265D4×C13—42no—
266D4×C13—42no—
267D4×C13—81no—
268C2×C4×C13—22no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—22no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—22no—
284C2×C4×C13—24no—
285C2×C4×C13—42no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—44no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—81no—
295C2×C4×C13—82no—
296C2×C4×C13—82no—
297C2×C4×C13—82no—
298C2×C4×C13#12011yescharacteristic
299C2×C4×C13#12011yescharacteristic
300C2×C4×C13C22×D411yescharacteristic
301C2×C4×C13C22×D411yescharacteristic
302C2×C4×C13C2×#4112yes—
303C2×C4×C132−1+412yes—
304C8×C13—24no—
305C8×C13—42no—
306C22×M16C22×C1311yescharacteristic
307#556—21no—
308#554—21no—
309#552—21no—
310#552—22no—
311#552—21no—
312#551—22no—
313#544C22×C1311yescharacteristic
314#542—21no—
315#541—21no—
316#536C22×C1311yescharacteristic
317#533—21no—
318#529—21no—
319#525C22×C1311yescharacteristic
320C2×C22⋊Q8C22×C1311yescharacteristic
321#520C22×C1311yescharacteristic
322#519C22×C1311yescharacteristic
323C2×#117C22×C1311yescharacteristic
324C22×C4⋊C4C22×C1311yescharacteristic
325#484—21no—
326#483—21no—
327#481—21no—
328#480—21no—
329#428—21no—
330#428—21no—
331#428C22×C1312yes—
332#428C22×C1312yes—
333#428C22×C1312yes—
334C2×#107—21no—
335C2×#106—21no—
336C2×#104C22×C1312yes—
337#417C22×C1312yes—
338C2×#101C22×C1312yes—
339#407C22×C1311yescharacteristic
340#400—22no—
341#391C22×C1312yes—
342#382C22×C1312yes—
343#381—22no—
344C4×C22⋊C4C22×C1311yescharacteristic
345#343C22×C1312yes—
346#339C22×C1312yes—
347#339C22×C1312yes—
348#339C22×C1312yes—
349C22×C13—21no—
350C22×C13—21no—
351C22×C13—21no—
352C22×C13—21no—
353C22×C13—21no—
354C22×C13—21no—
355C22×C13—21no—
356C22×C13—44no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13—41no—
360C22×C13#45412yes—
361C22×C13C2×#12011yescharacteristic
362C22×C13#54712yes—
363C4×C13—21no—
364C4×C13—21no—
365C4×C13—42no—
366C4×C13—41no—
367C4×C13—41no—
368C4×C13—41no—
369C4×C13—41no—
370C4×C13—42no—
371C4×C13—41no—
372C4×C13—41no—
373C4×C13—41no—
374C4×C13—82no—
375C4×C13—82no—
376C4×C13#52511yescharacteristic
377C4×C13#53611yescharacteristic
378C4×C13#54712yes—
379C2×#41C23×C1311yescharacteristic
380C22×Q8C23×C1311yescharacteristic
381C23×C4—21no—
382C23×C4C23×C1311yescharacteristic
383C2×M16—21no—
384C2×M16—24no—
385C2×M16C23×C1312yes—
386C2×M16C23×C1312yes—
387C22×C8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8—21no—
391#126—22no—
392#126—22no—
393#126—22no—
394#126—22no—
395#125—22no—
396#125—22no—
397#125—22no—
398#125—21no—
399#125—21no—
400#124—22no—
401#124—21no—
402#123—22no—
403#123—22no—
404#123—21no—
405#123—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—22no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415C22⋊Q8D4×C1311yescharacteristic
416C22⋊Q8D4×C1311yescharacteristic
417#121D4×C1311yescharacteristic
418#121D4×C1311yescharacteristic
419#120—21no—
420C4×Q8—22no—
421C4×Q8—21no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×D4—22no—
427C4×D4—21no—
428C4×D4—22no—
429C4×D4—21no—
430C4×D4—21no—
431#117—22no—
432#117—22no—
433#117—21no—
434#117—21no—
435#117—22no—
436#117—21no—
437#117D4×C1311yescharacteristic
438#117D4×C1311yescharacteristic
439#117C23×C1311yescharacteristic
440#117C23×C1311yescharacteristic
441#117C23×C1311yescharacteristic
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4D4×C1312yes—
449C2×C4⋊C4D4×C1311yescharacteristic
450C2×C4⋊C4D4×C1311yescharacteristic
451C2×C4⋊C4C23×C1312yes—
452C2×C4⋊C4C23×C1311yescharacteristic
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4D4×C1312yes—
456C2×C42—21no—
457C2×C42C23×C1312yes—
458#107—22no—
459#107—22no—
460#107—22no—
461#106—22no—
462#106—22no—
463#106—22no—
464#104—24no—
465#103—22no—
466#102—22no—
467#101—24no—
468C22⋊C8—21no—
469C22⋊C8—21no—
470#95—21no—
471#95—24no—
472#95—24no—
473C2×C13—22no—
474C2×C13—22no—
475C2×C13—41no—
476C2×C13—81no—
477C2×C13#240611yescharacteristic
478C2×C13C2×#45411yescharacteristic
479C2×C13#302211yescharacteristic
480C24C2×D4×C1311yescharacteristic
481#41—22no—
482#41—22no—
483C2×Q8—22no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8C2×D4×C1311yescharacteristic
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4C2×D4×C1311yescharacteristic
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—44no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4C2×D4×C1312yes—
505C22×C4C2×D4×C1311yescharacteristic
506C22×C4C2×D4×C1311yescharacteristic
507C22×C4C2×D4×C1311yescharacteristic
508C22×C4C2×D4×C1311yescharacteristic
509C22×C4C2×D4×C1311yescharacteristic
510C22×C4C2×D4×C1312yes—
511C22×C4C24×C1311yescharacteristic
512M16—24no—
513M16—22no—
514M16—22no—
515M16—22no—
516M16C13×#4114yes—
517C2×C8—24no—
518C2×C8—22no—
519C2×C8—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4C2×D4×C1311yescharacteristic
541C4⋊C4C2×D4×C1311yescharacteristic
542C4⋊C4C2×D4×C1311yescharacteristic
543C4⋊C4C2×D4×C1311yescharacteristic
544C4⋊C4C2×D4×C1311yescharacteristic
545C4⋊C4C2×D4×C1311yescharacteristic
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—21no—
554C22⋊C4—21no—
555C22⋊C4—21no—
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—42no—
561C42—22no—
562C42—22no—
563C42—22no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—22no—
570C42—22no—
571C13#2408511yescharacteristic, direct product factor, Sylow
572C23—22no—
573C23—22no—
574C23—21no—
575C23—41no—
576C23C13×#12011yescharacteristic
577C23C13×#12011yescharacteristic
578C23C22×D4×C1311yescharacteristic
579Q8—22no—
580Q8—41no—
581Q8—41no—
582Q8—42no—
583Q8—82no—
584D4—22no—
585D4—42no—
586D4—42no—
587D4—81no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—42no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—44no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—81no—
615C2×C4—82no—
616C2×C4—82no—
617C2×C4—82no—
618C2×C4C13×#12011yescharacteristic
619C2×C4C13×#12011yescharacteristic
620C2×C4C22×D4×C1311yescharacteristic
621C2×C4C22×D4×C1311yescharacteristic
622C2×C4C2×C13×#4112yes—
623C2×C4C13×2−1+412yes—
624C8—24no—
625C8—42no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—44no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22C13×#45412yes—
638C22C2×C13×#12011yescharacteristic
639C22C13×#54712yes—
640C4—21no—
641C4—21no—
642C4—41no—
643C4—41no—
644C4—41no—
645C4—42no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4—42no—
650C4—41no—
651C4—82no—
652C4—82no—
653C4C13×#52511yescharacteristic
654C4C13×#53611yescharacteristic
655C4C13×#54712yes—
656C2—22no—
657C2—22no—
658C2—41no—
659C2—81no—
660C2C13×#240611yescharacteristic
661C2C2×C13×#45411yescharacteristic
662C2C13×#302211yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C13×#428C2semidirect
4. C13×#2503C2semidirect
5. C13×#2061C2semidirect
6. C13×#2038C2semidirect
7. C13×#1901C2semidirect
9. C13×#1860C2semidirect
10. C13×#1857C2semidirect
11. C13×#1826C2semidirect
149. #24085C13direct (N × H)
243. C2×#428C2×C13semidirect
244. #2503C2×C13semidirect
245. #2061C2×C13semidirect
246. #2038C2×C13semidirect
247. #1901C2×C13semidirect
249. #1860C2×C13semidirect
250. #1857C2×C13semidirect
251. #1826C2×C13semidirect
571. C13#24085direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34952
C13×#30922
C2×C13×#4282
C13×#25032
C13×#20612
C13×#20382
C13×#19012
C13×#18712
C13×#18602
C13×#18572
C13×#18262
#2408513