Finite Group Databasebeta

← C13×#62153 #15748492

Subgroups — C13×#62153 #15748492

Order 3328.

1696 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3518C211yesmaximal, characteristic
2Q8×C13×#41C211yesmaximal, characteristic, complemented
3Q8×C13×Q16C211yesmaximal, characteristic, complemented
4Q8×C13×SD16C211yesmaximal, characteristic, complemented
5C13×#3363C211yesmaximal, characteristic, complemented
6C13×#3359C211yesmaximal, characteristic, complemented
7C13×#3357C213yesmaximal, complemented
8C13×#3356C213yesmaximal, complemented
9C13×#3329C213yesmaximal, complemented
10C13×#3328C213yesmaximal, complemented
11C13×#3252C213yesmaximal, complemented
12C13×#3231C213yesmaximal, complemented
13C13×#3108C213yesmaximal, complemented
14C13×#3078C213yesmaximal, complemented
15C13×#2991C211yesmaximal, characteristic, complemented
16Q82×C13C2211yescharacteristic
17Q82×C13C2211yescharacteristic
18C13×#557—21no—
19C13×#557C2211yescharacteristic
20C13×#556—23no—
21C13×#556C2213yes—
22C13×#555C2213yes—
23C13×#554—23no—
24C13×#554C2213yes—
25D4×Q8×C13C2213yes—
26D4×Q8×C13C2211yescharacteristic
27C13×#548—21no—
28C13×#542—23no—
29C13×#533—23no—
30C13×#533C2213yes—
31C13×#533C2213yes—
32C13×#529C2213yes—
33C13×#519—21no—
34C4×C13×#41—21no—
35C4×C13×#41C2211yescharacteristic
36C2×C4×Q8×C13C2213yes—
37C13×#500C2213yes—
38C13×#498C2213yes—
39C13×#487C2213yes—
40C13×#487C2213yes—
41C13×#485C2216yes—
42C13×#485C2216yes—
43C13×#483C2213yes—
44C13×#480C2213yes—
45C13×#479C2213yes—
46C13×#479C2216yes—
47C13×#479C2213yes—
48C13×#477C2213yes—
49C13×#477C2213yes—
50C13×#477C2213yes—
51C13×#476C2213yes—
52C13×#475C2213yes—
53C13×#475C2213yes—
54C13×#470C2216yes—
55C13×#468C2216yes—
56C13×#464C2211yescharacteristic
57C13×#464C2213yes—
58C13×#462C2213yes—
59C13×#461C2213yes—
60C13×#451C2213yes—
61C13×#448C2213yes—
62C8×Q8×C13C2211yescharacteristic
63C8×Q8×C13C2211yescharacteristic
64C4×C13×Q16C2213yes—
65C4×C13×Q16C2213yes—
66C4×C13×SD16C2213yes—
67C4×C13×SD16C2213yes—
68C13×#436C2213yes—
69C13×#436C2213yes—
70C13×#431C2213yes—
71C13×#428C2216yes—
72C13×#423C2213yes—
73C13×#419C2216yes—
74C2×C13×#41D411yescharacteristic
75C22×Q8×C13—21no—
76C22×Q8×C13C2313yes—
77C2×C13×Q16C2311yescharacteristic
78C2×C13×Q16C2313yes—
79C2×C13×SD16C2311yescharacteristic
80C2×C13×SD16C2313yes—
81C2×C13×M16C2316yes—
82C13×C4⋊Q8—23no—
83C13×C4⋊Q8—23no—
84C13×C4⋊Q8—23no—
85C13×C4⋊Q8C2313yes—
86C13×C4⋊Q8C2313yes—
87C13×C4⋊Q8C2313yes—
88C13×C4⋊Q8C2313yes—
89C13×#126—26no—
90C13×#126—23no—
91C13×#125—23no—
92C13×#125—23no—
93C13×#125—23no—
94C13×#125C2313yes—
95C13×#124—23no—
96C13×#124—26no—
97C13×#124C2311yescharacteristic
98C13×#123—23no—
99C13×C22⋊Q8—23no—
100C13×C22⋊Q8—23no—
101C13×C22⋊Q8—23no—
102C13×C22⋊Q8—23no—
103C13×C22⋊Q8—26no—
104C13×C22⋊Q8—26no—
105C13×C22⋊Q8C2313yes—
106C13×C22⋊Q8C2316yes—
107C13×#121—23no—
108C13×#121C2313yes—
109C4×Q8×C13—21no—
110C4×Q8×C13—21no—
111C4×Q8×C13—21no—
112C4×Q8×C13—23no—
113C4×Q8×C13—23no—
114C4×Q8×C13—23no—
115C4×Q8×C13—23no—
116C4×Q8×C13—23no—
117C4×Q8×C13—23no—
118C4×Q8×C13D411yescharacteristic
119C4×Q8×C13C2313yes—
120C4×Q8×C13C2313yes—
121C4×Q8×C13C2313yes—
122C4×Q8×C13C2311yescharacteristic
123C4×Q8×C13C2313yes—
124C4×Q8×C13C2311yescharacteristic
125C4×D4×C13—23no—
126C4×D4×C13—23no—
127C4×D4×C13—23no—
128C4×D4×C13D413yes—
129C4×D4×C13C2313yes—
130C4×D4×C13C2313yes—
131C13×#117—23no—
132C13×#117—23no—
133C13×#117—23no—
134C13×#117D413yes—
135C13×#117C2316yes—
136C2×C13×C4⋊C4—23no—
137C2×C13×C4⋊C4C2313yes—
138C2×C42×C13—23no—
139C2×C42×C13C2313yes—
140C13×#107C2313yes—
141C13×#107C2316yes—
142C13×#107C2313yes—
143C13×#106C2313yes—
144C13×#106C2316yes—
145C13×#106C2313yes—
146C13×C4⋊C8C2313yes—
147C13×C4⋊C8C2313yes—
148C13×C4⋊C8C2313yes—
149C13×C4⋊C8C2311yescharacteristic
150C13×#103C2313yes—
151C13×#103C2313yes—
152C13×#103C2316yes—
153C13×#103C2316yes—
154C13×#103C2313yes—
155C13×#103C2311yescharacteristic
156C13×#103C2313yes—
157C13×#103C2313yes—
158C13×#102C2311yescharacteristic
159C13×#102C2313yes—
160C13×C22⋊C8C2313yes—
161C13×C22⋊C8C2313yes—
162C4×C8×C13C2313yes—
163C4×C8×C13C2313yes—
164#62153C1311yesmaximal, characteristic, direct product factor, Sylow
165C13×#41—24no—
166C2×Q8×C13—23no—
167C2×Q8×C13—23no—
168C2×Q8×C13—23no—
169C2×Q8×C13—23no—
170C2×Q8×C13—26no—
171C2×Q8×C13—43no—
172C2×Q8×C13—44no—
173C2×Q8×C13C2×D411yescharacteristic
174C2×Q8×C13C2413yes—
175C2×Q8×C13C2411yescharacteristic
176C2×Q8×C13C2411yescharacteristic
177C2×D4×C13—23no—
178C2×D4×C13C2×D413yes—
179C2×D4×C13C2411yescharacteristic
180C22×C4×C13—23no—
181C22×C4×C13—23no—
182C22×C4×C13—23no—
183C22×C4×C13C2×D413yes—
184C22×C4×C13C2×D413yes—
185C22×C4×C13C2413yes—
186C13×Q16—22no—
187C13×Q16—43no—
188C13×SD16—22no—
189C13×SD16—43no—
190C13×M16—46no—
191C2×C8×C13C2411yescharacteristic
192C2×C8×C13C2411yescharacteristic
193C2×C8×C13C2413yes—
194C2×C8×C13C2413yes—
195C13×C4⋊C4—21no—
196C13×C4⋊C4—23no—
197C13×C4⋊C4—23no—
198C13×C4⋊C4—23no—
199C13×C4⋊C4—23no—
200C13×C4⋊C4—23no—
201C13×C4⋊C4—23no—
202C13×C4⋊C4—23no—
203C13×C4⋊C4—23no—
204C13×C4⋊C4—23no—
205C13×C4⋊C4—23no—
206C13×C4⋊C4—23no—
207C13×C4⋊C4—23no—
208C13×C4⋊C4—26no—
209C13×C4⋊C4—23no—
210C13×C4⋊C4C2×D413yes—
211C13×C4⋊C4C2×D413yes—
212C13×C4⋊C4C2411yescharacteristic
213C13×C4⋊C4C2413yes—
214C13×C4⋊C4C2413yes—
215C13×C4⋊C4C2413yes—
216C13×C22⋊C4—26no—
217C13×C22⋊C4—26no—
218C13×C22⋊C4—23no—
219C13×C22⋊C4—23no—
220C13×C22⋊C4—21no—
221C13×C22⋊C4—21no—
222C13×C22⋊C4—23no—
223C13×C22⋊C4C2×D416yes—
224C42×C13—21no—
225C42×C13—23no—
226C42×C13—23no—
227C42×C13—23no—
228C42×C13—26no—
229C42×C13—23no—
230C42×C13C2×D413yes—
231C42×C13C2×D413yes—
232C42×C13C2413yes—
233C42×C13C2411yescharacteristic
234#3518C2×C1311yescharacteristic
235Q8×#41C2×C1311yescharacteristic, complemented
236Q8×Q16C2×C1311yescharacteristic, complemented
237Q8×SD16C2×C1311yescharacteristic, complemented
238#3363C2×C1311yescharacteristic, complemented
239#3359C2×C1311yescharacteristic, complemented
240#3357C2×C1313yescomplemented
241#3356C2×C1313yescomplemented
242#3329C2×C1313yescomplemented
243#3328C2×C1313yescomplemented
244#3252C2×C1313yescomplemented
245#3231C2×C1313yescomplemented
246#3108C2×C1313yescomplemented
247#3078C2×C1313yescomplemented
248#2991C2×C1311yescharacteristic, complemented
249C23×C13—21no—
250C23×C13C22×D413yes—
251Q8×C13—21no—
252Q8×C13—21no—
253Q8×C13—23no—
254Q8×C13—23no—
255Q8×C13—21no—
256Q8×C13—46no—
257Q8×C13—46no—
258Q8×C13—83no—
259Q8×C13—83no—
260Q8×C13#13714yes—
261Q8×C132−1+412yes—
262D4×C13—26no—
263D4×C13—21no—
264D4×C13—21no—
265D4×C13—83no—
266C2×C4×C13—21no—
267C2×C4×C13—26no—
268C2×C4×C13—23no—
269C2×C4×C13—23no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—23no—
273C2×C4×C13—23no—
274C2×C4×C13—23no—
275C2×C4×C13—23no—
276C2×C4×C13—43no—
277C2×C4×C13—46no—
278C2×C4×C13—46no—
279C2×C4×C13—83no—
280C2×C4×C13C22×D411yescharacteristic
281C2×C4×C13C22×D413yes—
282C2×C4×C13C22×D411yescharacteristic
283C2×C4×C13C22×D413yes—
284C2×C4×C13C22×D413yes—
285C2×C4×C13C2511yescharacteristic
286C8×C13—21no—
287C8×C13—21no—
288C8×C13—23no—
289C8×C13—23no—
290Q82C22×C1311yescharacteristic
291Q82C22×C1311yescharacteristic
292#557—21no—
293#557C22×C1311yescharacteristic
294#556—23no—
295#556C22×C1313yes—
296#555C22×C1313yes—
297#554—23no—
298#554C22×C1313yes—
299D4×Q8C22×C1313yes—
300D4×Q8C22×C1311yescharacteristic
301#548—21no—
302#542—23no—
303#533—23no—
304#533C22×C1313yes—
305#533C22×C1313yes—
306#529C22×C1313yes—
307#519—21no—
308C4×#41—21no—
309C4×#41C22×C1311yescharacteristic
310C2×C4×Q8C22×C1313yes—
311#500C22×C1313yes—
312#498C22×C1313yes—
313#487C22×C1313yes—
314#487C22×C1313yes—
315#485C22×C1316yes—
316#485C22×C1316yes—
317#483C22×C1313yes—
318#480C22×C1313yes—
319#479C22×C1313yes—
320#479C22×C1316yes—
321#479C22×C1313yes—
322#477C22×C1313yes—
323#477C22×C1313yes—
324#477C22×C1313yes—
325#476C22×C1313yes—
326#475C22×C1313yes—
327#475C22×C1313yes—
328#470C22×C1316yes—
329#468C22×C1316yes—
330#464C22×C1311yescharacteristic
331#464C22×C1313yes—
332#462C22×C1313yes—
333#461C22×C1313yes—
334#451C22×C1313yes—
335#448C22×C1313yes—
336C8×Q8C22×C1311yescharacteristic
337C8×Q8C22×C1311yescharacteristic
338C4×Q16C22×C1313yes—
339C4×Q16C22×C1313yes—
340C4×SD16C22×C1313yes—
341C4×SD16C22×C1313yes—
342#436C22×C1313yes—
343#436C22×C1313yes—
344#431C22×C1313yes—
345#428C22×C1316yes—
346#423C22×C1313yes—
347#419C22×C1316yes—
348C22×C13—23no—
349C22×C13—23no—
350C22×C13—23no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13—41no—
354C22×C13C23×D411yescharacteristic
355C4×C13—21no—
356C4×C13—23no—
357C4×C13—23no—
358C4×C13—22no—
359C4×C13—21no—
360C4×C13—41no—
361C4×C13—43no—
362C4×C13—43no—
363C4×C13—43no—
364C4×C13—41no—
365C4×C13—43no—
366C4×C13C2×#13716yes—
367C4×C13C2×2−1+411yescharacteristic
368C4×C13#58511yescharacteristic
369C2×#41D4×C1311yescharacteristic
370C22×Q8—21no—
371C22×Q8C23×C1313yes—
372C2×Q16C23×C1311yescharacteristic
373C2×Q16C23×C1313yes—
374C2×SD16C23×C1311yescharacteristic
375C2×SD16C23×C1313yes—
376C2×M16C23×C1316yes—
377C4⋊Q8—23no—
378C4⋊Q8—23no—
379C4⋊Q8—23no—
380C4⋊Q8C23×C1313yes—
381C4⋊Q8C23×C1313yes—
382C4⋊Q8C23×C1313yes—
383C4⋊Q8C23×C1313yes—
384#126—26no—
385#126—23no—
386#125—23no—
387#125—23no—
388#125—23no—
389#125C23×C1313yes—
390#124—23no—
391#124—26no—
392#124C23×C1311yescharacteristic
393#123—23no—
394C22⋊Q8—23no—
395C22⋊Q8—23no—
396C22⋊Q8—23no—
397C22⋊Q8—23no—
398C22⋊Q8—26no—
399C22⋊Q8—26no—
400C22⋊Q8C23×C1313yes—
401C22⋊Q8C23×C1316yes—
402#121—23no—
403#121C23×C1313yes—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—23no—
408C4×Q8—23no—
409C4×Q8—23no—
410C4×Q8—23no—
411C4×Q8—23no—
412C4×Q8—23no—
413C4×Q8D4×C1311yescharacteristic
414C4×Q8C23×C1311yescharacteristic
415C4×Q8C23×C1313yes—
416C4×Q8C23×C1313yes—
417C4×Q8C23×C1313yes—
418C4×Q8C23×C1313yes—
419C4×Q8C23×C1311yescharacteristic
420C4×D4—23no—
421C4×D4—23no—
422C4×D4—23no—
423C4×D4D4×C1313yes—
424C4×D4C23×C1313yes—
425C4×D4C23×C1313yes—
426#117—23no—
427#117—23no—
428#117—23no—
429#117D4×C1313yes—
430#117C23×C1316yes—
431C2×C4⋊C4—23no—
432C2×C4⋊C4C23×C1313yes—
433C2×C42—23no—
434C2×C42C23×C1313yes—
435#107C23×C1313yes—
436#107C23×C1316yes—
437#107C23×C1313yes—
438#106C23×C1313yes—
439#106C23×C1316yes—
440#106C23×C1313yes—
441C4⋊C8C23×C1313yes—
442C4⋊C8C23×C1313yes—
443C4⋊C8C23×C1313yes—
444C4⋊C8C23×C1311yescharacteristic
445#103C23×C1313yes—
446#103C23×C1313yes—
447#103C23×C1316yes—
448#103C23×C1316yes—
449#103C23×C1313yes—
450#103C23×C1311yescharacteristic
451#103C23×C1313yes—
452#103C23×C1313yes—
453#102C23×C1311yescharacteristic
454#102C23×C1313yes—
455C22⋊C8C23×C1313yes—
456C22⋊C8C23×C1313yes—
457C4×C8C23×C1313yes—
458C4×C8C23×C1313yes—
459C2×C13—43no—
460C2×C13—81no—
461C2×C13#348911yescharacteristic
462C2×C13C22×#13711yescharacteristic
463C2×C13#358411yescharacteristic
464#41—24no—
465C2×Q8—23no—
466C2×Q8—23no—
467C2×Q8—23no—
468C2×Q8—23no—
469C2×Q8—26no—
470C2×Q8—43no—
471C2×Q8—44no—
472C2×Q8C2×D4×C1311yescharacteristic
473C2×Q8C24×C1313yes—
474C2×Q8C24×C1311yescharacteristic
475C2×Q8C24×C1311yescharacteristic
476C2×D4—23no—
477C2×D4C2×D4×C1313yes—
478C2×D4C24×C1311yescharacteristic
479C22×C4—23no—
480C22×C4—23no—
481C22×C4—23no—
482C22×C4C2×D4×C1313yes—
483C22×C4C2×D4×C1313yes—
484C22×C4C24×C1313yes—
485Q16—22no—
486Q16—43no—
487SD16—22no—
488SD16—43no—
489M16—46no—
490C2×C8C24×C1311yescharacteristic
491C2×C8C24×C1311yescharacteristic
492C2×C8C24×C1313yes—
493C2×C8C24×C1313yes—
494C4⋊C4—21no—
495C4⋊C4—23no—
496C4⋊C4—23no—
497C4⋊C4—23no—
498C4⋊C4—23no—
499C4⋊C4—23no—
500C4⋊C4—23no—
501C4⋊C4—23no—
502C4⋊C4—23no—
503C4⋊C4—23no—
504C4⋊C4—23no—
505C4⋊C4—23no—
506C4⋊C4—23no—
507C4⋊C4—26no—
508C4⋊C4—23no—
509C4⋊C4C2×D4×C1313yes—
510C4⋊C4C2×D4×C1313yes—
511C4⋊C4C24×C1311yescharacteristic
512C4⋊C4C24×C1313yes—
513C4⋊C4C24×C1313yes—
514C4⋊C4C24×C1313yes—
515C22⋊C4—26no—
516C22⋊C4—26no—
517C22⋊C4—23no—
518C22⋊C4—23no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—23no—
522C22⋊C4C2×D4×C1316yes—
523C42—21no—
524C42—23no—
525C42—23no—
526C42—23no—
527C42—26no—
528C42—23no—
529C42C2×D4×C1313yes—
530C42C2×D4×C1313yes—
531C42C24×C1313yes—
532C42C24×C1311yescharacteristic
533C13#6215311yescharacteristic, direct product factor, Sylow
534C23—21no—
535C23C22×D4×C1313yes—
536Q8—21no—
537Q8—21no—
538Q8—23no—
539Q8—23no—
540Q8—21no—
541Q8—46no—
542Q8—46no—
543Q8—83no—
544Q8—83no—
545Q8C13×#13714yes—
546Q8C13×2−1+412yes—
547D4—26no—
548D4—21no—
549D4—21no—
550D4—83no—
551C2×C4—21no—
552C2×C4—26no—
553C2×C4—23no—
554C2×C4—23no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—23no—
558C2×C4—23no—
559C2×C4—23no—
560C2×C4—23no—
561C2×C4—43no—
562C2×C4—46no—
563C2×C4—46no—
564C2×C4—83no—
565C2×C4C22×D4×C1311yescharacteristic
566C2×C4C22×D4×C1313yes—
567C2×C4C22×D4×C1311yescharacteristic
568C2×C4C22×D4×C1313yes—
569C2×C4C22×D4×C1313yes—
570C2×C4C25×C1311yescharacteristic
571C8—21no—
572C8—21no—
573C8—23no—
574C8—23no—
575C22—23no—
576C22—23no—
577C22—23no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22C23×D4×C1311yescharacteristic
582C4—21no—
583C4—21no—
584C4—23no—
585C4—23no—
586C4—22no—
587C4—43no—
588C4—41no—
589C4—43no—
590C4—43no—
591C4—43no—
592C4—41no—
593C4C2×C13×#13716yes—
594C4C2×C13×2−1+411yescharacteristic
595C4C13×#58511yescharacteristic
596C2—43no—
597C2—81no—
598C2C13×#348911yescharacteristic
599C2C22×C13×#13711yescharacteristic
600C2C13×#358411yescharacteristic
subgroupG/H
center, socleC22×C13C23×D4
commutator, Frattini, cosocleC2×C4C25×C13
prime radicalC13×#3518C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. Q8×C13×#41C2semidirect
3. Q8×C13×Q16C2semidirect
4. Q8×C13×SD16C2semidirect
5. C13×#3363C2semidirect
6. C13×#3359C2semidirect
7. C13×#3357C2semidirect
8. C13×#3356C2semidirect
9. C13×#3329C2semidirect
10. C13×#3328C2semidirect
11. C13×#3252C2semidirect
12. C13×#3231C2semidirect
13. C13×#3108C2semidirect
14. C13×#3078C2semidirect
15. C13×#2991C2semidirect
164. #62153C13direct (N × H)
235. Q8×#41C2×C13semidirect
236. Q8×Q16C2×C13semidirect
237. Q8×SD16C2×C13semidirect
238. #3363C2×C13semidirect
239. #3359C2×C13semidirect
240. #3357C2×C13semidirect
241. #3356C2×C13semidirect
242. #3329C2×C13semidirect
243. #3328C2×C13semidirect
244. #3252C2×C13semidirect
245. #3231C2×C13semidirect
246. #3108C2×C13semidirect
247. #3078C2×C13semidirect
248. #2991C2×C13semidirect
533. C13#62153direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35182
Q8×C13×#412
Q8×C13×Q162
Q8×C13×SD162
C13×#33632
C13×#33592
C13×#33572
C13×#33562
C13×#33292
C13×#33282
C13×#32522
C13×#32312
C13×#31082
C13×#30782
C13×#29912
#6215313