Finite Group Databasebeta

← C13×#19025 #15705364

Subgroups — C13×#19025 #15705364

Order 3328.

872 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3561C211yesmaximal, characteristic
2C13×#3237C211yesmaximal, characteristic, complemented
3C13×#3172C211yesmaximal, characteristic, complemented
4C13×#3140C211yesmaximal, characteristic, complemented
5C13×#1664C212yesmaximal, complemented
6C13×#1664C212yesmaximal, complemented
7C13×#1662C212yesmaximal, complemented
8C13×#1661C212yesmaximal, complemented
9C13×#1529C211yesmaximal, characteristic, complemented
10C13×#1527C211yesmaximal, characteristic, complemented
11C13×#1526C211yesmaximal, characteristic, complemented
12C13×#563C2212yes—
13C13×#562C2212yes—
14C13×#556—21no—
15C13×#551—22no—
16D4×Q8×C13—21no—
17C13×#548—21no—
18C13×#546—21no—
19C13×#543—21no—
20C13×#542—21no—
21C13×#542—22no—
22C13×#538—21no—
23C13×#536—21no—
24C13×#533C2211yescharacteristic
25C13×#533C2211yescharacteristic
26C13×#529C2211yescharacteristic
27C2×C13×#124C2211yescharacteristic
28C13×#501C2211yescharacteristic, complemented
29C13×#501C2212yescomplemented
30C13×#497C2211yescharacteristic, complemented
31C13×#491C2211yescharacteristic, complemented
32C13×#491C2212yescomplemented
33C13×#489C2212yes—
34C13×#489C2212yes—
35C13×#489C2211yescharacteristic, complemented
36C13×#488—22no—
37C13×#485—22no—
38C13×#477—21no—
39C13×#475—21no—
40C13×#470—21no—
41C13×#468—21no—
42C4×C13×Q16—21no—
43C4×C13×SD16—21no—
44C13×#432C2211yescharacteristic
45C13×#419—21no—
46C13×#418—21no—
47C4×C13×M16C2211yescharacteristic
48C4×C13×M16C2211yescharacteristic
49C13×#330C2212yescomplemented
50C13×#330C2212yescomplemented
51C13×#330C2212yescomplemented
52C13×#329C2212yes—
53C13×#329C2212yes—
54C13×#329C2212yescomplemented
55C2×C13×#41—21no—
56C22×Q8×C13—21no—
57C22×Q8×C13D411yescharacteristic
58C22×D4×C13D411yescharacteristic
59C2×C13×Q16—21no—
60C2×C13×SD16—21no—
61C2×C13×M16—21no—
62C2×C13×M16—21no—
63C13×C4⋊Q8—21no—
64C13×C4⋊Q8—22no—
65C13×C4⋊Q8D411yescharacteristic
66C13×C4⋊Q8D411yescharacteristic
67C13×C4⋊Q8C2311yescharacteristic
68C13×C4⋊Q8C2311yescharacteristic
69C13×#126—22no—
70C13×#126—22no—
71C13×#126—22no—
72C13×#126—21no—
73C13×#125—21no—
74C13×#125C2311yescharacteristic
75C13×#125C2312yes—
76C13×#124—21no—
77C13×#124—22no—
78C13×#124—22no—
79C13×#124—21no—
80C13×#124—21no—
81C13×#124D412yes—
82C13×#124C2312yes—
83C13×#124C2311yescharacteristic
84C13×#123—22no—
85C13×#123—22no—
86C13×#123—21no—
87C13×#123—22no—
88C13×#123—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—21no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8—21no—
96C13×C22⋊Q8—21no—
97C13×C22⋊Q8—22no—
98C13×C22⋊Q8—22no—
99C13×C22⋊Q8—21no—
100C13×C22⋊Q8—21no—
101C13×C22⋊Q8D411yescharacteristic
102C13×#121—21no—
103C13×#121—22no—
104C13×#121—22no—
105C13×#121D411yescharacteristic
106C13×#120—22no—
107C4×Q8×C13—21no—
108C4×Q8×C13—21no—
109C4×Q8×C13—21no—
110C4×Q8×C13—21no—
111C4×Q8×C13—21no—
112C4×Q8×C13D411yescharacteristic
113C4×D4×C13—22no—
114C4×D4×C13—21no—
115C4×D4×C13—22no—
116C4×D4×C13—21no—
117C4×D4×C13D411yescharacteristic
118C13×#117—22no—
119C13×#117—21no—
120C13×#117—21no—
121C13×#117D412yes—
122C2×C13×C22⋊C4—22no—
123C2×C13×C22⋊C4—21no—
124C2×C13×C22⋊C4—21no—
125C2×C42×C13C2311yescharacteristic
126C13×#107—21no—
127C13×#107—22no—
128C13×#106—21no—
129C13×#106—22no—
130C13×C4⋊C8—21no—
131C13×#103—22no—
132C13×#103—22no—
133C13×#103—21no—
134C13×#103—21no—
135C13×#103—21no—
136C13×#103—22no—
137C13×#103—22no—
138C13×#102—22no—
139C13×#102—22no—
140C13×#102—21no—
141C13×C22⋊C8—21no—
142C13×#97C2312yes—
143C13×#97C2311yescharacteristic
144C13×#97C2311yescharacteristic
145C13×#97C2312yes—
146C4×C8×C13—21no—
147C4×C8×C13—21no—
148#19025C1311yesmaximal, characteristic, direct product factor, Sylow
149C24×C13—21no—
150C13×#41—82no—
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—42no—
158C2×Q8×C13—82no—
159C2×Q8×C13C2×D412yes—
160C2×Q8×C13C2×D411yescharacteristic
161C2×D4×C13—21no—
162C2×D4×C13—22no—
163C2×D4×C13—22no—
164C2×D4×C13—21no—
165C2×D4×C13—42no—
166C2×D4×C13C2×D412yes—
167C2×D4×C13C2×D411yescharacteristic
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C13×Q16—42no—
177C13×SD16—42no—
178C13×M16—42no—
179C13×M16—42no—
180C2×C8×C13—21no—
181C2×C8×C13—22no—
182C2×C8×C13—21no—
183C2×C8×C13—22no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4—21no—
197C13×C4⋊C4—21no—
198C13×C4⋊C4—21no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—41no—
201C13×C4⋊C4—41no—
202C13×C4⋊C4C2×D412yes—
203C13×C4⋊C4C2×D411yescharacteristic
204C13×C4⋊C4C2×D412yes—
205C13×C4⋊C4C2×D411yescharacteristic
206C13×C22⋊C4—22no—
207C13×C22⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—22no—
211C13×C22⋊C4—21no—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—22no—
214C13×C22⋊C4—22no—
215C13×C22⋊C4—21no—
216C13×C22⋊C4—21no—
217C13×C22⋊C4—22no—
218C13×C22⋊C4—22no—
219C13×C22⋊C4—21no—
220C13×C22⋊C4—21no—
221C13×C22⋊C4—41no—
222C42×C13—22no—
223C42×C13—22no—
224C42×C13—21no—
225C42×C13—41no—
226C42×C13C2×D411yescharacteristic
227C42×C13C2×D411yescharacteristic
228C42×C13C2×D411yescharacteristic
229C42×C13C2411yescharacteristic
230#3561C2×C1311yescharacteristic
231#3237C2×C1311yescharacteristic, complemented
232#3172C2×C1311yescharacteristic, complemented
233#3140C2×C1311yescharacteristic, complemented
234#1664C2×C1312yescomplemented
235#1664C2×C1312yescomplemented
236#1662C2×C1312yescomplemented
237#1661C2×C1312yescomplemented
238#1529C2×C1311yescharacteristic, complemented
239#1527C2×C1311yescharacteristic, complemented
240#1526C2×C1311yescharacteristic, complemented
241C23×C13—22no—
242C23×C13—21no—
243C23×C13—42no—
244C23×C13—81no—
245C23×C13—81no—
246C23×C13#12011yescharacteristic
247Q8×C13—41no—
248Q8×C13—42no—
249Q8×C13—41no—
250Q8×C13—41no—
251Q8×C13—42no—
252Q8×C13—42no—
253Q8×C13—42no—
254Q8×C13—81no—
255Q8×C13—82no—
256D4×C13—41no—
257D4×C13—42no—
258D4×C13—42no—
259D4×C13—42no—
260D4×C13—82no—
261D4×C13—82no—
262C2×C4×C13—22no—
263C2×C4×C13—21no—
264C2×C4×C13—22no—
265C2×C4×C13—21no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—21no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—42no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—81no—
275C2×C4×C13—82no—
276C2×C4×C13—82no—
277C2×C4×C13—82no—
278C2×C4×C13#12011yescharacteristic
279C2×C4×C13#12011yescharacteristic
280C2×C4×C13#12011yescharacteristic
281C2×C4×C13C22×D411yescharacteristic
282C2×C4×C13C22×D411yescharacteristic
283C2×C4×C13C22×D411yescharacteristic
284C8×C13—22no—
285C8×C13—42no—
286C8×C13—42no—
287C8×C13—41no—
288#563C22×C1312yes—
289#562C22×C1312yes—
290#556—21no—
291#551—22no—
292D4×Q8—21no—
293#548—21no—
294#546—21no—
295#543—21no—
296#542—21no—
297#542—22no—
298#538—21no—
299#536—21no—
300#533C22×C1311yescharacteristic
301#533C22×C1311yescharacteristic
302#529C22×C1311yescharacteristic
303C2×#124C22×C1311yescharacteristic
304#501C22×C1311yescharacteristic, complemented
305#501C22×C1312yescomplemented
306#497C22×C1311yescharacteristic, complemented
307#491C22×C1311yescharacteristic, complemented
308#491C22×C1312yescomplemented
309#489C22×C1312yes—
310#489C22×C1312yes—
311#489C22×C1311yescharacteristic, complemented
312#488—22no—
313#485—22no—
314#477—21no—
315#475—21no—
316#470—21no—
317#468—21no—
318C4×Q16—21no—
319C4×SD16—21no—
320#432C22×C1311yescharacteristic
321#419—21no—
322#418—21no—
323C4×M16C22×C1311yescharacteristic
324C4×M16C22×C1311yescharacteristic
325#330C22×C1312yescomplemented
326#330C22×C1312yescomplemented
327#330C22×C1312yescomplemented
328#329C22×C1312yes—
329#329C22×C1312yes—
330#329C22×C1312yescomplemented
331C22×C13—21no—
332C22×C13—21no—
333C22×C13—21no—
334C22×C13—41no—
335C22×C13—42no—
336C22×C13—42no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—42no—
340C22×C13—162no—
341C22×C13C2×#12011yescharacteristic
342C4×C13—21no—
343C4×C13—21no—
344C4×C13—21no—
345C4×C13—21no—
346C4×C13—21no—
347C4×C13—41no—
348C4×C13—42no—
349C4×C13—42no—
350C4×C13—41no—
351C4×C13—42no—
352C4×C13—41no—
353C4×C13—81no—
354C4×C13—81no—
355C4×C13#45512yes—
356C2×#41—21no—
357C22×Q8—21no—
358C22×Q8D4×C1311yescharacteristic
359C22×D4D4×C1311yescharacteristic
360C2×Q16—21no—
361C2×SD16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C4⋊Q8—21no—
365C4⋊Q8—22no—
366C4⋊Q8D4×C1311yescharacteristic
367C4⋊Q8D4×C1311yescharacteristic
368C4⋊Q8C23×C1311yescharacteristic
369C4⋊Q8C23×C1311yescharacteristic
370#126—22no—
371#126—22no—
372#126—22no—
373#126—21no—
374#125—21no—
375#125C23×C1311yescharacteristic
376#125C23×C1312yes—
377#124—21no—
378#124—22no—
379#124—22no—
380#124—21no—
381#124—21no—
382#124D4×C1312yes—
383#124C23×C1312yes—
384#124C23×C1311yescharacteristic
385#123—22no—
386#123—22no—
387#123—21no—
388#123—22no—
389#123—22no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—21no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8D4×C1311yescharacteristic
403#121—21no—
404#121—22no—
405#121—22no—
406#121D4×C1311yescharacteristic
407#120—22no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8D4×C1311yescharacteristic
414C4×D4—22no—
415C4×D4—21no—
416C4×D4—22no—
417C4×D4—21no—
418C4×D4D4×C1311yescharacteristic
419#117—22no—
420#117—21no—
421#117—21no—
422#117D4×C1312yes—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C42C23×C1311yescharacteristic
427#107—21no—
428#107—22no—
429#106—21no—
430#106—22no—
431C4⋊C8—21no—
432#103—22no—
433#103—22no—
434#103—21no—
435#103—21no—
436#103—21no—
437#103—22no—
438#103—22no—
439#102—22no—
440#102—22no—
441#102—21no—
442C22⋊C8—21no—
443#97C23×C1312yes—
444#97C23×C1311yescharacteristic
445#97C23×C1311yescharacteristic
446#97C23×C1312yes—
447C4×C8—21no—
448C4×C8—21no—
449C2×C13—41no—
450C2×C13—81no—
451C2×C13—82no—
452C2×C13C2×#45511yescharacteristic
453C2×C13#301811yescharacteristic
454C2×C13#302011yescharacteristic
455C24—21no—
456#41—82no—
457C2×Q8—22no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—42no—
464C2×Q8—82no—
465C2×Q8C2×D4×C1312yes—
466C2×Q8C2×D4×C1311yescharacteristic
467C2×D4—21no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—42no—
472C2×D4C2×D4×C1312yes—
473C2×D4C2×D4×C1311yescharacteristic
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4C2×D4×C1311yescharacteristic
480C22×C4C2×D4×C1311yescharacteristic
481C22×C4C2×D4×C1311yescharacteristic
482Q16—42no—
483SD16—42no—
484M16—42no—
485M16—42no—
486C2×C8—21no—
487C2×C8—22no—
488C2×C8—21no—
489C2×C8—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4C2×D4×C1312yes—
509C4⋊C4C2×D4×C1311yescharacteristic
510C4⋊C4C2×D4×C1312yes—
511C4⋊C4C2×D4×C1311yescharacteristic
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—41no—
528C42—22no—
529C42—22no—
530C42—21no—
531C42—41no—
532C42C2×D4×C1311yescharacteristic
533C42C2×D4×C1311yescharacteristic
534C42C2×D4×C1311yescharacteristic
535C42C24×C1311yescharacteristic
536C13#1902511yescharacteristic, direct product factor, Sylow
537C23—22no—
538C23—21no—
539C23—42no—
540C23—81no—
541C23—81no—
542C23C13×#12011yescharacteristic
543Q8—41no—
544Q8—42no—
545Q8—41no—
546Q8—41no—
547Q8—42no—
548Q8—42no—
549Q8—42no—
550Q8—81no—
551Q8—82no—
552D4—41no—
553D4—42no—
554D4—42no—
555D4—42no—
556D4—82no—
557D4—82no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—81no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4C13×#12011yescharacteristic
575C2×C4C13×#12011yescharacteristic
576C2×C4C13×#12011yescharacteristic
577C2×C4C22×D4×C1311yescharacteristic
578C2×C4C22×D4×C1311yescharacteristic
579C2×C4C22×D4×C1311yescharacteristic
580C8—22no—
581C8—42no—
582C8—42no—
583C8—41no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—41no—
588C22—42no—
589C22—42no—
590C22—41no—
591C22—41no—
592C22—42no—
593C22—162no—
594C22C2×C13×#12011yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—42no—
602C4—42no—
603C4—41no—
604C4—42no—
605C4—41no—
606C4—81no—
607C4—81no—
608C4C13×#45512yes—
609C2—41no—
610C2—82no—
611C2—81no—
612C2C2×C13×#45511yescharacteristic
613C2C13×#301811yescharacteristic
614C2C13×#302011yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3561C2
LCSG ▷ C42 ▷ 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×#3237C2semidirect
3. C13×#3172C2semidirect
4. C13×#3140C2semidirect
5. C13×#1664C2semidirect
6. C13×#1664C2semidirect
7. C13×#1662C2semidirect
8. C13×#1661C2semidirect
9. C13×#1529C2semidirect
10. C13×#1527C2semidirect
11. C13×#1526C2semidirect
28. C13×#501C22semidirect
29. C13×#501C22semidirect
30. C13×#497C22semidirect
31. C13×#491C22semidirect
32. C13×#491C22semidirect
35. C13×#489C22semidirect
49. C13×#330C22semidirect
50. C13×#330C22semidirect
51. C13×#330C22semidirect
54. C13×#329C22semidirect
148. #19025C13direct (N × H)
231. #3237C2×C13semidirect
232. #3172C2×C13semidirect
233. #3140C2×C13semidirect
234. #1664C2×C13semidirect
235. #1664C2×C13semidirect
236. #1662C2×C13semidirect
237. #1661C2×C13semidirect
238. #1529C2×C13semidirect
239. #1527C2×C13semidirect
240. #1526C2×C13semidirect
304. #501C22×C13semidirect
305. #501C22×C13semidirect
306. #497C22×C13semidirect
307. #491C22×C13semidirect
308. #491C22×C13semidirect
311. #489C22×C13semidirect
325. #330C22×C13semidirect
326. #330C22×C13semidirect
327. #330C22×C13semidirect
330. #329C22×C13semidirect
536. C13#19025direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35612
C13×#32372
C13×#31722
C13×#31402
C13×#16642
C13×#16622
C13×#16612
C13×#15292
C13×#15272
C13×#15262
#1902513