Finite Group Databasebeta

← C13×#19030 #15705369

Subgroups — C13×#19030 #15705369

Order 3328.

902 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3559C211yesmaximal, characteristic, complemented
2C13×#3214C211yesmaximal, characteristic, complemented
3C13×#3171C211yesmaximal, characteristic, complemented
4C13×#3142C211yesmaximal, characteristic, complemented
5C13×#1664C212yesmaximal, complemented
6C13×#1662C212yesmaximal, complemented
7C13×#1657C212yesmaximal, complemented
8C13×#1656C212yesmaximal, complemented
9C13×#1529C211yesmaximal, characteristic, complemented
10C13×#1528C211yesmaximal, characteristic, complemented
11C13×#1525C211yesmaximal, characteristic, complemented
12C13×#563C2212yes—
13C13×#562C2212yes—
14C13×#554—21no—
15C13×#553—21no—
16C13×#553—21no—
17C13×#547—22no—
18C13×#547—21no—
19C13×#544—21no—
20C13×#540—21no—
21C13×#539—22no—
22C13×#539—21no—
23C13×#537—21no—
24C13×#532C2211yescharacteristic
25C13×#532C2211yescharacteristic
26C13×#529C2211yescharacteristic
27C2×C13×#125C2211yescharacteristic
28C13×#501C2211yescharacteristic
29C13×#496C2211yescharacteristic
30C13×#496C2212yes—
31C13×#491C2212yes—
32C13×#490C2212yes—
33C13×#490C2211yescharacteristic
34C13×#489C2211yescharacteristic
35C13×#489C2212yes—
36C13×#488—22no—
37C13×#469—21no—
38C13×#468—21no—
39C13×#461—21no—
40C13×#459—21no—
41C13×#449—22no—
42C4×C13×SD16—21no—
43C4×C13×D8—21no—
44C13×#432C2211yescharacteristic
45C13×#417—21no—
46C13×#417—21no—
47C4×C13×M16C2211yescharacteristic
48C4×C13×M16C2211yescharacteristic
49C13×#330C2212yes—
50C13×#330C2212yes—
51C13×#330C2212yes—
52C13×#329C2212yes—
53C13×#329C2212yes—
54C13×#329C2212yes—
55C2×C13×#41—22no—
56C2×C13×#41—21no—
57C2×C13×#41D412yes—
58C2×C13×SD16—21no—
59C2×C13×SD16—22no—
60C2×C13×D8—21no—
61C2×C13×D8—22no—
62C2×C13×M16—21no—
63C2×C13×M16—21no—
64C13×C4⋊Q8—21no—
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8D411yescharacteristic
67C13×C4⋊Q8C2311yescharacteristic
68C13×#127D411yescharacteristic
69C13×#127C2311yescharacteristic
70C13×#126—22no—
71C13×#126—22no—
72C13×#126—21no—
73C13×#125—22no—
74C13×#125—21no—
75C13×#125—21no—
76C13×#125—21no—
77C13×#125D412yes—
78C13×#125C2312yes—
79C13×#125C2311yescharacteristic
80C13×#124—21no—
81C13×#124C2311yescharacteristic
82C13×#124C2312yes—
83C13×#123—22no—
84C13×#123—22no—
85C13×#123—22no—
86C13×#123—22no—
87C13×#123—21no—
88C13×#123—22no—
89C13×#123—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8—22no—
96C13×C22⋊Q8D411yescharacteristic
97C13×#121—22no—
98C13×#121—22no—
99C13×#121—21no—
100C13×#121—21no—
101C13×#121—22no—
102C13×#121—22no—
103C13×#121—21no—
104C13×#121—21no—
105C13×#121—21no—
106C13×#121—21no—
107C13×#121D411yescharacteristic
108C4×Q8×C13D411yescharacteristic
109C4×D4×C13—22no—
110C4×D4×C13—22no—
111C4×D4×C13—21no—
112C4×D4×C13—21no—
113C4×D4×C13—21no—
114C4×D4×C13—21no—
115C4×D4×C13—21no—
116C4×D4×C13—21no—
117C4×D4×C13—21no—
118C4×D4×C13D411yescharacteristic
119C13×#117—21no—
120C13×#117—21no—
121C2×C13×C4⋊C4—22no—
122C2×C13×C4⋊C4—21no—
123C2×C13×C4⋊C4—21no—
124C2×C13×C4⋊C4—21no—
125C2×C13×C4⋊C4D411yescharacteristic
126C2×C13×C4⋊C4D411yescharacteristic
127C2×C42×C13C2311yescharacteristic
128C13×#107—21no—
129C13×#106—21no—
130C13×C4⋊C8—21no—
131C13×#103—21no—
132C13×#103—22no—
133C13×#103—22no—
134C13×#103—22no—
135C13×#102—21no—
136C13×#102—22no—
137C13×#102—22no—
138C13×#102—22no—
139C13×#102—21no—
140C13×#102—21no—
141C13×C22⋊C8—21no—
142C13×#97C2312yes—
143C13×#97C2311yescharacteristic
144C13×#97C2311yescharacteristic
145C13×#97C2312yes—
146C4×C8×C13—21no—
147C4×C8×C13—21no—
148#19030C1311yesmaximal, characteristic, direct product factor, Sylow
149C13×#41—44no—
150C13×#41—84no—
151C13×#41—82no—
152C2×Q8×C13—22no—
153C2×Q8×C13—21no—
154C2×Q8×C13C2×D411yescharacteristic
155C2×Q8×C13C2×D412yes—
156C2×D4×C13—22no—
157C2×D4×C13—21no—
158C2×D4×C13—22no—
159C2×D4×C13—22no—
160C2×D4×C13—21no—
161C2×D4×C13—21no—
162C2×D4×C13—21no—
163C2×D4×C13—21no—
164C2×D4×C13—21no—
165C2×D4×C13—41no—
166C2×D4×C13C2×D411yescharacteristic
167C2×D4×C13C2×D412yes—
168C22×C4×C13—21no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—22no—
175C22×C4×C13—41no—
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D411yescharacteristic
179C13×SD16—42no—
180C13×SD16—82no—
181C13×D8—42no—
182C13×D8—82no—
183C13×M16—42no—
184C13×M16—42no—
185C2×C8×C13—21no—
186C2×C8×C13—21no—
187C2×C8×C13—22no—
188C2×C8×C13—22no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4—21no—
197C13×C4⋊C4—22no—
198C13×C4⋊C4—21no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—21no—
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⋊C4C2×D412yes—
208C13×C4⋊C4C2×D412yes—
209C13×C4⋊C4C2×D411yescharacteristic
210C13×C4⋊C4C2×D411yescharacteristic
211C13×C22⋊C4—22no—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—22no—
214C13×C22⋊C4—22no—
215C13×C22⋊C4—22no—
216C13×C22⋊C4—21no—
217C13×C22⋊C4—21no—
218C13×C22⋊C4—21no—
219C13×C22⋊C4—21no—
220C13×C22⋊C4—22no—
221C13×C22⋊C4—22no—
222C13×C22⋊C4—21no—
223C13×C22⋊C4—41no—
224C13×C22⋊C4—41no—
225C42×C13—22no—
226C42×C13—21no—
227C42×C13C2×D411yescharacteristic
228C42×C13C2×D411yescharacteristic
229C42×C13C2×D411yescharacteristic
230C42×C13C2411yescharacteristic
231#3559C2×C1311yescharacteristic, complemented
232#3214C2×C1311yescharacteristic, complemented
233#3171C2×C1311yescharacteristic, complemented
234#3142C2×C1311yescharacteristic, complemented
235#1664C2×C1312yescomplemented
236#1662C2×C1312yescomplemented
237#1657C2×C1312yescomplemented
238#1656C2×C1312yescomplemented
239#1529C2×C1311yescharacteristic, complemented
240#1528C2×C1311yescharacteristic, complemented
241#1525C2×C1311yescharacteristic, complemented
242C23×C13—21no—
243C23×C13—22no—
244C23×C13—41no—
245C23×C13#12011yescharacteristic
246Q8×C13—41no—
247Q8×C13—42no—
248Q8×C13—42no—
249Q8×C13—82no—
250D4×C13—41no—
251D4×C13—42no—
252D4×C13—41no—
253D4×C13—41no—
254D4×C13—41no—
255D4×C13—41no—
256D4×C13—42no—
257D4×C13—44no—
258D4×C13—42no—
259D4×C13—42no—
260D4×C13—81no—
261D4×C13—82no—
262D4×C13—82no—
263D4×C13—82no—
264C2×C4×C13—22no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—21no—
270C2×C4×C13—22no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—41no—
276C2×C4×C13—82no—
277C2×C4×C13—81no—
278C2×C4×C13—82no—
279C2×C4×C13—82no—
280C2×C4×C13—82no—
281C2×C4×C13—82no—
282C2×C4×C13#12011yescharacteristic
283C2×C4×C13#12011yescharacteristic
284C2×C4×C13#12011yescharacteristic
285C2×C4×C13C22×D411yescharacteristic
286C2×C4×C13C22×D411yescharacteristic
287C2×C4×C13C22×D411yescharacteristic
288C8×C13—22no—
289C8×C13—42no—
290C8×C13—41no—
291C8×C13—42no—
292#563C22×C1312yes—
293#562C22×C1312yes—
294#554—21no—
295#553—21no—
296#553—21no—
297#547—22no—
298#547—21no—
299#544—21no—
300#540—21no—
301#539—22no—
302#539—21no—
303#537—21no—
304#532C22×C1311yescharacteristic
305#532C22×C1311yescharacteristic
306#529C22×C1311yescharacteristic
307C2×#125C22×C1311yescharacteristic
308#501C22×C1311yescharacteristic
309#496C22×C1311yescharacteristic
310#496C22×C1312yes—
311#491C22×C1312yes—
312#490C22×C1312yes—
313#490C22×C1311yescharacteristic
314#489C22×C1311yescharacteristic
315#489C22×C1312yes—
316#488—22no—
317#469—21no—
318#468—21no—
319#461—21no—
320#459—21no—
321#449—22no—
322C4×SD16—21no—
323C4×D8—21no—
324#432C22×C1311yescharacteristic
325#417—21no—
326#417—21no—
327C4×M16C22×C1311yescharacteristic
328C4×M16C22×C1311yescharacteristic
329#330C22×C1312yes—
330#330C22×C1312yes—
331#330C22×C1312yes—
332#329C22×C1312yes—
333#329C22×C1312yes—
334#329C22×C1312yes—
335C22×C13—21no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13—41no—
339C22×C13—42no—
340C22×C13—42no—
341C22×C13—41no—
342C22×C13—42no—
343C22×C13—41no—
344C22×C13—81no—
345C22×C13—81no—
346C22×C13—81no—
347C22×C13C2×#12011yescharacteristic
348C4×C13—21no—
349C4×C13—21no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—41no—
354C4×C13—42no—
355C4×C13—41no—
356C4×C13—42no—
357C4×C13—42no—
358C4×C13—41no—
359C4×C13—81no—
360C4×C13#45412yes—
361C2×#41—22no—
362C2×#41—21no—
363C2×#41D4×C1312yes—
364C2×SD16—21no—
365C2×SD16—22no—
366C2×D8—21no—
367C2×D8—22no—
368C2×M16—21no—
369C2×M16—21no—
370C4⋊Q8—21no—
371C4⋊Q8—22no—
372C4⋊Q8D4×C1311yescharacteristic
373C4⋊Q8C23×C1311yescharacteristic
374#127D4×C1311yescharacteristic
375#127C23×C1311yescharacteristic
376#126—22no—
377#126—22no—
378#126—21no—
379#125—22no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125D4×C1312yes—
384#125C23×C1312yes—
385#125C23×C1311yescharacteristic
386#124—21no—
387#124C23×C1311yescharacteristic
388#124C23×C1312yes—
389#123—22no—
390#123—22no—
391#123—22no—
392#123—22no—
393#123—21no—
394#123—22no—
395#123—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8D4×C1311yescharacteristic
403#121—22no—
404#121—22no—
405#121—21no—
406#121—21no—
407#121—22no—
408#121—22no—
409#121—21no—
410#121—21no—
411#121—21no—
412#121—21no—
413#121D4×C1311yescharacteristic
414C4×Q8D4×C1311yescharacteristic
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—21no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4D4×C1311yescharacteristic
425#117—21no—
426#117—21no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4D4×C1311yescharacteristic
432C2×C4⋊C4D4×C1311yescharacteristic
433C2×C42C23×C1311yescharacteristic
434#107—21no—
435#106—21no—
436C4⋊C8—21no—
437#103—21no—
438#103—22no—
439#103—22no—
440#103—22no—
441#102—21no—
442#102—22no—
443#102—22no—
444#102—22no—
445#102—21no—
446#102—21no—
447C22⋊C8—21no—
448#97C23×C1312yes—
449#97C23×C1311yescharacteristic
450#97C23×C1311yescharacteristic
451#97C23×C1312yes—
452C4×C8—21no—
453C4×C8—21no—
454C2×C13—41no—
455C2×C13—81no—
456C2×C13—82no—
457C2×C13—161no—
458C2×C13C2×#45411yescharacteristic
459C2×C13#301811yescharacteristic
460C2×C13#301911yescharacteristic
461#41—44no—
462#41—84no—
463#41—82no—
464C2×Q8—22no—
465C2×Q8—21no—
466C2×Q8C2×D4×C1311yescharacteristic
467C2×Q8C2×D4×C1312yes—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—41no—
478C2×D4C2×D4×C1311yescharacteristic
479C2×D4C2×D4×C1312yes—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—41no—
488C22×C4C2×D4×C1311yescharacteristic
489C22×C4C2×D4×C1311yescharacteristic
490C22×C4C2×D4×C1311yescharacteristic
491SD16—42no—
492SD16—82no—
493D8—42no—
494D8—82no—
495M16—42no—
496M16—42no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—22no—
500C2×C8—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4C2×D4×C1312yes—
520C4⋊C4C2×D4×C1312yes—
521C4⋊C4C2×D4×C1311yescharacteristic
522C4⋊C4C2×D4×C1311yescharacteristic
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—21no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C42—22no—
538C42—21no—
539C42C2×D4×C1311yescharacteristic
540C42C2×D4×C1311yescharacteristic
541C42C2×D4×C1311yescharacteristic
542C42C24×C1311yescharacteristic
543C13#1903011yescharacteristic, direct product factor, Sylow
544C23—21no—
545C23—22no—
546C23—41no—
547C23C13×#12011yescharacteristic
548Q8—41no—
549Q8—42no—
550Q8—42no—
551Q8—82no—
552D4—41no—
553D4—42no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—42no—
559D4—44no—
560D4—42no—
561D4—42no—
562D4—81no—
563D4—82no—
564D4—82no—
565D4—82no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—82no—
579C2×C4—81no—
580C2×C4—82no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—82no—
584C2×C4C13×#12011yescharacteristic
585C2×C4C13×#12011yescharacteristic
586C2×C4C13×#12011yescharacteristic
587C2×C4C22×D4×C1311yescharacteristic
588C2×C4C22×D4×C1311yescharacteristic
589C2×C4C22×D4×C1311yescharacteristic
590C8—22no—
591C8—42no—
592C8—41no—
593C8—42no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—41no—
598C22—42no—
599C22—42no—
600C22—41no—
601C22—42no—
602C22—41no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22C2×C13×#12011yescharacteristic
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—21no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—42no—
616C4—42no—
617C4—41no—
618C4—81no—
619C4C13×#45412yes—
620C2—41no—
621C2—81no—
622C2—82no—
623C2—161no—
624C2C2×C13×#45411yescharacteristic
625C2C13×#301811yescharacteristic
626C2C13×#301911yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
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
1. C13×#3559C2semidirect
2. C13×#3214C2semidirect
3. C13×#3171C2semidirect
4. C13×#3142C2semidirect
5. C13×#1664C2semidirect
6. C13×#1662C2semidirect
7. C13×#1657C2semidirect
8. C13×#1656C2semidirect
9. C13×#1529C2semidirect
10. C13×#1528C2semidirect
11. C13×#1525C2semidirect
148. #19030C13direct (N × H)
231. #3559C2×C13semidirect
232. #3214C2×C13semidirect
233. #3171C2×C13semidirect
234. #3142C2×C13semidirect
235. #1664C2×C13semidirect
236. #1662C2×C13semidirect
237. #1657C2×C13semidirect
238. #1656C2×C13semidirect
239. #1529C2×C13semidirect
240. #1528C2×C13semidirect
241. #1525C2×C13semidirect
543. C13#19030direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35592
C13×#32142
C13×#31712
C13×#31422
C13×#16642
C13×#16622
C13×#16572
C13×#16562
C13×#15292
C13×#15282
C13×#15252
#1903013