Finite Group Databasebeta

← C13×#18307 #15704646

Subgroups — C13×#18307 #15704646

Order 3328.

934 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×#3461C211yesmaximal, characteristic, complemented
2C13×#3211C212yesmaximal, complemented
3C13×#2632C211yesmaximal, characteristic, complemented
4C13×#1605C211yesmaximal, characteristic, complemented
5C13×#1604C211yesmaximal, characteristic, complemented
6C13×#1603C212yesmaximal, complemented
7C13×#1599C211yesmaximal, characteristic, complemented
8C13×#1598C211yesmaximal, characteristic
9C13×#1597C212yesmaximal, complemented
10C13×#1521C212yesmaximal, complemented
11C13×#1461C211yesmaximal, characteristic, complemented
12C13×#544C2211yescharacteristic
13C13×#542—22no—
14C13×#541—22no—
15C13×#539—21no—
16C13×#539C2212yes—
17C13×#537C2211yescharacteristic
18C13×#536—21no—
19C13×#533—22no—
20C13×#529—22no—
21C13×#529—21no—
22C13×#529C2212yes—
23C2×C13×#124C2211yescharacteristic
24C4×C13×#41—21no—
25C2×C4×Q8×C13C2211yescharacteristic
26C13×#495—22no—
27C13×#488—22no—
28C13×#464—22no—
29C13×#463—22no—
30C13×#451C2212yes—
31C13×#450C2212yes—
32C13×#448C2212yes—
33C13×#447C2212yes—
34C13×#431C2212yes—
35C13×#399—21no—
36C13×#395C2211yescharacteristic
37C13×#395C2211yescharacteristic
38C13×#394C2211yescharacteristic
39C13×#394C2211yescharacteristic
40C13×#393—21no—
41C13×#388—21no—
42C13×#388—21no—
43C13×#383C2211yescharacteristic
44C13×#328C2212yes—
45C13×#328C2212yes—
46C13×#327C2212yes—
47C13×#327C2212yes—
48C13×#324C2212yes—
49C13×#324C2211yescharacteristic
50C13×#324C2211yescharacteristic
51C2×C13×#41—21no—
52C22×Q8×C13D411yescharacteristic
53C22×Q8×C13C2311yescharacteristic
54C22×D4×C13C2311yescharacteristic
55C2×C13×Q16—22no—
56C2×C13×SD16—22no—
57C2×C13×SD16—22no—
58C2×C13×D8—22no—
59C13×C4⋊Q8—22no—
60C13×C4⋊Q8—22no—
61C13×#126—22no—
62C13×#126—22no—
63C13×#126—22no—
64C13×#126—22no—
65C13×#125—21no—
66C13×#125—22no—
67C13×#125—22no—
68C13×#125—22no—
69C13×#125D412yes—
70C13×#124—22no—
71C13×#124—21no—
72C13×#124—22no—
73C13×#124—22no—
74C13×#124D412yes—
75C13×#123—22no—
76C13×#123—22no—
77C13×#123—22no—
78C13×#123—22no—
79C13×C22⋊Q8—22no—
80C13×C22⋊Q8—22no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—21no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8C2312yes—
86C13×#121—22no—
87C13×#121—21no—
88C13×#121C2312yes—
89C4×Q8×C13—21no—
90C4×Q8×C13—21no—
91C4×Q8×C13—21no—
92C4×Q8×C13—22no—
93C4×Q8×C13—22no—
94C4×Q8×C13D412yes—
95C4×D4×C13—21no—
96C4×D4×C13—21no—
97C4×D4×C13—21no—
98C4×D4×C13—22no—
99C4×D4×C13—22no—
100C4×D4×C13D412yes—
101C13×#117—22no—
102C13×#117—22no—
103C13×#117—21no—
104C13×#117—22no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4D411yescharacteristic
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C13×C22⋊C4—21no—
111C2×C13×C22⋊C4—21no—
112C2×C13×C22⋊C4—21no—
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C42×C13—22no—
117C2×C42×C13D411yescharacteristic
118C2×C42×C13D411yescharacteristic
119C2×C42×C13C2311yescharacteristic
120C13×C4⋊C8—22no—
121C13×#103—22no—
122C13×#103—22no—
123C13×#102—22no—
124C13×#102—22no—
125C13×C22⋊C8C2312yes—
126C13×C22⋊C8C2312yes—
127C4×C8×C13—22no—
128C13×#95—21no—
129C13×#95—21no—
130C13×#95—21no—
131C13×#95—21no—
132C13×#95C2311yescharacteristic
133C13×#95C2311yescharacteristic
134#18307C1311yesmaximal, characteristic, direct product factor, Sylow
135C24×C13—21no—
136C13×#41—42no—
137C13×#41—42no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13—22no—
141C2×Q8×C13—22no—
142C2×Q8×C13—22no—
143C2×Q8×C13—41no—
144C2×Q8×C13—81no—
145C2×Q8×C13C2×D412yes—
146C2×D4×C13—21no—
147C2×D4×C13—22no—
148C2×D4×C13—21no—
149C2×D4×C13—22no—
150C2×D4×C13—81no—
151C2×D4×C13C2×D412yes—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2411yescharacteristic
165C13×Q16—82no—
166C13×SD16—82no—
167C13×SD16—82no—
168C13×D8—82no—
169C2×C8×C13—22no—
170C2×C8×C13—22no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—81no—
187C13×C4⋊C4—81no—
188C13×C4⋊C4C2×D412yes—
189C13×C4⋊C4C2×D412yes—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—42no—
200C13×C22⋊C4—41no—
201C13×C22⋊C4—41no—
202C13×C22⋊C4—42no—
203C13×C22⋊C4—42no—
204C13×C22⋊C4—81no—
205C13×C22⋊C4—81no—
206C42×C13—22no—
207C42×C13—22no—
208C42×C13—21no—
209C42×C13—22no—
210C42×C13—21no—
211C42×C13—21no—
212C42×C13—21no—
213C42×C13C2×D412yes—
214C42×C13C2×D412yes—
215#3461C2×C1311yescharacteristic, complemented
216#3211C2×C1312yescomplemented
217#2632C2×C1311yescharacteristic, complemented
218#1605C2×C1311yescharacteristic, complemented
219#1604C2×C1311yescharacteristic, complemented
220#1603C2×C1312yescomplemented
221#1599C2×C1311yescharacteristic, complemented
222#1598C2×C1311yescharacteristic
223#1597C2×C1312yescomplemented
224#1521C2×C1312yescomplemented
225#1461C2×C1311yescharacteristic, complemented
226C23×C13—22no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13—41no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13C22×D411yescharacteristic
235Q8×C13—44no—
236Q8×C13—42no—
237Q8×C13—42no—
238Q8×C13—42no—
239Q8×C13—42no—
240Q8×C13—81no—
241D4×C13—42no—
242D4×C13—42no—
243D4×C13—42no—
244D4×C13—42no—
245D4×C13—42no—
246D4×C13—42no—
247D4×C13—81no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—22no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—44no—
263C2×C4×C13—44no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—82no—
276C2×C4×C13#12011yescharacteristic
277C2×C4×C13#12011yescharacteristic
278C2×C4×C13#12012yes—
279C2×C4×C13#13512yes—
280C2×C4×C13C22×D412yes—
281C8×C13—42no—
282C8×C13—42no—
283#544C22×C1311yescharacteristic
284#542—22no—
285#541—22no—
286#539—21no—
287#539C22×C1312yes—
288#537C22×C1311yescharacteristic
289#536—21no—
290#533—22no—
291#529—22no—
292#529—21no—
293#529C22×C1312yes—
294C2×#124C22×C1311yescharacteristic
295C4×#41—21no—
296C2×C4×Q8C22×C1311yescharacteristic
297#495—22no—
298#488—22no—
299#464—22no—
300#463—22no—
301#451C22×C1312yes—
302#450C22×C1312yes—
303#448C22×C1312yes—
304#447C22×C1312yes—
305#431C22×C1312yes—
306#399—21no—
307#395C22×C1311yescharacteristic
308#395C22×C1311yescharacteristic
309#394C22×C1311yescharacteristic
310#394C22×C1311yescharacteristic
311#393—21no—
312#388—21no—
313#388—21no—
314#383C22×C1311yescharacteristic
315#328C22×C1312yes—
316#328C22×C1312yes—
317#327C22×C1312yes—
318#327C22×C1312yes—
319#324C22×C1312yes—
320#324C22×C1311yescharacteristic
321#324C22×C1311yescharacteristic
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—42no—
325C22×C13—42no—
326C22×C13—42no—
327C22×C13—81no—
328C22×C13—81no—
329C22×C13—81no—
330C22×C13—81no—
331C22×C13—81no—
332C22×C13—81no—
333C22×C13—81no—
334C22×C13C2×#12011yescharacteristic
335C22×C13C2×#13511yescharacteristic
336C22×C13#57511yescharacteristic
337C4×C13—22no—
338C4×C13—22no—
339C4×C13—21no—
340C4×C13—21no—
341C4×C13—22no—
342C4×C13—41no—
343C4×C13—42no—
344C4×C13—42no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13—42no—
348C4×C13—81no—
349C4×C13—81no—
350C4×C13—81no—
351C2×#41—21no—
352C22×Q8D4×C1311yescharacteristic
353C22×Q8C23×C1311yescharacteristic
354C22×D4C23×C1311yescharacteristic
355C2×Q16—22no—
356C2×SD16—22no—
357C2×SD16—22no—
358C2×D8—22no—
359C4⋊Q8—22no—
360C4⋊Q8—22no—
361#126—22no—
362#126—22no—
363#126—22no—
364#126—22no—
365#125—21no—
366#125—22no—
367#125—22no—
368#125—22no—
369#125D4×C1312yes—
370#124—22no—
371#124—21no—
372#124—22no—
373#124—22no—
374#124D4×C1312yes—
375#123—22no—
376#123—22no—
377#123—22no—
378#123—22no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8—21no—
384C22⋊Q8—22no—
385C22⋊Q8C23×C1312yes—
386#121—22no—
387#121—21no—
388#121C23×C1312yes—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—22no—
393C4×Q8—22no—
394C4×Q8D4×C1312yes—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4D4×C1312yes—
401#117—22no—
402#117—22no—
403#117—21no—
404#117—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4D4×C1311yescharacteristic
408C2×C4⋊C4C23×C1311yescharacteristic
409C2×C4⋊C4C23×C1311yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C42—22no—
417C2×C42D4×C1311yescharacteristic
418C2×C42D4×C1311yescharacteristic
419C2×C42C23×C1311yescharacteristic
420C4⋊C8—22no—
421#103—22no—
422#103—22no—
423#102—22no—
424#102—22no—
425C22⋊C8C23×C1312yes—
426C22⋊C8C23×C1312yes—
427C4×C8—22no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95C23×C1311yescharacteristic
433#95C23×C1311yescharacteristic
434C2×C13—21no—
435C2×C13—21no—
436C2×C13—82no—
437C2×C13—161no—
438C2×C13#300211yescharacteristic
439C2×C13#302011yescharacteristic
440C2×C13#302711yescharacteristic
441C24—21no—
442#41—42no—
443#41—42no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—41no—
450C2×Q8—81no—
451C2×Q8C2×D4×C1312yes—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—21no—
455C2×D4—22no—
456C2×D4—81no—
457C2×D4C2×D4×C1312yes—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4C2×D4×C1311yescharacteristic
465C22×C4C2×D4×C1311yescharacteristic
466C22×C4C2×D4×C1311yescharacteristic
467C22×C4C2×D4×C1311yescharacteristic
468C22×C4C2×D4×C1311yescharacteristic
469C22×C4C2×D4×C1311yescharacteristic
470C22×C4C24×C1311yescharacteristic
471Q16—82no—
472SD16—82no—
473SD16—82no—
474D8—82no—
475C2×C8—22no—
476C2×C8—22no—
477C4⋊C4—21no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4C2×D4×C1312yes—
495C4⋊C4C2×D4×C1312yes—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—42no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—81no—
511C22⋊C4—81no—
512C42—22no—
513C42—22no—
514C42—21no—
515C42—22no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42C2×D4×C1312yes—
520C42C2×D4×C1312yes—
521C13#1830711yescharacteristic, direct product factor, Sylow
522C23—22no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23C22×D4×C1311yescharacteristic
531Q8—44no—
532Q8—42no—
533Q8—42no—
534Q8—42no—
535Q8—42no—
536Q8—81no—
537D4—42no—
538D4—42no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—42no—
543D4—81no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4C13×#12011yescharacteristic
573C2×C4C13×#12011yescharacteristic
574C2×C4C13×#12012yes—
575C2×C4C13×#13512yes—
576C2×C4C22×D4×C1312yes—
577C8—42no—
578C8—42no—
579C22—21no—
580C22—21no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22C2×C13×#12011yescharacteristic
592C22C2×C13×#13511yescharacteristic
593C22C13×#57511yescharacteristic
594C4—21no—
595C4—21no—
596C4—22no—
597C4—22no—
598C4—22no—
599C4—42no—
600C4—41no—
601C4—41no—
602C4—42no—
603C4—41no—
604C4—42no—
605C4—81no—
606C4—81no—
607C4—81no—
608C2—21no—
609C2—21no—
610C2—82no—
611C2—161no—
612C2C13×#300211yescharacteristic
613C2C13×#302011yescharacteristic
614C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#1598C2
LCSG ▷ C22×C4 ▷ 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×#3461C2semidirect
2. C13×#3211C2semidirect
3. C13×#2632C2semidirect
4. C13×#1605C2semidirect
5. C13×#1604C2semidirect
6. C13×#1603C2semidirect
7. C13×#1599C2semidirect
9. C13×#1597C2semidirect
10. C13×#1521C2semidirect
11. C13×#1461C2semidirect
134. #18307C13direct (N × H)
215. #3461C2×C13semidirect
216. #3211C2×C13semidirect
217. #2632C2×C13semidirect
218. #1605C2×C13semidirect
219. #1604C2×C13semidirect
220. #1603C2×C13semidirect
221. #1599C2×C13semidirect
223. #1597C2×C13semidirect
224. #1521C2×C13semidirect
225. #1461C2×C13semidirect
521. C13#18307direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34612
C13×#32112
C13×#26322
C13×#16052
C13×#16042
C13×#16032
C13×#15992
C13×#15982
C13×#15972
C13×#15212
C13×#14612
#1830713