Finite Group Databasebeta

← C13×#18468 #15704807

Subgroups — C13×#18468 #15704807

Order 3328.

870 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3559C211yesmaximal, characteristic
2C13×#3234C211yesmaximal, characteristic, complemented
3C13×#3232C211yesmaximal, characteristic, complemented
4C13×#2822C211yesmaximal, characteristic, complemented
5C13×#1616C212yesmaximal, complemented
6C13×#1615C212yesmaximal, complemented
7C13×#1610C212yesmaximal, complemented
8C13×#1609C212yesmaximal, complemented
9C13×#1517C211yesmaximal, characteristic, complemented
10C13×#1512C211yesmaximal, characteristic, complemented
11C13×#1470C211yesmaximal, characteristic, complemented
12C13×#563—21no—
13C13×#562—21no—
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×#539C2212yes—
23C13×#537C2212yes—
24C13×#532C2211yescharacteristic
25C13×#529C2211yescharacteristic
26C2×C13×#125C2211yescharacteristic
27C2×C13×#125C2211yescharacteristic
28C13×#501—21no—
29C13×#499—21no—
30C13×#490—21no—
31C13×#488—21no—
32C13×#484C2211yescharacteristic
33C13×#483C2211yescharacteristic
34C13×#481C2212yes—
35C13×#481C2211yescharacteristic
36C13×#480C2212yes—
37C13×#480C2211yescharacteristic
38C13×#479—21no—
39C13×#478—21no—
40C13×#478—22no—
41C13×#432C2211yescharacteristic
42C13×#431C2211yescharacteristic
43C13×#400—21no—
44C13×#400C2212yes—
45C13×#398—21no—
46C13×#398—22no—
47C13×#398C2212yes—
48C13×#382C2211yescharacteristic
49C13×#328C2212yes—
50C13×#327C2212yes—
51C13×#327C2212yes—
52C13×#327C2212yes—
53C13×#324C2212yes—
54C13×#324C2212yes—
55C2×C13×#41—21no—
56C2×C13×#41—22no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8—22no—
59C13×C4⋊Q8D411yescharacteristic
60C13×#127D411yescharacteristic
61C13×#126—22no—
62C13×#126—22no—
63C13×#126—21no—
64C13×#125—21no—
65C13×#125—22no—
66C13×#125—21no—
67C13×#125—21no—
68C13×#125—21no—
69C13×#125—21no—
70C13×#125—21no—
71C13×#125—21no—
72C13×#125—21no—
73C13×#125—21no—
74C13×#125D411yescharacteristic
75C13×#124—21no—
76C13×#124D411yescharacteristic
77C13×#123—22no—
78C13×#123—22no—
79C13×#123—22no—
80C13×#123—22no—
81C13×#123—22no—
82C13×#123—21no—
83C13×#123—22no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8C2311yescharacteristic
91C13×#121—21no—
92C13×#121—22no—
93C13×#121—21no—
94C13×#121—22no—
95C13×#121—22no—
96C13×#121—21no—
97C13×#121—22no—
98C13×#121C2311yescharacteristic
99C13×#121C2312yes—
100C4×Q8×C13D411yescharacteristic
101C4×D4×C13—22no—
102C4×D4×C13—21no—
103C4×D4×C13—21no—
104C4×D4×C13—21no—
105C4×D4×C13—22no—
106C4×D4×C13—21no—
107C4×D4×C13D411yescharacteristic
108C4×D4×C13D412yes—
109C13×#117—21no—
110C13×#117—21no—
111C2×C13×C4⋊C4—22no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4—21no—
115C2×C13×C4⋊C4—21no—
116C2×C13×C4⋊C4—22no—
117C2×C13×C4⋊C4D411yescharacteristic
118C2×C13×C4⋊C4D412yes—
119C2×C13×C4⋊C4D411yescharacteristic
120C2×C13×C4⋊C4C2311yescharacteristic
121C2×C13×C4⋊C4C2311yescharacteristic
122C2×C13×C4⋊C4C2312yes—
123C2×C42×C13C2311yescharacteristic
124C13×#107—22no—
125C13×#107—21no—
126C13×#107—21no—
127C13×#106—22no—
128C13×#106—21no—
129C13×#106—21no—
130C13×C4⋊C8—21no—
131C13×C4⋊C8—21no—
132C13×#103—21no—
133C13×#103—21no—
134C13×#102—21no—
135C13×#102—22no—
136C13×#102—21no—
137C13×#102—22no—
138C13×C22⋊C8C2311yescharacteristic
139C13×C22⋊C8C2311yescharacteristic
140C13×C22⋊C8C2312yes—
141C13×#97—21no—
142C4×C8×C13—21no—
143C13×#95—21no—
144C13×#95—22no—
145C13×#95—22no—
146C13×#95—22no—
147C13×#95C2312yes—
148#18468C1311yesmaximal, characteristic, direct product factor, Sylow
149C13×#41—81no—
150C13×#41—81no—
151C13×#41—82no—
152C13×#41—82no—
153C2×Q8×C13—22no—
154C2×Q8×C13—21no—
155C2×Q8×C13C2×D411yescharacteristic
156C2×D4×C13—21no—
157C2×D4×C13—22no—
158C2×D4×C13—22no—
159C2×D4×C13—22no—
160C2×D4×C13—21no—
161C2×D4×C13—21no—
162C2×D4×C13C2×D411yescharacteristic
163C2×D4×C13C2×D412yes—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—21no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13C2×D412yes—
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2411yescharacteristic
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—22no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—22no—
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—21no—
201C13×C4⋊C4—41no—
202C13×C4⋊C4—41no—
203C13×C4⋊C4—41no—
204C13×C4⋊C4—41no—
205C13×C4⋊C4—81no—
206C13×C4⋊C4—82no—
207C13×C4⋊C4C2×D412yes—
208C13×C4⋊C4C2×D411yescharacteristic
209C13×C4⋊C4C2×D411yescharacteristic
210C13×C22⋊C4—22no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—22no—
214C13×C22⋊C4—22no—
215C13×C22⋊C4—21no—
216C13×C22⋊C4—21no—
217C13×C22⋊C4—21no—
218C13×C22⋊C4—21no—
219C13×C22⋊C4—22no—
220C13×C22⋊C4—21no—
221C13×C22⋊C4—22no—
222C42×C13—22no—
223C42×C13—21no—
224C42×C13C2×D411yescharacteristic
225C42×C13C2×D411yescharacteristic
226C42×C13C2×D411yescharacteristic
227C42×C13C2×D411yescharacteristic
228#3559C2×C1311yescharacteristic
229#3234C2×C1311yescharacteristic, complemented
230#3232C2×C1311yescharacteristic, complemented
231#2822C2×C1311yescharacteristic, complemented
232#1616C2×C1312yescomplemented
233#1615C2×C1312yescomplemented
234#1610C2×C1312yescomplemented
235#1609C2×C1312yescomplemented
236#1517C2×C1311yescharacteristic, complemented
237#1512C2×C1311yescharacteristic, complemented
238#1470C2×C1311yescharacteristic, complemented
239C23×C13—21no—
240C23×C13—22no—
241C23×C13C22×D411yescharacteristic
242Q8×C13—41no—
243Q8×C13—81no—
244Q8×C13—82no—
245D4×C13—42no—
246D4×C13—42no—
247D4×C13—41no—
248D4×C13—42no—
249D4×C13—41no—
250D4×C13—42no—
251D4×C13—41no—
252D4×C13—81no—
253D4×C13—82no—
254D4×C13—82no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—21no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—42no—
268C2×C4×C13—42no—
269C2×C4×C13—42no—
270C2×C4×C13—42no—
271C2×C4×C13—42no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—42no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—82no—
278C2×C4×C13—82no—
279C2×C4×C13—82no—
280C2×C4×C13—82no—
281C2×C4×C13#12011yescharacteristic
282C2×C4×C13#12011yescharacteristic
283C2×C4×C13#12011yescharacteristic
284C2×C4×C13#12011yescharacteristic
285C2×C4×C13C22×D411yescharacteristic
286C2×C4×C13C22×D411yescharacteristic
287C8×C13—42no—
288C8×C13—41no—
289C8×C13—41no—
290#563—21no—
291#562—21no—
292#554—21no—
293#553—21no—
294#553—21no—
295#547—22no—
296#547—21no—
297#544—21no—
298#540—21no—
299#539—22no—
300#539C22×C1312yes—
301#537C22×C1312yes—
302#532C22×C1311yescharacteristic
303#529C22×C1311yescharacteristic
304C2×#125C22×C1311yescharacteristic
305C2×#125C22×C1311yescharacteristic
306#501—21no—
307#499—21no—
308#490—21no—
309#488—21no—
310#484C22×C1311yescharacteristic
311#483C22×C1311yescharacteristic
312#481C22×C1312yes—
313#481C22×C1311yescharacteristic
314#480C22×C1312yes—
315#480C22×C1311yescharacteristic
316#479—21no—
317#478—21no—
318#478—22no—
319#432C22×C1311yescharacteristic
320#431C22×C1311yescharacteristic
321#400—21no—
322#400C22×C1312yes—
323#398—21no—
324#398—22no—
325#398C22×C1312yes—
326#382C22×C1311yescharacteristic
327#328C22×C1312yes—
328#327C22×C1312yes—
329#327C22×C1312yes—
330#327C22×C1312yes—
331#324C22×C1312yes—
332#324C22×C1312yes—
333C22×C13—21no—
334C22×C13—21no—
335C22×C13—42no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—42no—
339C22×C13—42no—
340C22×C13—41no—
341C22×C13C2×#12011yescharacteristic
342C22×C13#57611yescharacteristic
343C22×C13#57711yescharacteristic
344C4×C13—21no—
345C4×C13—21no—
346C4×C13—21no—
347C4×C13—21no—
348C4×C13—21no—
349C4×C13—21no—
350C4×C13—42no—
351C4×C13—42no—
352C4×C13—41no—
353C4×C13—41no—
354C4×C13—42no—
355C4×C13—41no—
356C4×C13—82no—
357C4×C13—81no—
358C4×C13—81no—
359C2×#41—21no—
360C2×#41—22no—
361C4⋊Q8—21no—
362C4⋊Q8—22no—
363C4⋊Q8D4×C1311yescharacteristic
364#127D4×C1311yescharacteristic
365#126—22no—
366#126—22no—
367#126—21no—
368#125—21no—
369#125—22no—
370#125—21no—
371#125—21no—
372#125—21no—
373#125—21no—
374#125—21no—
375#125—21no—
376#125—21no—
377#125—21no—
378#125D4×C1311yescharacteristic
379#124—21no—
380#124D4×C1311yescharacteristic
381#123—22no—
382#123—22no—
383#123—22no—
384#123—22no—
385#123—22no—
386#123—21no—
387#123—22no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8C23×C1311yescharacteristic
395#121—21no—
396#121—22no—
397#121—21no—
398#121—22no—
399#121—22no—
400#121—21no—
401#121—22no—
402#121C23×C1311yescharacteristic
403#121C23×C1312yes—
404C4×Q8D4×C1311yescharacteristic
405C4×D4—22no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—22no—
410C4×D4—21no—
411C4×D4D4×C1311yescharacteristic
412C4×D4D4×C1312yes—
413#117—21no—
414#117—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4D4×C1311yescharacteristic
422C2×C4⋊C4D4×C1312yes—
423C2×C4⋊C4D4×C1311yescharacteristic
424C2×C4⋊C4C23×C1311yescharacteristic
425C2×C4⋊C4C23×C1311yescharacteristic
426C2×C4⋊C4C23×C1312yes—
427C2×C42C23×C1311yescharacteristic
428#107—22no—
429#107—21no—
430#107—21no—
431#106—22no—
432#106—21no—
433#106—21no—
434C4⋊C8—21no—
435C4⋊C8—21no—
436#103—21no—
437#103—21no—
438#102—21no—
439#102—22no—
440#102—21no—
441#102—22no—
442C22⋊C8C23×C1311yescharacteristic
443C22⋊C8C23×C1311yescharacteristic
444C22⋊C8C23×C1312yes—
445#97—21no—
446C4×C8—21no—
447#95—21no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95C23×C1312yes—
452C2×C13—21no—
453C2×C13—21no—
454C2×C13—81no—
455C2×C13—82no—
456C2×C13#301211yescharacteristic
457C2×C13#302011yescharacteristic
458C2×C13#302811yescharacteristic
459#41—81no—
460#41—81no—
461#41—82no—
462#41—82no—
463C2×Q8—22no—
464C2×Q8—21no—
465C2×Q8C2×D4×C1311yescharacteristic
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4C2×D4×C1311yescharacteristic
473C2×D4C2×D4×C1312yes—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4C2×D4×C1312yes—
483C22×C4C2×D4×C1311yescharacteristic
484C22×C4C2×D4×C1312yes—
485C22×C4C2×D4×C1311yescharacteristic
486C22×C4C24×C1311yescharacteristic
487C2×C8—21no—
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—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—81no—
516C4⋊C4—82no—
517C4⋊C4C2×D4×C1312yes—
518C4⋊C4C2×D4×C1311yescharacteristic
519C4⋊C4C2×D4×C1311yescharacteristic
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—22no—
530C22⋊C4—21no—
531C22⋊C4—22no—
532C42—22no—
533C42—21no—
534C42C2×D4×C1311yescharacteristic
535C42C2×D4×C1311yescharacteristic
536C42C2×D4×C1311yescharacteristic
537C42C2×D4×C1311yescharacteristic
538C13#1846811yescharacteristic, direct product factor, Sylow
539C23—21no—
540C23—22no—
541C23C22×D4×C1311yescharacteristic
542Q8—41no—
543Q8—81no—
544Q8—82no—
545D4—42no—
546D4—41no—
547D4—42no—
548D4—42no—
549D4—41no—
550D4—42no—
551D4—41no—
552D4—81no—
553D4—82no—
554D4—82no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4—82no—
580C2×C4—82no—
581C2×C4C13×#12011yescharacteristic
582C2×C4C13×#12011yescharacteristic
583C2×C4C13×#12011yescharacteristic
584C2×C4C13×#12011yescharacteristic
585C2×C4C22×D4×C1311yescharacteristic
586C2×C4C22×D4×C1311yescharacteristic
587C8—42no—
588C8—41no—
589C8—41no—
590C22—21no—
591C22—21no—
592C22—42no—
593C22—41no—
594C22—41no—
595C22—42no—
596C22—42no—
597C22—41no—
598C22C2×C13×#12011yescharacteristic
599C22C13×#57611yescharacteristic
600C22C13×#57711yescharacteristic
601C4—21no—
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—42no—
609C4—41no—
610C4—41no—
611C4—42no—
612C4—41no—
613C4—82no—
614C4—81no—
615C4—81no—
616C2—21no—
617C2—21no—
618C2—81no—
619C2—82no—
620C2C13×#301211yescharacteristic
621C2C13×#302011yescharacteristic
622C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3559C2
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
2. C13×#3234C2semidirect
3. C13×#3232C2semidirect
4. C13×#2822C2semidirect
5. C13×#1616C2semidirect
6. C13×#1615C2semidirect
7. C13×#1610C2semidirect
8. C13×#1609C2semidirect
9. C13×#1517C2semidirect
10. C13×#1512C2semidirect
11. C13×#1470C2semidirect
148. #18468C13direct (N × H)
229. #3234C2×C13semidirect
230. #3232C2×C13semidirect
231. #2822C2×C13semidirect
232. #1616C2×C13semidirect
233. #1615C2×C13semidirect
234. #1610C2×C13semidirect
235. #1609C2×C13semidirect
236. #1517C2×C13semidirect
237. #1512C2×C13semidirect
238. #1470C2×C13semidirect
538. C13#18468direct (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×#32342
C13×#32322
C13×#28222
C13×#16162
C13×#16152
C13×#16102
C13×#16092
C13×#15172
C13×#15122
C13×#14702
#1846813