Finite Group Databasebeta

← C13×#18455 #15704794

Subgroups — C13×#18455 #15704794

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3538C211yesmaximal, characteristic
2C13×#3196C211yesmaximal, characteristic
3C13×#3189C211yesmaximal, characteristic, complemented
4C13×#2817C211yesmaximal, characteristic, complemented
5C13×#1617C212yesmaximal, complemented
6C13×#1615C212yesmaximal, complemented
7C13×#1605C212yesmaximal, complemented
8C13×#1603C212yesmaximal, complemented
9C13×#1516C211yesmaximal, characteristic
10C13×#1511C211yesmaximal, characteristic, complemented
11C13×#1472C211yesmaximal, characteristic, complemented
12C13×#563—22no—
13C13×#552—21no—
14C13×#552—21no—
15C13×#551—22no—
16D4×Q8×C13—21no—
17D4×Q8×C13—21no—
18C13×#544—21no—
19C13×#544C2212yes—
20C13×#541—21no—
21C13×#539—21no—
22C13×#539C2212yes—
23C13×#536—21no—
24C13×#525C2211yescharacteristic
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C13×C22⋊Q8C2211yescharacteristic
27C2×C13×C22⋊Q8C2211yescharacteristic
28C13×#485—21no—
29C13×#484—21no—
30C13×#484C2212yes—
31C13×#484C2211yescharacteristic
32C13×#481C2211yescharacteristic
33C13×#470—21no—
34C13×#468—21no—
35C13×#467—22no—
36C13×#452—21no—
37C13×#451—21no—
38C13×#451C2212yes—
39C13×#451C2211yescharacteristic
40C13×#448C2211yescharacteristic
41C13×#407C2211yescharacteristic
42C2×C13×C22⋊C8C2211yescharacteristic
43C13×#400—21no—
44C13×#400C2212yes—
45C13×#397—22no—
46C13×#395—21no—
47C13×#395C2212yes—
48C13×#381C2211yescharacteristic
49C13×#328C2212yes—
50C13×#328C2212yes—
51C13×#328C2212yes—
52C13×#327C2212yes—
53C13×#324C2212yes—
54C13×#324C2212yes—
55C2×C13×#41D411yescharacteristic
56C22×Q8×C13—21no—
57C22×Q8×C13D411yescharacteristic
58C22×Q8×C13D411yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C2×C13×Q16—22no—
62C2×C13×Q16—21no—
63C2×C13×SD16—21no—
64C2×C13×M16—21no—
65C22×C8×C13—21no—
66C13×C4⋊Q8—21no—
67C13×C4⋊Q8—22no—
68C13×C4⋊Q8—22no—
69C13×C4⋊Q8—22no—
70C13×#126—22no—
71C13×#126—22no—
72C13×#126—22no—
73C13×#126—22no—
74C13×#125—21no—
75C13×#125—22no—
76C13×#125—22no—
77C13×#125—22no—
78C13×#125—22no—
79C13×#124—22no—
80C13×#123—22no—
81C13×#123—22no—
82C13×#123—22no—
83C13×#123—21no—
84C13×#123—22no—
85C13×C22⋊Q8—21no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—21no—
91C13×C22⋊Q8—21no—
92C13×C22⋊Q8—21no—
93C13×C22⋊Q8—21no—
94C13×C22⋊Q8—21no—
95C13×C22⋊Q8—21no—
96C13×C22⋊Q8—22no—
97C13×C22⋊Q8—21no—
98C13×C22⋊Q8—21no—
99C13×C22⋊Q8—21no—
100C13×C22⋊Q8—21no—
101C13×C22⋊Q8D412yes—
102C13×C22⋊Q8D411yescharacteristic
103C13×C22⋊Q8C2312yes—
104C13×C22⋊Q8C2311yescharacteristic
105C13×#121D411yescharacteristic
106C13×#121C2311yescharacteristic
107C13×#120—21no—
108C4×Q8×C13—21no—
109C4×Q8×C13—21no—
110C4×D4×C13—22no—
111C4×D4×C13—21no—
112C4×D4×C13—21no—
113C4×D4×C13—22no—
114C13×#117—21no—
115C13×#117—22no—
116C13×#117—22no—
117C13×#117D411yescharacteristic
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—22no—
121C2×C13×C4⋊C4D411yescharacteristic
122C2×C13×C4⋊C4D411yescharacteristic
123C2×C13×C4⋊C4C2311yescharacteristic
124C2×C13×C4⋊C4C2312yes—
125C2×C13×C22⋊C4—21no—
126C2×C13×C22⋊C4—21no—
127C2×C13×C22⋊C4—21no—
128C2×C13×C22⋊C4D412yes—
129C13×#107—22no—
130C13×#107—21no—
131C13×#106—21no—
132C13×#103—22no—
133C13×#103—21no—
134C13×#103—21no—
135C13×#103—22no—
136C13×#103—21no—
137C13×#102—21no—
138C13×C22⋊C8—21no—
139C13×C22⋊C8—21no—
140C13×C22⋊C8C2312yes—
141C13×C22⋊C8C2311yescharacteristic
142C13×C22⋊C8C2311yescharacteristic
143C13×#95—21no—
144C13×#95—22no—
145C13×#95—22no—
146C13×#95—22no—
147C13×#95C2312yes—
148#18455C1311yesmaximal, characteristic, direct product factor, Sylow
149C24×C13C2×D411yescharacteristic
150C13×#41—81no—
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—81no—
158C2×Q8×C13—81no—
159C2×Q8×C13—82no—
160C2×Q8×C13—81no—
161C2×Q8×C13C2×D412yes—
162C2×Q8×C13C2×D411yescharacteristic
163C2×D4×C13—21no—
164C2×D4×C13—21no—
165C2×D4×C13—21no—
166C2×D4×C13C2×D411yescharacteristic
167C22×C4×C13—21no—
168C22×C4×C13—22no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—22no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—81no—
175C22×C4×C13C2×D412yes—
176C22×C4×C13C2×D412yes—
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2411yescharacteristic
183C13×Q16—82no—
184C13×Q16—81no—
185C13×SD16—81no—
186C13×M16—81no—
187C2×C8×C13—21no—
188C2×C8×C13—22no—
189C2×C8×C13—21no—
190C2×C8×C13—81no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—22no—
198C13×C4⋊C4—22no—
199C13×C4⋊C4—22no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—22no—
205C13×C4⋊C4—22no—
206C13×C4⋊C4—22no—
207C13×C4⋊C4—21no—
208C13×C4⋊C4—21no—
209C13×C4⋊C4—21no—
210C13×C4⋊C4—41no—
211C13×C4⋊C4—41no—
212C13×C4⋊C4—82no—
213C13×C4⋊C4C2×D411yescharacteristic
214C13×C4⋊C4C2×D412yes—
215C13×C4⋊C4C2×D411yescharacteristic
216C13×C22⋊C4—22no—
217C13×C22⋊C4—22no—
218C13×C22⋊C4—22no—
219C13×C22⋊C4—22no—
220C13×C22⋊C4—22no—
221C13×C22⋊C4—22no—
222C13×C22⋊C4—21no—
223C13×C22⋊C4—21no—
224C13×C22⋊C4—22no—
225C13×C22⋊C4—21no—
226C13×C22⋊C4—21no—
227C13×C22⋊C4—21no—
228C13×C22⋊C4—41no—
229C13×C22⋊C4—41no—
230C13×C22⋊C4—81no—
231C42×C13—22no—
232C42×C13—22no—
233C42×C13—22no—
234C42×C13—21no—
235#3538C2×C1311yescharacteristic
236#3196C2×C1311yescharacteristic
237#3189C2×C1311yescharacteristic, complemented
238#2817C2×C1311yescharacteristic, complemented
239#1617C2×C1312yescomplemented
240#1615C2×C1312yescomplemented
241#1605C2×C1312yescomplemented
242#1603C2×C1312yescomplemented
243#1516C2×C1311yescharacteristic
244#1511C2×C1311yescharacteristic, complemented
245#1472C2×C1311yescharacteristic, complemented
246C23×C13—22no—
247C23×C13—21no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13#12011yescharacteristic
251C23×C13#12011yescharacteristic
252C23×C13C22×D411yescharacteristic
253Q8×C13—42no—
254Q8×C13—42no—
255Q8×C13—42no—
256Q8×C13—41no—
257Q8×C13—41no—
258Q8×C13—41no—
259Q8×C13—42no—
260Q8×C13—81no—
261Q8×C13—82no—
262D4×C13—41no—
263D4×C13—42no—
264D4×C13—42no—
265D4×C13—81no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—21no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—24no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13—42no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—42no—
290C2×C4×C13—81no—
291C2×C4×C13—82no—
292C2×C4×C13#12011yescharacteristic
293C2×C4×C13#12011yescharacteristic
294C2×C4×C13C22×D411yescharacteristic
295C2×C4×C13C22×D411yescharacteristic
296C8×C13—42no—
297C8×C13—41no—
298C8×C13—41no—
299#563—22no—
300#552—21no—
301#552—21no—
302#551—22no—
303D4×Q8—21no—
304D4×Q8—21no—
305#544—21no—
306#544C22×C1312yes—
307#541—21no—
308#539—21no—
309#539C22×C1312yes—
310#536—21no—
311#525C22×C1311yescharacteristic
312C2×C22⋊Q8C22×C1311yescharacteristic
313C2×C22⋊Q8C22×C1311yescharacteristic
314C2×C22⋊Q8C22×C1311yescharacteristic
315#485—21no—
316#484—21no—
317#484C22×C1312yes—
318#484C22×C1311yescharacteristic
319#481C22×C1311yescharacteristic
320#470—21no—
321#468—21no—
322#467—22no—
323#452—21no—
324#451—21no—
325#451C22×C1312yes—
326#451C22×C1311yescharacteristic
327#448C22×C1311yescharacteristic
328#407C22×C1311yescharacteristic
329C2×C22⋊C8C22×C1311yescharacteristic
330#400—21no—
331#400C22×C1312yes—
332#397—22no—
333#395—21no—
334#395C22×C1312yes—
335#381C22×C1311yescharacteristic
336#328C22×C1312yes—
337#328C22×C1312yes—
338#328C22×C1312yes—
339#327C22×C1312yes—
340#324C22×C1312yes—
341#324C22×C1312yes—
342C22×C13—21no—
343C22×C13—21no—
344C22×C13—21no—
345C22×C13—21no—
346C22×C13—21no—
347C22×C13—21no—
348C22×C13—21no—
349C22×C13—21no—
350C22×C13—41no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13—82no—
354C22×C13C2×#12011yescharacteristic
355C22×C13#57812yes—
356C4×C13—21no—
357C4×C13—21no—
358C4×C13—21no—
359C4×C13—21no—
360C4×C13—42no—
361C4×C13—41no—
362C4×C13—42no—
363C4×C13—41no—
364C4×C13—41no—
365C4×C13—42no—
366C4×C13—42no—
367C4×C13—82no—
368C4×C13—81no—
369C4×C13—81no—
370C2×#41D4×C1311yescharacteristic
371C22×Q8—21no—
372C22×Q8D4×C1311yescharacteristic
373C22×Q8D4×C1311yescharacteristic
374C22×Q8C23×C1311yescharacteristic
375C23×C4C23×C1311yescharacteristic
376C2×Q16—22no—
377C2×Q16—21no—
378C2×SD16—21no—
379C2×M16—21no—
380C22×C8—21no—
381C4⋊Q8—21no—
382C4⋊Q8—22no—
383C4⋊Q8—22no—
384C4⋊Q8—22no—
385#126—22no—
386#126—22no—
387#126—22no—
388#126—22no—
389#125—21no—
390#125—22no—
391#125—22no—
392#125—22no—
393#125—22no—
394#124—22no—
395#123—22no—
396#123—22no—
397#123—22no—
398#123—21no—
399#123—22no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—22no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8D4×C1312yes—
417C22⋊Q8D4×C1311yescharacteristic
418C22⋊Q8C23×C1312yes—
419C22⋊Q8C23×C1311yescharacteristic
420#121D4×C1311yescharacteristic
421#121C23×C1311yescharacteristic
422#120—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×D4—22no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—22no—
429#117—21no—
430#117—22no—
431#117—22no—
432#117D4×C1311yescharacteristic
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4D4×C1311yescharacteristic
437C2×C4⋊C4D4×C1311yescharacteristic
438C2×C4⋊C4C23×C1311yescharacteristic
439C2×C4⋊C4C23×C1312yes—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4D4×C1312yes—
444#107—22no—
445#107—21no—
446#106—21no—
447#103—22no—
448#103—21no—
449#103—21no—
450#103—22no—
451#103—21no—
452#102—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C22⋊C8C23×C1312yes—
456C22⋊C8C23×C1311yescharacteristic
457C22⋊C8C23×C1311yescharacteristic
458#95—21no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95C23×C1312yes—
463C2×C13—22no—
464C2×C13—41no—
465C2×C13—41no—
466C2×C13—81no—
467C2×C13#301111yescharacteristic
468C2×C13#302011yescharacteristic
469C2×C13#302611yescharacteristic
470C24C2×D4×C1311yescharacteristic
471#41—81no—
472C2×Q8—22no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—81no—
479C2×Q8—81no—
480C2×Q8—82no—
481C2×Q8—81no—
482C2×Q8C2×D4×C1312yes—
483C2×Q8C2×D4×C1311yescharacteristic
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4C2×D4×C1311yescharacteristic
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—81no—
496C22×C4C2×D4×C1312yes—
497C22×C4C2×D4×C1312yes—
498C22×C4C2×D4×C1311yescharacteristic
499C22×C4C2×D4×C1311yescharacteristic
500C22×C4C2×D4×C1311yescharacteristic
501C22×C4C2×D4×C1311yescharacteristic
502C22×C4C2×D4×C1311yescharacteristic
503C22×C4C24×C1311yescharacteristic
504Q16—82no—
505Q16—81no—
506SD16—81no—
507M16—81no—
508C2×C8—21no—
509C2×C8—22no—
510C2×C8—21no—
511C2×C8—81no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—82no—
534C4⋊C4C2×D4×C1311yescharacteristic
535C4⋊C4C2×D4×C1312yes—
536C4⋊C4C2×D4×C1311yescharacteristic
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—22no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—81no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—21no—
556C13#1845511yescharacteristic, direct product factor, Sylow
557C23—22no—
558C23—21no—
559C23—41no—
560C23—41no—
561C23C13×#12011yescharacteristic
562C23C13×#12011yescharacteristic
563C23C22×D4×C1311yescharacteristic
564Q8—42no—
565Q8—41no—
566Q8—42no—
567Q8—42no—
568Q8—41no—
569Q8—41no—
570Q8—42no—
571Q8—81no—
572Q8—82no—
573D4—41no—
574D4—42no—
575D4—42no—
576D4—81no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—81no—
602C2×C4—82no—
603C2×C4C13×#12011yescharacteristic
604C2×C4C13×#12011yescharacteristic
605C2×C4C22×D4×C1311yescharacteristic
606C2×C4C22×D4×C1311yescharacteristic
607C8—42no—
608C8—41no—
609C8—41no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—82no—
622C22C2×C13×#12011yescharacteristic
623C22C13×#57812yes—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—42no—
629C4—41no—
630C4—42no—
631C4—41no—
632C4—41no—
633C4—42no—
634C4—42no—
635C4—82no—
636C4—81no—
637C4—81no—
638C2—22no—
639C2—41no—
640C2—41no—
641C2—81no—
642C2C13×#301111yescharacteristic
643C2C13×#302011yescharacteristic
644C2C13×#302611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#3189C2semidirect
4. C13×#2817C2semidirect
5. C13×#1617C2semidirect
6. C13×#1615C2semidirect
7. C13×#1605C2semidirect
8. C13×#1603C2semidirect
10. C13×#1511C2semidirect
11. C13×#1472C2semidirect
148. #18455C13direct (N × H)
237. #3189C2×C13semidirect
238. #2817C2×C13semidirect
239. #1617C2×C13semidirect
240. #1615C2×C13semidirect
241. #1605C2×C13semidirect
242. #1603C2×C13semidirect
244. #1511C2×C13semidirect
245. #1472C2×C13semidirect
556. C13#18455direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35382
C13×#31962
C13×#31892
C13×#28172
C13×#16172
C13×#16152
C13×#16052
C13×#16032
C13×#15162
C13×#15112
C13×#14722
#1845513