Finite Group Databasebeta

← C13×#18454 #15704793

Subgroups — C13×#18454 #15704793

Order 3328.

936 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3538C211yesmaximal, characteristic, complemented
2C13×#3194C211yesmaximal, characteristic
3C13×#3187C211yesmaximal, characteristic, complemented
4C13×#2816C211yesmaximal, characteristic, complemented
5C13×#1611C212yesmaximal, complemented
6C13×#1609C212yesmaximal, complemented
7C13×#1599C212yesmaximal, complemented
8C13×#1597C212yesmaximal, complemented
9C13×#1516C211yesmaximal, characteristic, complemented
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×#121C2211yescharacteristic
28C13×#483C2212yes—
29C13×#483C2211yescharacteristic
30C13×#482—21no—
31C13×#481—21no—
32C13×#480C2211yescharacteristic
33C13×#469—21no—
34C13×#468—21no—
35C13×#465—22no—
36C13×#450C2212yes—
37C13×#450C2211yescharacteristic
38C13×#449—21no—
39C13×#448—21no—
40C13×#447C2211yescharacteristic
41C13×#407C2211yescharacteristic
42C2×C13×C22⋊C8C2211yescharacteristic
43C13×#399—21no—
44C13×#398C2212yes—
45C13×#394—22no—
46C13×#394C2212yes—
47C13×#393—21no—
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×D4×C13—21no—
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C2×C13×SD16—22no—
63C2×C13×SD16—21no—
64C2×C13×D8—21no—
65C2×C13×M16—21no—
66C22×C8×C13—21no—
67C13×C4⋊Q8—21no—
68C13×C4⋊Q8—22no—
69C13×C4⋊Q8—22no—
70C13×C4⋊Q8—22no—
71C13×#126—22no—
72C13×#126—22no—
73C13×#126—22no—
74C13×#126—22no—
75C13×#125—21no—
76C13×#125—22no—
77C13×#125—22no—
78C13×#125—22no—
79C13×#125—22no—
80C13×#124—22no—
81C13×#123—22no—
82C13×#123—22no—
83C13×#123—22no—
84C13×#123—21no—
85C13×#123—22no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—21no—
92C13×C22⋊Q8—21no—
93C13×C22⋊Q8—21no—
94C13×C22⋊Q8—21no—
95C13×C22⋊Q8—21no—
96C13×C22⋊Q8—21no—
97C13×C22⋊Q8—22no—
98C13×C22⋊Q8D412yes—
99C13×C22⋊Q8D411yescharacteristic
100C13×C22⋊Q8C2312yes—
101C13×C22⋊Q8C2311yescharacteristic
102C13×#121—21no—
103C13×#121—21no—
104C13×#121—21no—
105C13×#121—21no—
106C13×#121D411yescharacteristic
107C13×#121C2311yescharacteristic
108C13×#120—21no—
109C4×Q8×C13—21no—
110C4×Q8×C13—21no—
111C4×D4×C13—22no—
112C4×D4×C13—21no—
113C4×D4×C13—21no—
114C4×D4×C13—22no—
115C13×#117—21no—
116C13×#117—22no—
117C13×#117—22no—
118C13×#117D411yescharacteristic
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⋊C4—22no—
129C2×C13×C22⋊C4—22no—
130C2×C13×C22⋊C4D412yes—
131C13×#107—21no—
132C13×#106—22no—
133C13×#106—21no—
134C13×#103—22no—
135C13×#103—21no—
136C13×#102—21no—
137C13×#102—21no—
138C13×#102—22no—
139C13×#102—21no—
140C13×C22⋊C8—21no—
141C13×C22⋊C8—21no—
142C13×C22⋊C8C2312yes—
143C13×C22⋊C8C2311yescharacteristic
144C13×C22⋊C8C2311yescharacteristic
145C13×#95—21no—
146C13×#95—22no—
147C13×#95C2312yes—
148#18454C1311yesmaximal, characteristic, direct product factor, Sylow
149C24×C13—21no—
150C24×C13C2×D411yescharacteristic
151C13×#41—81no—
152C2×Q8×C13—22no—
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13—81no—
157C2×Q8×C13—82no—
158C2×Q8×C13—81no—
159C2×Q8×C13C2×D412yes—
160C2×Q8×C13C2×D411yescharacteristic
161C2×D4×C13—21no—
162C2×D4×C13—21no—
163C2×D4×C13—21no—
164C2×D4×C13—21no—
165C2×D4×C13—21no—
166C2×D4×C13—41no—
167C2×D4×C13—41no—
168C2×D4×C13—81no—
169C2×D4×C13—82no—
170C2×D4×C13C2×D411yescharacteristic
171C22×C4×C13—21no—
172C22×C4×C13—22no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—22no—
176C22×C4×C13—21no—
177C22×C4×C13—81no—
178C22×C4×C13C2×D412yes—
179C22×C4×C13C2×D412yes—
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2×D411yescharacteristic
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2411yescharacteristic
186C13×SD16—82no—
187C13×SD16—81no—
188C13×D8—81no—
189C13×M16—81no—
190C2×C8×C13—21no—
191C2×C8×C13—22no—
192C2×C8×C13—21no—
193C2×C8×C13—81no—
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—22no—
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⋊C4—22no—
208C13×C4⋊C4—22no—
209C13×C4⋊C4—22no—
210C13×C4⋊C4—21no—
211C13×C4⋊C4—21no—
212C13×C4⋊C4—21no—
213C13×C4⋊C4—82no—
214C13×C4⋊C4C2×D412yes—
215C13×C4⋊C4C2×D411yescharacteristic
216C13×C4⋊C4C2×D411yescharacteristic
217C13×C22⋊C4—22no—
218C13×C22⋊C4—22no—
219C13×C22⋊C4—22no—
220C13×C22⋊C4—22no—
221C13×C22⋊C4—22no—
222C13×C22⋊C4—22no—
223C13×C22⋊C4—21no—
224C13×C22⋊C4—21no—
225C13×C22⋊C4—22no—
226C13×C22⋊C4—21no—
227C13×C22⋊C4—21no—
228C13×C22⋊C4—21no—
229C13×C22⋊C4—41no—
230C13×C22⋊C4—41no—
231C13×C22⋊C4—82no—
232C13×C22⋊C4—82no—
233C13×C22⋊C4—81no—
234C42×C13—22no—
235C42×C13—22no—
236C42×C13—22no—
237C42×C13—21no—
238#3538C2×C1311yescharacteristic, complemented
239#3194C2×C1311yescharacteristic
240#3187C2×C1311yescharacteristic, complemented
241#2816C2×C1311yescharacteristic, complemented
242#1611C2×C1312yescomplemented
243#1609C2×C1312yescomplemented
244#1599C2×C1312yescomplemented
245#1597C2×C1312yescomplemented
246#1516C2×C1311yescharacteristic, complemented
247#1511C2×C1311yescharacteristic, complemented
248#1472C2×C1311yescharacteristic, complemented
249C23×C13—22no—
250C23×C13—21no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—42no—
254C23×C13—42no—
255C23×C13—41no—
256C23×C13—42no—
257C23×C13#12011yescharacteristic
258C23×C13#12011yescharacteristic
259C23×C13C22×D411yescharacteristic
260Q8×C13—42no—
261Q8×C13—42no—
262Q8×C13—42no—
263Q8×C13—41no—
264Q8×C13—81no—
265Q8×C13—82no—
266D4×C13—41no—
267D4×C13—41no—
268D4×C13—41no—
269D4×C13—42no—
270D4×C13—42no—
271D4×C13—42no—
272D4×C13—81no—
273D4×C13—82no—
274D4×C13—82no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—21no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—41no—
296C2×C4×C13—42no—
297C2×C4×C13—42no—
298C2×C4×C13—81no—
299C2×C4×C13—82no—
300C2×C4×C13#12011yescharacteristic
301C2×C4×C13#12011yescharacteristic
302C2×C4×C13C22×D411yescharacteristic
303C2×C4×C13C22×D411yescharacteristic
304C8×C13—42no—
305C8×C13—41no—
306C8×C13—41no—
307#563—22no—
308#552—21no—
309#552—21no—
310#551—22no—
311D4×Q8—21no—
312D4×Q8—21no—
313#544—21no—
314#544C22×C1312yes—
315#541—21no—
316#539—21no—
317#539C22×C1312yes—
318#536—21no—
319#525C22×C1311yescharacteristic
320C2×C22⋊Q8C22×C1311yescharacteristic
321C2×C22⋊Q8C22×C1311yescharacteristic
322C2×#121C22×C1311yescharacteristic
323#483C22×C1312yes—
324#483C22×C1311yescharacteristic
325#482—21no—
326#481—21no—
327#480C22×C1311yescharacteristic
328#469—21no—
329#468—21no—
330#465—22no—
331#450C22×C1312yes—
332#450C22×C1311yescharacteristic
333#449—21no—
334#448—21no—
335#447C22×C1311yescharacteristic
336#407C22×C1311yescharacteristic
337C2×C22⋊C8C22×C1311yescharacteristic
338#399—21no—
339#398C22×C1312yes—
340#394—22no—
341#394C22×C1312yes—
342#393—21no—
343#381C22×C1311yescharacteristic
344#328C22×C1312yes—
345#328C22×C1312yes—
346#328C22×C1312yes—
347#327C22×C1312yes—
348#324C22×C1312yes—
349#324C22×C1312yes—
350C22×C13—21no—
351C22×C13—21no—
352C22×C13—21no—
353C22×C13—21no—
354C22×C13—21no—
355C22×C13—21no—
356C22×C13—21no—
357C22×C13—21no—
358C22×C13—41no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13—82no—
362C22×C13—84no—
363C22×C13—81no—
364C22×C13—81no—
365C22×C13—81no—
366C22×C13C2×#12011yescharacteristic
367C22×C13#57712yes—
368C4×C13—21no—
369C4×C13—21no—
370C4×C13—21no—
371C4×C13—21no—
372C4×C13—42no—
373C4×C13—41no—
374C4×C13—42no—
375C4×C13—41no—
376C4×C13—41no—
377C4×C13—42no—
378C4×C13—42no—
379C4×C13—82no—
380C4×C13—81no—
381C2×#41D4×C1311yescharacteristic
382C22×Q8—21no—
383C22×Q8D4×C1311yescharacteristic
384C22×Q8D4×C1311yescharacteristic
385C22×D4—21no—
386C22×D4C23×C1311yescharacteristic
387C23×C4C23×C1311yescharacteristic
388C2×SD16—22no—
389C2×SD16—21no—
390C2×D8—21no—
391C2×M16—21no—
392C22×C8—21no—
393C4⋊Q8—21no—
394C4⋊Q8—22no—
395C4⋊Q8—22no—
396C4⋊Q8—22no—
397#126—22no—
398#126—22no—
399#126—22no—
400#126—22no—
401#125—21no—
402#125—22no—
403#125—22no—
404#125—22no—
405#125—22no—
406#124—22no—
407#123—22no—
408#123—22no—
409#123—22no—
410#123—21no—
411#123—22no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C22⋊Q8—22no—
424C22⋊Q8D4×C1312yes—
425C22⋊Q8D4×C1311yescharacteristic
426C22⋊Q8C23×C1312yes—
427C22⋊Q8C23×C1311yescharacteristic
428#121—21no—
429#121—21no—
430#121—21no—
431#121—21no—
432#121D4×C1311yescharacteristic
433#121C23×C1311yescharacteristic
434#120—21no—
435C4×Q8—21no—
436C4×Q8—21no—
437C4×D4—22no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—22no—
441#117—21no—
442#117—22no—
443#117—22no—
444#117D4×C1311yescharacteristic
445C2×C4⋊C4—21no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4D4×C1311yescharacteristic
448C2×C4⋊C4D4×C1311yescharacteristic
449C2×C4⋊C4C23×C1311yescharacteristic
450C2×C4⋊C4C23×C1312yes—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4D4×C1312yes—
457#107—21no—
458#106—22no—
459#106—21no—
460#103—22no—
461#103—21no—
462#102—21no—
463#102—21no—
464#102—22no—
465#102—21no—
466C22⋊C8—21no—
467C22⋊C8—21no—
468C22⋊C8C23×C1312yes—
469C22⋊C8C23×C1311yescharacteristic
470C22⋊C8C23×C1311yescharacteristic
471#95—21no—
472#95—22no—
473#95C23×C1312yes—
474C2×C13—22no—
475C2×C13—41no—
476C2×C13—41no—
477C2×C13—81no—
478C2×C13—161no—
479C2×C13#301011yescharacteristic
480C2×C13#302011yescharacteristic
481C2×C13#302611yescharacteristic
482C24—21no—
483C24C2×D4×C1311yescharacteristic
484#41—81no—
485C2×Q8—22no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—81no—
490C2×Q8—82no—
491C2×Q8—81no—
492C2×Q8C2×D4×C1312yes—
493C2×Q8C2×D4×C1311yescharacteristic
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—41no—
500C2×D4—41no—
501C2×D4—81no—
502C2×D4—82no—
503C2×D4C2×D4×C1311yescharacteristic
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—81no—
511C22×C4C2×D4×C1312yes—
512C22×C4C2×D4×C1312yes—
513C22×C4C2×D4×C1311yescharacteristic
514C22×C4C2×D4×C1311yescharacteristic
515C22×C4C2×D4×C1311yescharacteristic
516C22×C4C2×D4×C1311yescharacteristic
517C22×C4C2×D4×C1311yescharacteristic
518C22×C4C24×C1311yescharacteristic
519SD16—82no—
520SD16—81no—
521D8—81no—
522M16—81no—
523C2×C8—21no—
524C2×C8—22no—
525C2×C8—21no—
526C2×C8—81no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—82no—
547C4⋊C4C2×D4×C1312yes—
548C4⋊C4C2×D4×C1311yescharacteristic
549C4⋊C4C2×D4×C1311yescharacteristic
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—22no—
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—82no—
565C22⋊C4—82no—
566C22⋊C4—81no—
567C42—22no—
568C42—22no—
569C42—22no—
570C42—21no—
571C13#1845411yescharacteristic, direct product factor, Sylow
572C23—22no—
573C23—21no—
574C23—41no—
575C23—41no—
576C23—42no—
577C23—42no—
578C23—41no—
579C23—42no—
580C23C13×#12011yescharacteristic
581C23C13×#12011yescharacteristic
582C23C22×D4×C1311yescharacteristic
583Q8—42no—
584Q8—41no—
585Q8—42no—
586Q8—42no—
587Q8—81no—
588Q8—82no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—42no—
593D4—42no—
594D4—42no—
595D4—81no—
596D4—82no—
597D4—82no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—81no—
622C2×C4—82no—
623C2×C4C13×#12011yescharacteristic
624C2×C4C13×#12011yescharacteristic
625C2×C4C22×D4×C1311yescharacteristic
626C2×C4C22×D4×C1311yescharacteristic
627C8—42no—
628C8—41no—
629C8—41no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—82no—
642C22—84no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22C2×C13×#12011yescharacteristic
647C22C13×#57712yes—
648C4—21no—
649C4—21no—
650C4—21no—
651C4—21no—
652C4—42no—
653C4—41no—
654C4—42no—
655C4—41no—
656C4—41no—
657C4—42no—
658C4—42no—
659C4—82no—
660C4—81no—
661C2—22no—
662C2—41no—
663C2—41no—
664C2—81no—
665C2—161no—
666C2C13×#301011yescharacteristic
667C2C13×#302011yescharacteristic
668C2C13×#302611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3194C2
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
1. C13×#3538C2semidirect
3. C13×#3187C2semidirect
4. C13×#2816C2semidirect
5. C13×#1611C2semidirect
6. C13×#1609C2semidirect
7. C13×#1599C2semidirect
8. C13×#1597C2semidirect
9. C13×#1516C2semidirect
10. C13×#1511C2semidirect
11. C13×#1472C2semidirect
148. #18454C13direct (N × H)
238. #3538C2×C13semidirect
240. #3187C2×C13semidirect
241. #2816C2×C13semidirect
242. #1611C2×C13semidirect
243. #1609C2×C13semidirect
244. #1599C2×C13semidirect
245. #1597C2×C13semidirect
246. #1516C2×C13semidirect
247. #1511C2×C13semidirect
248. #1472C2×C13semidirect
571. C13#18454direct (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×#31942
C13×#31872
C13×#28162
C13×#16112
C13×#16092
C13×#15992
C13×#15972
C13×#15162
C13×#15112
C13×#14722
#1845413