Finite Group Databasebeta

← C13×#18238 #15704577

Subgroups — C13×#18238 #15704577

Order 3328.

900 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3538C211yesmaximal, characteristic
2C13×#3095C211yesmaximal, characteristic, complemented
3C13×#3091C211yesmaximal, characteristic
4C13×#2625C211yesmaximal, characteristic, complemented
5C13×#1617C212yesmaximal, complemented
6C13×#1615C212yesmaximal, complemented
7C13×#1611C212yesmaximal, complemented
8C13×#1609C212yesmaximal, complemented
9C13×#1520C211yesmaximal, characteristic, complemented
10C13×#1513C211yesmaximal, characteristic
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×#117C2211yescharacteristic
28C13×#485—21no—
29C13×#485—22no—
30C13×#484C2211yescharacteristic
31C13×#484C2212yes—
32C13×#483C2211yescharacteristic
33C13×#483C2212yes—
34C13×#482—21no—
35C13×#481C2211yescharacteristic
36C13×#480C2211yescharacteristic
37C13×#428—21no—
38C13×#427—21no—
39C13×#419—21no—
40C13×#416—21no—
41C13×#407C2211yescharacteristic
42C2×C13×C22⋊C8C2211yescharacteristic
43C13×#400C2212yes—
44C13×#398C2212yes—
45C13×#397—22no—
46C13×#391—21no—
47C13×#389—21no—
48C13×#380C2211yescharacteristic
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
59C23×C4×C13C2311yescharacteristic
60C2×C13×M16—21no—
61C22×C8×C13—21no—
62C13×C4⋊Q8—21no—
63C13×C4⋊Q8—22no—
64C13×C4⋊Q8—22no—
65C13×C4⋊Q8—22no—
66C13×#126—22no—
67C13×#126—22no—
68C13×#126—22no—
69C13×#126—22no—
70C13×#125—21no—
71C13×#125—22no—
72C13×#125—22no—
73C13×#125—22no—
74C13×#125—22no—
75C13×#124—22no—
76C13×#123—22no—
77C13×#123—22no—
78C13×#123—22no—
79C13×#123—21no—
80C13×#123—22no—
81C13×C22⋊Q8—21no—
82C13×C22⋊Q8—21no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—21no—
91C13×C22⋊Q8—21no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8D412yes—
94C13×C22⋊Q8D411yescharacteristic
95C13×C22⋊Q8C2312yes—
96C13×C22⋊Q8C2311yescharacteristic
97C13×#121D411yescharacteristic
98C13×#121C2311yescharacteristic
99C13×#120—21no—
100C4×Q8×C13—21no—
101C4×Q8×C13—21no—
102C4×D4×C13—22no—
103C4×D4×C13—21no—
104C4×D4×C13—21no—
105C4×D4×C13—22no—
106C13×#117—21no—
107C13×#117—22no—
108C13×#117—22no—
109C13×#117—21no—
110C13×#117—21no—
111C13×#117—21no—
112C13×#117—21no—
113C13×#117D411yescharacteristic
114C2×C13×C4⋊C4—21no—
115C2×C13×C4⋊C4—21no—
116C2×C13×C4⋊C4—22no—
117C2×C13×C4⋊C4D411yescharacteristic
118C2×C13×C4⋊C4D411yescharacteristic
119C2×C13×C4⋊C4C2311yescharacteristic
120C2×C13×C4⋊C4C2311yescharacteristic
121C2×C13×C4⋊C4C2312yes—
122C2×C13×C22⋊C4—21no—
123C2×C13×C22⋊C4—21no—
124C2×C13×C22⋊C4—21no—
125C2×C13×C22⋊C4D412yes—
126C2×C42×C13—21no—
127C13×#107—21no—
128C13×#107—21no—
129C13×#107—22no—
130C13×#106—21no—
131C13×#106—21no—
132C13×#106—22no—
133C13×#103—21no—
134C13×#103—21no—
135C13×#103—22no—
136C13×#103—22no—
137C13×#102—21no—
138C13×#102—21no—
139C13×C22⋊C8—21no—
140C13×C22⋊C8—21no—
141C13×C22⋊C8C2312yes—
142C13×C22⋊C8C2311yescharacteristic
143C13×C22⋊C8C2311yescharacteristic
144C13×#95—22no—
145C13×#95—22no—
146C13×#95—22no—
147C13×#95C2312yes—
148#18238C1311yesmaximal, characteristic, direct product factor, Sylow
149C24×C13C2×D411yescharacteristic
150C13×#41—42no—
151C2×Q8×C13—22no—
152C2×Q8×C13—21no—
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13—42no—
156C2×Q8×C13—42no—
157C2×Q8×C13—82no—
158C2×Q8×C13C2×D412yes—
159C2×Q8×C13C2×D411yescharacteristic
160C2×D4×C13—21no—
161C2×D4×C13—21no—
162C2×D4×C13—21no—
163C2×D4×C13C2×D411yescharacteristic
164C22×C4×C13—21no—
165C22×C4×C13—22no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—22no—
170C22×C4×C13—21no—
171C22×C4×C13—42no—
172C22×C4×C13C2×D412yes—
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D412yes—
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2411yescharacteristic
180C13×M16—42no—
181C2×C8×C13—21no—
182C2×C8×C13—21no—
183C2×C8×C13—22no—
184C2×C8×C13—42no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—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—21no—
198C13×C4⋊C4—22no—
199C13×C4⋊C4—22no—
200C13×C4⋊C4—22no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—42no—
207C13×C4⋊C4—82no—
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—22no—
217C13×C22⋊C4—21no—
218C13×C22⋊C4—21no—
219C13×C22⋊C4—22no—
220C13×C22⋊C4—21no—
221C13×C22⋊C4—21no—
222C13×C22⋊C4—21no—
223C13×C22⋊C4—41no—
224C13×C22⋊C4—41no—
225C13×C22⋊C4—81no—
226C42×C13—22no—
227C42×C13—22no—
228C42×C13—22no—
229C42×C13—21no—
230C42×C13—41no—
231C42×C13—41no—
232#3538C2×C1311yescharacteristic
233#3095C2×C1311yescharacteristic, complemented
234#3091C2×C1311yescharacteristic
235#2625C2×C1311yescharacteristic, complemented
236#1617C2×C1312yescomplemented
237#1615C2×C1312yescomplemented
238#1611C2×C1312yescomplemented
239#1609C2×C1312yescomplemented
240#1520C2×C1311yescharacteristic, complemented
241#1513C2×C1311yescharacteristic
242#1472C2×C1311yescharacteristic, complemented
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13#12011yescharacteristic
249C23×C13#12011yescharacteristic
250C23×C13C22×D411yescharacteristic
251Q8×C13—42no—
252Q8×C13—41no—
253Q8×C13—42no—
254Q8×C13—42no—
255Q8×C13—81no—
256Q8×C13—82no—
257D4×C13—41no—
258D4×C13—42no—
259D4×C13—41no—
260D4×C13—41no—
261D4×C13—81no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
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—22no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—42no—
278C2×C4×C13—42no—
279C2×C4×C13—42no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—42no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—81no—
289C2×C4×C13—82no—
290C2×C4×C13#12011yescharacteristic
291C2×C4×C13#12011yescharacteristic
292C2×C4×C13C22×D411yescharacteristic
293C2×C4×C13C22×D411yescharacteristic
294C8×C13—41no—
295C8×C13—41no—
296C8×C13—42no—
297#563—22no—
298#552—21no—
299#552—21no—
300#551—22no—
301D4×Q8—21no—
302D4×Q8—21no—
303#544—21no—
304#544C22×C1312yes—
305#541—21no—
306#539—21no—
307#539C22×C1312yes—
308#536—21no—
309#525C22×C1311yescharacteristic
310C2×C22⋊Q8C22×C1311yescharacteristic
311C2×C22⋊Q8C22×C1311yescharacteristic
312C2×#117C22×C1311yescharacteristic
313#485—21no—
314#485—22no—
315#484C22×C1311yescharacteristic
316#484C22×C1312yes—
317#483C22×C1311yescharacteristic
318#483C22×C1312yes—
319#482—21no—
320#481C22×C1311yescharacteristic
321#480C22×C1311yescharacteristic
322#428—21no—
323#427—21no—
324#419—21no—
325#416—21no—
326#407C22×C1311yescharacteristic
327C2×C22⋊C8C22×C1311yescharacteristic
328#400C22×C1312yes—
329#398C22×C1312yes—
330#397—22no—
331#391—21no—
332#389—21no—
333#380C22×C1311yescharacteristic
334#328C22×C1312yes—
335#328C22×C1312yes—
336#328C22×C1312yes—
337#327C22×C1312yes—
338#324C22×C1312yes—
339#324C22×C1312yes—
340C22×C13—21no—
341C22×C13—21no—
342C22×C13—21no—
343C22×C13—21no—
344C22×C13—21no—
345C22×C13—21no—
346C22×C13—21no—
347C22×C13—21no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13—81no—
352C22×C13—81no—
353C22×C13C2×#12011yescharacteristic
354C22×C13#57711yescharacteristic
355C22×C13#57811yescharacteristic
356C4×C13—21no—
357C4×C13—21no—
358C4×C13—21no—
359C4×C13—42no—
360C4×C13—41no—
361C4×C13—42no—
362C4×C13—41no—
363C4×C13—41no—
364C4×C13—42no—
365C4×C13—42no—
366C4×C13—82no—
367C4×C13—81no—
368C4×C13—81no—
369C4×C13#45812yes—
370C2×#41D4×C1311yescharacteristic
371C22×Q8—21no—
372C22×Q8D4×C1311yescharacteristic
373C22×Q8D4×C1311yescharacteristic
374C23×C4C23×C1311yescharacteristic
375C2×M16—21no—
376C22×C8—21no—
377C4⋊Q8—21no—
378C4⋊Q8—22no—
379C4⋊Q8—22no—
380C4⋊Q8—22no—
381#126—22no—
382#126—22no—
383#126—22no—
384#126—22no—
385#125—21no—
386#125—22no—
387#125—22no—
388#125—22no—
389#125—22no—
390#124—22no—
391#123—22no—
392#123—22no—
393#123—22no—
394#123—21no—
395#123—22no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8—22no—
408C22⋊Q8D4×C1312yes—
409C22⋊Q8D4×C1311yescharacteristic
410C22⋊Q8C23×C1312yes—
411C22⋊Q8C23×C1311yescharacteristic
412#121D4×C1311yescharacteristic
413#121C23×C1311yescharacteristic
414#120—21no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×D4—22no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—22no—
421#117—21no—
422#117—22no—
423#117—22no—
424#117—21no—
425#117—21no—
426#117—21no—
427#117—21no—
428#117D4×C1311yescharacteristic
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4D4×C1311yescharacteristic
433C2×C4⋊C4D4×C1311yescharacteristic
434C2×C4⋊C4C23×C1311yescharacteristic
435C2×C4⋊C4C23×C1311yescharacteristic
436C2×C4⋊C4C23×C1312yes—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4D4×C1312yes—
441C2×C42—21no—
442#107—21no—
443#107—21no—
444#107—22no—
445#106—21no—
446#106—21no—
447#106—22no—
448#103—21no—
449#103—21no—
450#103—22no—
451#103—22no—
452#102—21no—
453#102—21no—
454C22⋊C8—21no—
455C22⋊C8—21no—
456C22⋊C8C23×C1312yes—
457C22⋊C8C23×C1311yescharacteristic
458C22⋊C8C23×C1311yescharacteristic
459#95—22no—
460#95—22no—
461#95—22no—
462#95C23×C1312yes—
463C2×C13—21no—
464C2×C13—21no—
465C2×C13—41no—
466C2×C13—41no—
467C2×C13—81no—
468C2×C13#301311yescharacteristic
469C2×C13#302011yescharacteristic
470C2×C13C2×#45811yescharacteristic
471C24C2×D4×C1311yescharacteristic
472#41—42no—
473C2×Q8—22no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—82no—
480C2×Q8C2×D4×C1312yes—
481C2×Q8C2×D4×C1311yescharacteristic
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4C2×D4×C1311yescharacteristic
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—42no—
494C22×C4C2×D4×C1312yes—
495C22×C4C2×D4×C1311yescharacteristic
496C22×C4C2×D4×C1311yescharacteristic
497C22×C4C2×D4×C1311yescharacteristic
498C22×C4C2×D4×C1312yes—
499C22×C4C2×D4×C1311yescharacteristic
500C22×C4C2×D4×C1311yescharacteristic
501C22×C4C24×C1311yescharacteristic
502M16—42no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—22no—
506C2×C8—42no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—82no—
530C4⋊C4C2×D4×C1312yes—
531C4⋊C4C2×D4×C1311yescharacteristic
532C4⋊C4C2×D4×C1311yescharacteristic
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—22no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—81no—
548C42—22no—
549C42—22no—
550C42—22no—
551C42—21no—
552C42—41no—
553C42—41no—
554C13#1823811yescharacteristic, direct product factor, Sylow
555C23—21no—
556C23—21no—
557C23—21no—
558C23—41no—
559C23—41no—
560C23C13×#12011yescharacteristic
561C23C13×#12011yescharacteristic
562C23C22×D4×C1311yescharacteristic
563Q8—42no—
564Q8—41no—
565Q8—42no—
566Q8—42no—
567Q8—81no—
568Q8—82no—
569D4—41no—
570D4—42no—
571D4—41no—
572D4—41no—
573D4—81no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—81no—
601C2×C4—82no—
602C2×C4C13×#12011yescharacteristic
603C2×C4C13×#12011yescharacteristic
604C2×C4C22×D4×C1311yescharacteristic
605C2×C4C22×D4×C1311yescharacteristic
606C8—41no—
607C8—41no—
608C8—42no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—81no—
621C22—81no—
622C22C2×C13×#12011yescharacteristic
623C22C13×#57711yescharacteristic
624C22C13×#57811yescharacteristic
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—
638C4C13×#45812yes—
639C2—21no—
640C2—21no—
641C2—41no—
642C2—41no—
643C2—81no—
644C2C13×#301311yescharacteristic
645C2C13×#302011yescharacteristic
646C2C2×C13×#45811yescharacteristic
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
2. C13×#3095C2semidirect
4. C13×#2625C2semidirect
5. C13×#1617C2semidirect
6. C13×#1615C2semidirect
7. C13×#1611C2semidirect
8. C13×#1609C2semidirect
9. C13×#1520C2semidirect
11. C13×#1472C2semidirect
148. #18238C13direct (N × H)
233. #3095C2×C13semidirect
235. #2625C2×C13semidirect
236. #1617C2×C13semidirect
237. #1615C2×C13semidirect
238. #1611C2×C13semidirect
239. #1609C2×C13semidirect
240. #1520C2×C13semidirect
242. #1472C2×C13semidirect
554. C13#18238direct (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×#30952
C13×#30912
C13×#26252
C13×#16172
C13×#16152
C13×#16112
C13×#16092
C13×#15202
C13×#15132
C13×#14722
#1823813