Finite Group Databasebeta

← C13×#18695 #15705034

Subgroups — C13×#18695 #15705034

Order 3328.

866 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3552C211yesmaximal, characteristic
2C13×#3238C211yesmaximal, characteristic, complemented
3C13×#3238C211yesmaximal, characteristic, complemented
4C2×C13×#487C211yesmaximal, characteristic, complemented
5C13×#1638C212yesmaximal, complemented
6C13×#1637C212yesmaximal, complemented
7C13×#1636C212yesmaximal, complemented
8C13×#1635C212yesmaximal, complemented
9C13×#1556C211yesmaximal, characteristic, complemented
10C13×#1494C211yesmaximal, characteristic, complemented
11C13×#1494C211yesmaximal, characteristic, complemented
12C13×#563—22no—
13C13×#557C2211yescharacteristic
14C13×#556C2211yescharacteristic
15C13×#554—21no—
16C13×#553—21no—
17D4×Q8×C13—21no—
18D4×Q8×C13C2211yescharacteristic
19C13×#548—21no—
20C13×#547C2211yescharacteristic
21C13×#544—21no—
22C13×#542—21no—
23C13×#541—21no—
24C13×#539—22no—
25C13×#536—21no—
26C2×C13×C4⋊Q8C2211yescharacteristic
27C2×C13×C4⋊Q8C2211yescharacteristic
28C13×#529C2211yescharacteristic
29C13×#529C2211yescharacteristic
30C13×#501—21no—
31C13×#501—21no—
32C13×#489—21no—
33C13×#489—21no—
34C13×#487—22no—
35C13×#487C2212yes—
36C13×#487C2212yes—
37C13×#483—21no—
38C13×#483—21no—
39C13×#480—21no—
40C13×#480—21no—
41C13×#477C2212yes—
42C13×#477C2212yes—
43C13×#476C2212yes—
44C13×#476C2212yes—
45C13×#432C2211yescharacteristic
46C13×#432C2211yescharacteristic
47C2×C13×#103—22no—
48C2×C4×C8×C13C2211yescharacteristic
49C13×#332C2212yes—
50C13×#332C2212yes—
51C13×Q8⋊C8C2212yes—
52C13×Q8⋊C8C2212yes—
53C13×D4⋊C8C2212yes—
54C13×D4⋊C8C2212yes—
55C2×C13×#41—21no—
56C22×Q8×C13—21no—
57C22×Q8×C13—21no—
58C22×Q8×C13—21no—
59C22×C8×C13—21no—
60C13×C4⋊Q8—22no—
61C13×C4⋊Q8—21no—
62C13×C4⋊Q8—21no—
63C13×C4⋊Q8—21no—
64C13×C4⋊Q8—21no—
65C13×C4⋊Q8—21no—
66C13×C4⋊Q8—21no—
67C13×C4⋊Q8—21no—
68C13×C4⋊Q8D412yes—
69C13×C4⋊Q8C2312yes—
70C13×C4⋊Q8C2311yescharacteristic
71C13×C4⋊Q8C2311yescharacteristic
72C13×#126—22no—
73C13×#126—22no—
74C13×#126—22no—
75C13×#126—21no—
76C13×#126—21no—
77C13×#125—22no—
78C13×#125—22no—
79C13×#125—22no—
80C13×#125—21no—
81C13×#125D411yescharacteristic
82C13×#125D411yescharacteristic
83C13×#124—22no—
84C13×#124—21no—
85C13×#124D411yescharacteristic
86C13×#124D411yescharacteristic
87C13×#123—22no—
88C13×#123—22no—
89C13×#123—21no—
90C13×#123—21no—
91C13×#123—22no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8—22no—
96C13×C22⋊Q8—22no—
97C13×C22⋊Q8—21no—
98C13×C22⋊Q8—22no—
99C13×C22⋊Q8—21no—
100C13×C22⋊Q8—21no—
101C13×C22⋊Q8D411yescharacteristic
102C13×C22⋊Q8D411yescharacteristic
103C13×#121—22no—
104C13×#121—21no—
105C13×#121D411yescharacteristic
106C13×#121D411yescharacteristic
107C4×Q8×C13—21no—
108C4×Q8×C13—21no—
109C4×Q8×C13—21no—
110C4×Q8×C13C2311yescharacteristic
111C4×Q8×C13C2311yescharacteristic
112C4×D4×C13—22no—
113C4×D4×C13—22no—
114C4×D4×C13—21no—
115C4×D4×C13—21no—
116C4×D4×C13—21no—
117C4×D4×C13C2311yescharacteristic
118C4×D4×C13C2311yescharacteristic
119C13×#117—21no—
120C13×#117—21no—
121C13×#117—21no—
122C2×C13×C4⋊C4—21no—
123C2×C13×C4⋊C4—21no—
124C2×C13×C4⋊C4—21no—
125C2×C13×C4⋊C4—21no—
126C2×C13×C4⋊C4D412yes—
127C2×C42×C13C2311yescharacteristic
128C13×#107—22no—
129C13×#107—22no—
130C13×#106—22no—
131C13×#106—22no—
132C13×C4⋊C8C2312yes—
133C13×C4⋊C8C2312yes—
134C13×#103—22no—
135C13×#103—22no—
136C13×#103—24no—
137C13×#103—24no—
138C13×#102—22no—
139C13×#102—22no—
140C13×C22⋊C8—21no—
141C13×C22⋊C8—21no—
142C13×#97—21no—
143C13×#97—21no—
144C4×C8×C13—21no—
145C4×C8×C13C2312yes—
146#18695C1311yesmaximal, characteristic, direct product factor, Sylow
147C13×#41—82no—
148C2×Q8×C13—22no—
149C2×Q8×C13—22no—
150C2×Q8×C13—21no—
151C2×Q8×C13—21no—
152C2×Q8×C13—22no—
153C2×Q8×C13—44no—
154C2×Q8×C13—41no—
155C2×Q8×C13—82no—
156C2×Q8×C13—82no—
157C2×Q8×C13C2×D411yescharacteristic
158C2×Q8×C13C2×D411yescharacteristic
159C2×D4×C13—21no—
160C2×D4×C13—21no—
161C2×D4×C13—22no—
162C2×D4×C13C2×D411yescharacteristic
163C2×D4×C13C2×D411yescharacteristic
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—41no—
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C2×C8×C13—22no—
174C2×C8×C13—22no—
175C2×C8×C13—22no—
176C2×C8×C13—42no—
177C13×C4⋊C4—22no—
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—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—41no—
198C13×C4⋊C4—41no—
199C13×C4⋊C4C2×D412yes—
200C13×C4⋊C4C2×D412yes—
201C13×C4⋊C4C2×D411yescharacteristic
202C13×C4⋊C4C2×D411yescharacteristic
203C13×C4⋊C4C2×D411yescharacteristic
204C13×C4⋊C4C2×D411yescharacteristic
205C13×C22⋊C4—22no—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—21no—
210C13×C22⋊C4—21no—
211C13×C22⋊C4—21no—
212C13×C22⋊C4—21no—
213C13×C22⋊C4—21no—
214C13×C22⋊C4—21no—
215C13×C22⋊C4—21no—
216C13×C22⋊C4—21no—
217C13×C22⋊C4—21no—
218C13×C22⋊C4—21no—
219C42×C13—22no—
220C42×C13—22no—
221C42×C13—21no—
222C42×C13—21no—
223C42×C13C2×D411yescharacteristic
224C42×C13C2×D411yescharacteristic
225C42×C13C2×D411yescharacteristic
226C42×C13C2411yescharacteristic
227#3552C2×C1311yescharacteristic
228#3238C2×C1311yescharacteristic, complemented
229#3238C2×C1311yescharacteristic, complemented
230C2×#487C2×C1311yescharacteristic, complemented
231#1638C2×C1312yescomplemented
232#1637C2×C1312yescomplemented
233#1636C2×C1312yescomplemented
234#1635C2×C1312yescomplemented
235#1556C2×C1311yescharacteristic, complemented
236#1494C2×C1311yescharacteristic, complemented
237#1494C2×C1311yescharacteristic, complemented
238C23×C13—21no—
239C23×C13—21no—
240C23×C13#12011yescharacteristic
241Q8×C13—22no—
242Q8×C13—22no—
243Q8×C13—44no—
244Q8×C13—42no—
245Q8×C13—42no—
246Q8×C13—82no—
247Q8×C13—82no—
248Q8×C13—82no—
249D4×C13—22no—
250D4×C13—22no—
251D4×C13—42no—
252D4×C13—42no—
253D4×C13—82no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—21no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13—42no—
268C2×C4×C13—82no—
269C2×C4×C13—82no—
270C2×C4×C13—82no—
271C2×C4×C13—82no—
272C2×C4×C13#12011yescharacteristic
273C2×C4×C13#12011yescharacteristic
274C2×C4×C13#12011yescharacteristic
275C2×C4×C13C22×D411yescharacteristic
276C2×C4×C13C22×D411yescharacteristic
277C2×C4×C13C22×D411yescharacteristic
278C8×C13—42no—
279C8×C13—42no—
280C8×C13—42no—
281#563—22no—
282#557C22×C1311yescharacteristic
283#556C22×C1311yescharacteristic
284#554—21no—
285#553—21no—
286D4×Q8—21no—
287D4×Q8C22×C1311yescharacteristic
288#548—21no—
289#547C22×C1311yescharacteristic
290#544—21no—
291#542—21no—
292#541—21no—
293#539—22no—
294#536—21no—
295C2×C4⋊Q8C22×C1311yescharacteristic
296C2×C4⋊Q8C22×C1311yescharacteristic
297#529C22×C1311yescharacteristic
298#529C22×C1311yescharacteristic
299#501—21no—
300#501—21no—
301#489—21no—
302#489—21no—
303#487—22no—
304#487C22×C1312yes—
305#487C22×C1312yes—
306#483—21no—
307#483—21no—
308#480—21no—
309#480—21no—
310#477C22×C1312yes—
311#477C22×C1312yes—
312#476C22×C1312yes—
313#476C22×C1312yes—
314#432C22×C1311yescharacteristic
315#432C22×C1311yescharacteristic
316C2×#103—22no—
317C2×C4×C8C22×C1311yescharacteristic
318#332C22×C1312yes—
319#332C22×C1312yes—
320Q8⋊C8C22×C1312yes—
321Q8⋊C8C22×C1312yes—
322D4⋊C8C22×C1312yes—
323D4⋊C8C22×C1312yes—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13—41no—
327C22×C13—41no—
328C22×C13—41no—
329C22×C13—41no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13#45412yes—
333C22×C13C2×#12011yescharacteristic
334C4×C13—21no—
335C4×C13—21no—
336C4×C13—21no—
337C4×C13—21no—
338C4×C13—41no—
339C4×C13—42no—
340C4×C13—41no—
341C4×C13—42no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13—41no—
345C4×C13—41no—
346C4×C13—82no—
347C4×C13#57712yes—
348C4×C13#57812yes—
349C2×#41—21no—
350C22×Q8—21no—
351C22×Q8—21no—
352C22×Q8—21no—
353C22×C8—21no—
354C4⋊Q8—22no—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8D4×C1312yes—
363C4⋊Q8C23×C1312yes—
364C4⋊Q8C23×C1311yescharacteristic
365C4⋊Q8C23×C1311yescharacteristic
366#126—22no—
367#126—22no—
368#126—22no—
369#126—21no—
370#126—21no—
371#125—22no—
372#125—22no—
373#125—22no—
374#125—21no—
375#125D4×C1311yescharacteristic
376#125D4×C1311yescharacteristic
377#124—22no—
378#124—21no—
379#124D4×C1311yescharacteristic
380#124D4×C1311yescharacteristic
381#123—22no—
382#123—22no—
383#123—21no—
384#123—21no—
385#123—22no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—21no—
392C22⋊Q8—22no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8D4×C1311yescharacteristic
396C22⋊Q8D4×C1311yescharacteristic
397#121—22no—
398#121—21no—
399#121D4×C1311yescharacteristic
400#121D4×C1311yescharacteristic
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8C23×C1311yescharacteristic
405C4×Q8C23×C1311yescharacteristic
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4C23×C1311yescharacteristic
412C4×D4C23×C1311yescharacteristic
413#117—21no—
414#117—21no—
415#117—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4D4×C1312yes—
421C2×C42C23×C1311yescharacteristic
422#107—22no—
423#107—22no—
424#106—22no—
425#106—22no—
426C4⋊C8C23×C1312yes—
427C4⋊C8C23×C1312yes—
428#103—22no—
429#103—22no—
430#103—24no—
431#103—24no—
432#102—22no—
433#102—22no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436#97—21no—
437#97—21no—
438C4×C8—21no—
439C4×C8C23×C1312yes—
440C2×C13—22no—
441C2×C13—81no—
442C2×C13—81no—
443C2×C13#300911yescharacteristic
444C2×C13#301111yescharacteristic
445C2×C13C2×#45411yescharacteristic
446#41—82no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—22no—
452C2×Q8—44no—
453C2×Q8—41no—
454C2×Q8—82no—
455C2×Q8—82no—
456C2×Q8C2×D4×C1311yescharacteristic
457C2×Q8C2×D4×C1311yescharacteristic
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4C2×D4×C1311yescharacteristic
462C2×D4C2×D4×C1311yescharacteristic
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4C2×D4×C1311yescharacteristic
470C22×C4C2×D4×C1311yescharacteristic
471C22×C4C2×D4×C1311yescharacteristic
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—42no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4C2×D4×C1312yes—
499C4⋊C4C2×D4×C1312yes—
500C4⋊C4C2×D4×C1311yescharacteristic
501C4⋊C4C2×D4×C1311yescharacteristic
502C4⋊C4C2×D4×C1311yescharacteristic
503C4⋊C4C2×D4×C1311yescharacteristic
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C42—22no—
519C42—22no—
520C42—21no—
521C42—21no—
522C42C2×D4×C1311yescharacteristic
523C42C2×D4×C1311yescharacteristic
524C42C2×D4×C1311yescharacteristic
525C42C24×C1311yescharacteristic
526C13#1869511yescharacteristic, direct product factor, Sylow
527C23—21no—
528C23—21no—
529C23C13×#12011yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—44no—
533Q8—42no—
534Q8—42no—
535Q8—82no—
536Q8—82no—
537Q8—82no—
538D4—22no—
539D4—22no—
540D4—42no—
541D4—42no—
542D4—82no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4C13×#12011yescharacteristic
562C2×C4C13×#12011yescharacteristic
563C2×C4C13×#12011yescharacteristic
564C2×C4C22×D4×C1311yescharacteristic
565C2×C4C22×D4×C1311yescharacteristic
566C2×C4C22×D4×C1311yescharacteristic
567C8—42no—
568C8—42no—
569C8—42no—
570C22—21no—
571C22—21no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22C13×#45412yes—
579C22C2×C13×#12011yescharacteristic
580C4—21no—
581C4—21no—
582C4—21no—
583C4—21no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—42no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—82no—
593C4C13×#57712yes—
594C4C13×#57812yes—
595C2—22no—
596C2—81no—
597C2—81no—
598C2C13×#300911yescharacteristic
599C2C13×#301111yescharacteristic
600C2C2×C13×#45411yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3552C2
LCSG ▷ C42 ▷ 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×#3238C2semidirect
3. C13×#3238C2semidirect
4. C2×C13×#487C2semidirect
5. C13×#1638C2semidirect
6. C13×#1637C2semidirect
7. C13×#1636C2semidirect
8. C13×#1635C2semidirect
9. C13×#1556C2semidirect
10. C13×#1494C2semidirect
11. C13×#1494C2semidirect
146. #18695C13direct (N × H)
228. #3238C2×C13semidirect
229. #3238C2×C13semidirect
230. C2×#487C2×C13semidirect
231. #1638C2×C13semidirect
232. #1637C2×C13semidirect
233. #1636C2×C13semidirect
234. #1635C2×C13semidirect
235. #1556C2×C13semidirect
236. #1494C2×C13semidirect
237. #1494C2×C13semidirect
526. C13#18695direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35522
C13×#32382
C2×C13×#4872
C13×#16382
C13×#16372
C13×#16362
C13×#16352
C13×#15562
C13×#14942
#1869513