Finite Group Databasebeta

← C13×#18690 #15705029

Subgroups — C13×#18690 #15705029

Order 3328.

878 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3544C211yesmaximal, characteristic
2C13×#3239C211yesmaximal, characteristic, complemented
3C13×#3218C211yesmaximal, characteristic, complemented
4C2×C13×#487C211yesmaximal, characteristic, complemented
5C13×#1646C212yesmaximal, complemented
6C13×#1645C212yesmaximal, complemented
7C13×#1644C212yesmaximal, complemented
8C13×#1643C212yesmaximal, complemented
9C13×#1558C211yesmaximal, characteristic, complemented
10C13×#1494C211yesmaximal, characteristic, complemented
11C13×#1494C211yesmaximal, characteristic, complemented
12C13×#563—22no—
13Q82×C13C2211yescharacteristic
14C13×#555C2211yescharacteristic
15C13×#554C2211yescharacteristic
16C13×#554C2211yescharacteristic
17C13×#552—21no—
18C13×#552—21no—
19C13×#547—21no—
20C13×#547—21no—
21C13×#544—21no—
22C13×#544—21no—
23C13×#542—21no—
24C13×#542—21no—
25C13×#536—22no—
26C2×C13×C4⋊Q8C2211yescharacteristic
27C2×C13×C4⋊Q8C2211yescharacteristic
28C13×#529C2211yescharacteristic
29C13×#529C2211yescharacteristic
30C13×#501—21no—
31C13×#497—21no—
32C13×#491—21no—
33C13×#489—21no—
34C13×#487—22no—
35C13×#487C2212yes—
36C13×#487C2212yes—
37C13×#484—21no—
38C13×#481—21no—
39C13×#475C2212yes—
40C13×#474C2212yes—
41C13×#462C2212yes—
42C13×#461C2212yes—
43C13×#451—21no—
44C13×#448—21no—
45C13×#432C2211yescharacteristic
46C13×#432C2211yescharacteristic
47C2×C13×#103—22no—
48C2×C4×C8×C13C2211yescharacteristic
49C13×#333C2212yes—
50C13×#333C2212yes—
51C13×Q8⋊C8C2212yes—
52C13×Q8⋊C8C2212yes—
53C13×D4⋊C8C2212yes—
54C13×D4⋊C8C2212yes—
55C2×C13×#41—22no—
56C22×Q8×C13—21no—
57C22×Q8×C13D412yes—
58C2×C13×Q16—22no—
59C2×C13×SD16—22no—
60C22×C8×C13—21no—
61C13×C4⋊Q8—22no—
62C13×C4⋊Q8—22no—
63C13×C4⋊Q8—21no—
64C13×C4⋊Q8—21no—
65C13×C4⋊Q8—21no—
66C13×C4⋊Q8—21no—
67C13×C4⋊Q8—21no—
68C13×C4⋊Q8—21no—
69C13×C4⋊Q8—21no—
70C13×C4⋊Q8D412yes—
71C13×C4⋊Q8C2312yes—
72C13×C4⋊Q8C2311yescharacteristic
73C13×C4⋊Q8C2311yescharacteristic
74C13×#126—22no—
75C13×#126—22no—
76C13×#126—21no—
77C13×#126—21no—
78C13×#125—22no—
79C13×#125—22no—
80C13×#125—21no—
81C13×#125—21no—
82C13×#125D411yescharacteristic
83C13×#125D411yescharacteristic
84C13×#124—22no—
85C13×#124—22no—
86C13×#124D411yescharacteristic
87C13×#124D411yescharacteristic
88C13×#123—22no—
89C13×#123—22no—
90C13×#123—22no—
91C13×#123—22no—
92C13×#123—21no—
93C13×#123—21no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8—22no—
96C13×C22⋊Q8—22no—
97C13×C22⋊Q8—22no—
98C13×C22⋊Q8—22no—
99C13×C22⋊Q8—22no—
100C13×C22⋊Q8—21no—
101C13×C22⋊Q8—21no—
102C13×C22⋊Q8D411yescharacteristic
103C13×C22⋊Q8D411yescharacteristic
104C13×#121—21no—
105C13×#121—21no—
106C13×#121D411yescharacteristic
107C13×#121D411yescharacteristic
108C4×Q8×C13—21no—
109C4×Q8×C13—21no—
110C4×Q8×C13C2311yescharacteristic
111C4×Q8×C13C2311yescharacteristic
112C4×D4×C13—21no—
113C4×D4×C13—21no—
114C4×D4×C13—21no—
115C4×D4×C13—21no—
116C4×D4×C13C2311yescharacteristic
117C4×D4×C13C2311yescharacteristic
118C13×#117—22no—
119C13×#117—21no—
120C13×#117—21no—
121C13×#117—21no—
122C13×#117—21no—
123C2×C13×C4⋊C4—21no—
124C2×C13×C4⋊C4—21no—
125C2×C13×C4⋊C4—21no—
126C2×C13×C4⋊C4—21no—
127C2×C13×C4⋊C4—21no—
128C2×C13×C4⋊C4—21no—
129C2×C42×C13C2311yescharacteristic
130C13×#107—22no—
131C13×#106—22no—
132C13×C4⋊C8C2312yes—
133C13×C4⋊C8C2312yes—
134C13×#103—24no—
135C13×#103—24no—
136C13×#103—22no—
137C13×#103—22no—
138C13×#103—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#18690C1311yesmaximal, characteristic, direct product factor, Sylow
147C13×#41—84no—
148C2×Q8×C13—22no—
149C2×Q8×C13—22no—
150C2×Q8×C13—22no—
151C2×Q8×C13—44no—
152C2×Q8×C13—41no—
153C2×Q8×C13—82no—
154C2×Q8×C13C2×D411yescharacteristic
155C2×Q8×C13C2×D411yescharacteristic
156C2×Q8×C13C2×D412yes—
157C2×Q8×C13C2×D412yes—
158C2×D4×C13—21no—
159C2×D4×C13—21no—
160C2×D4×C13—22no—
161C2×D4×C13C2×D411yescharacteristic
162C2×D4×C13C2×D411yescharacteristic
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—41no—
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C13×Q16—82no—
173C13×SD16—82no—
174C2×C8×C13—22no—
175C2×C8×C13—22no—
176C2×C8×C13—22no—
177C2×C8×C13—42no—
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—22no—
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—21no—
196C13×C4⋊C4—21no—
197C13×C4⋊C4—21no—
198C13×C4⋊C4—22no—
199C13×C4⋊C4—22no—
200C13×C4⋊C4—41no—
201C13×C4⋊C4—41no—
202C13×C4⋊C4C2×D411yescharacteristic
203C13×C4⋊C4C2×D411yescharacteristic
204C13×C4⋊C4C2×D411yescharacteristic
205C13×C4⋊C4C2×D411yescharacteristic
206C13×C22⋊C4—22no—
207C13×C22⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—22no—
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—
219C13×C22⋊C4—21no—
220C42×C13—22no—
221C42×C13—22no—
222C42×C13—21no—
223C42×C13—21no—
224C42×C13C2×D411yescharacteristic
225C42×C13C2×D411yescharacteristic
226C42×C13C2×D411yescharacteristic
227C42×C13C2411yescharacteristic
228#3544C2×C1311yescharacteristic
229#3239C2×C1311yescharacteristic, complemented
230#3218C2×C1311yescharacteristic, complemented
231C2×#487C2×C1311yescharacteristic, complemented
232#1646C2×C1312yescomplemented
233#1645C2×C1312yescomplemented
234#1644C2×C1312yescomplemented
235#1643C2×C1312yescomplemented
236#1558C2×C1311yescharacteristic, complemented
237#1494C2×C1311yescharacteristic, complemented
238#1494C2×C1311yescharacteristic, complemented
239C23×C13—21no—
240C23×C13—21no—
241C23×C13#12011yescharacteristic
242Q8×C13—22no—
243Q8×C13—22no—
244Q8×C13—42no—
245Q8×C13—42no—
246Q8×C13—42no—
247Q8×C13—42no—
248Q8×C13—82no—
249Q8×C13—82no—
250Q8×C13—82no—
251D4×C13—22no—
252D4×C13—22no—
253D4×C13—42no—
254D4×C13—42no—
255D4×C13—82no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—22no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—22no—
267C2×C4×C13—44no—
268C2×C4×C13—42no—
269C2×C4×C13—42no—
270C2×C4×C13—42no—
271C2×C4×C13—82no—
272C2×C4×C13—82no—
273C2×C4×C13—82no—
274C2×C4×C13#12011yescharacteristic
275C2×C4×C13#12011yescharacteristic
276C2×C4×C13#12011yescharacteristic
277C2×C4×C13C22×D411yescharacteristic
278C2×C4×C13C22×D411yescharacteristic
279C2×C4×C13C22×D411yescharacteristic
280C8×C13—42no—
281C8×C13—42no—
282C8×C13—42no—
283#563—22no—
284Q82C22×C1311yescharacteristic
285#555C22×C1311yescharacteristic
286#554C22×C1311yescharacteristic
287#554C22×C1311yescharacteristic
288#552—21no—
289#552—21no—
290#547—21no—
291#547—21no—
292#544—21no—
293#544—21no—
294#542—21no—
295#542—21no—
296#536—22no—
297C2×C4⋊Q8C22×C1311yescharacteristic
298C2×C4⋊Q8C22×C1311yescharacteristic
299#529C22×C1311yescharacteristic
300#529C22×C1311yescharacteristic
301#501—21no—
302#497—21no—
303#491—21no—
304#489—21no—
305#487—22no—
306#487C22×C1312yes—
307#487C22×C1312yes—
308#484—21no—
309#481—21no—
310#475C22×C1312yes—
311#474C22×C1312yes—
312#462C22×C1312yes—
313#461C22×C1312yes—
314#451—21no—
315#448—21no—
316#432C22×C1311yescharacteristic
317#432C22×C1311yescharacteristic
318C2×#103—22no—
319C2×C4×C8C22×C1311yescharacteristic
320#333C22×C1312yes—
321#333C22×C1312yes—
322Q8⋊C8C22×C1312yes—
323Q8⋊C8C22×C1312yes—
324D4⋊C8C22×C1312yes—
325D4⋊C8C22×C1312yes—
326C22×C13—21no—
327C22×C13—21no—
328C22×C13—41no—
329C22×C13—41no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13—41no—
333C22×C13—41no—
334C22×C13#45512yes—
335C22×C13C2×#12011yescharacteristic
336C4×C13—21no—
337C4×C13—21no—
338C4×C13—21no—
339C4×C13—21no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13—82no—
349C4×C13#57712yes—
350C4×C13#57812yes—
351C2×#41—22no—
352C22×Q8—21no—
353C22×Q8D4×C1312yes—
354C2×Q16—22no—
355C2×SD16—22no—
356C22×C8—21no—
357C4⋊Q8—22no—
358C4⋊Q8—22no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8D4×C1312yes—
367C4⋊Q8C23×C1312yes—
368C4⋊Q8C23×C1311yescharacteristic
369C4⋊Q8C23×C1311yescharacteristic
370#126—22no—
371#126—22no—
372#126—21no—
373#126—21no—
374#125—22no—
375#125—22no—
376#125—21no—
377#125—21no—
378#125D4×C1311yescharacteristic
379#125D4×C1311yescharacteristic
380#124—22no—
381#124—22no—
382#124D4×C1311yescharacteristic
383#124D4×C1311yescharacteristic
384#123—22no—
385#123—22no—
386#123—22no—
387#123—22no—
388#123—21no—
389#123—21no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8D4×C1311yescharacteristic
399C22⋊Q8D4×C1311yescharacteristic
400#121—21no—
401#121—21no—
402#121D4×C1311yescharacteristic
403#121D4×C1311yescharacteristic
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8C23×C1311yescharacteristic
407C4×Q8C23×C1311yescharacteristic
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4C23×C1311yescharacteristic
413C4×D4C23×C1311yescharacteristic
414#117—22no—
415#117—21no—
416#117—21no—
417#117—21no—
418#117—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C42C23×C1311yescharacteristic
426#107—22no—
427#106—22no—
428C4⋊C8C23×C1312yes—
429C4⋊C8C23×C1312yes—
430#103—24no—
431#103—24no—
432#103—22no—
433#103—22no—
434#103—22no—
435#102—22no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438#97—21no—
439#97—21no—
440C4×C8—21no—
441C4×C8C23×C1312yes—
442C2×C13—22no—
443C2×C13—81no—
444C2×C13—81no—
445C2×C13#301011yescharacteristic
446C2×C13#301111yescharacteristic
447C2×C13C2×#45511yescharacteristic
448#41—84no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—44no—
453C2×Q8—41no—
454C2×Q8—82no—
455C2×Q8C2×D4×C1311yescharacteristic
456C2×Q8C2×D4×C1311yescharacteristic
457C2×Q8C2×D4×C1312yes—
458C2×Q8C2×D4×C1312yes—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4C2×D4×C1311yescharacteristic
463C2×D4C2×D4×C1311yescharacteristic
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—41no—
470C22×C4C2×D4×C1311yescharacteristic
471C22×C4C2×D4×C1311yescharacteristic
472C22×C4C2×D4×C1311yescharacteristic
473Q16—82no—
474SD16—82no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—42no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C1311yescharacteristic
504C4⋊C4C2×D4×C1311yescharacteristic
505C4⋊C4C2×D4×C1311yescharacteristic
506C4⋊C4C2×D4×C1311yescharacteristic
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C42—22no—
522C42—22no—
523C42—21no—
524C42—21no—
525C42C2×D4×C1311yescharacteristic
526C42C2×D4×C1311yescharacteristic
527C42C2×D4×C1311yescharacteristic
528C42C24×C1311yescharacteristic
529C13#1869011yescharacteristic, direct product factor, Sylow
530C23—21no—
531C23—21no—
532C23C13×#12011yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—42no—
536Q8—42no—
537Q8—42no—
538Q8—42no—
539Q8—82no—
540Q8—82no—
541Q8—82no—
542D4—22no—
543D4—22no—
544D4—42no—
545D4—42no—
546D4—82no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—44no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4C13×#12011yescharacteristic
566C2×C4C13×#12011yescharacteristic
567C2×C4C13×#12011yescharacteristic
568C2×C4C22×D4×C1311yescharacteristic
569C2×C4C22×D4×C1311yescharacteristic
570C2×C4C22×D4×C1311yescharacteristic
571C8—42no—
572C8—42no—
573C8—42no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22C13×#45512yes—
583C22C2×C13×#12011yescharacteristic
584C4—21no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—82no—
597C4C13×#57712yes—
598C4C13×#57812yes—
599C2—22no—
600C2—81no—
601C2—81no—
602C2C13×#301011yescharacteristic
603C2C13×#301111yescharacteristic
604C2C2×C13×#45511yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3544C2
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×#3239C2semidirect
3. C13×#3218C2semidirect
4. C2×C13×#487C2semidirect
5. C13×#1646C2semidirect
6. C13×#1645C2semidirect
7. C13×#1644C2semidirect
8. C13×#1643C2semidirect
9. C13×#1558C2semidirect
10. C13×#1494C2semidirect
11. C13×#1494C2semidirect
146. #18690C13direct (N × H)
229. #3239C2×C13semidirect
230. #3218C2×C13semidirect
231. C2×#487C2×C13semidirect
232. #1646C2×C13semidirect
233. #1645C2×C13semidirect
234. #1644C2×C13semidirect
235. #1643C2×C13semidirect
236. #1558C2×C13semidirect
237. #1494C2×C13semidirect
238. #1494C2×C13semidirect
529. C13#18690direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35442
C13×#32392
C13×#32182
C2×C13×#4872
C13×#16462
C13×#16452
C13×#16442
C13×#16432
C13×#15582
C13×#14942
#1869013