Finite Group Databasebeta

← C13×#23951 #15710290

Subgroups — C13×#23951 #15710290

Order 3328.

1234 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3492C211yesmaximal, characteristic, complemented
2C13×#3005C212yesmaximal, complemented
3C13×#2311C211yesmaximal, characteristic, complemented
4C13×#2028C211yesmaximal, characteristic, complemented
5C13×#2027C211yesmaximal, characteristic, complemented
6C13×#2007C211yesmaximal, characteristic, complemented
7C13×#2006C211yesmaximal, characteristic, complemented
8C13×#1897C212yesmaximal, complemented
9C13×#1883C212yesmaximal, complemented
10C13×#1882C212yesmaximal, complemented
11C13×#1821C211yesmaximal, characteristic, complemented
12C22×C13×#41C2211yescharacteristic
13C2×C13×#137C2212yes—
14C2×C13×AGL(1,ℤ/8)C2212yes—
15C13×#554—22no—
16C13×#553—22no—
17C13×#552—22no—
18C13×#547—22no—
19C13×#544C2211yescharacteristic
20C13×#539—22no—
21C13×#537C2211yescharacteristic
22C13×#525—22no—
23C13×#525C2212yes—
24C13×#520C2212yes—
25C2×C13×#117C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C13×#452—22no—
28C13×#452—22no—
29C13×#449—22no—
30C13×#449—22no—
31C2×C13×#104C2212yes—
32C2×C13×#104C2212yes—
33C13×#419C2212yes—
34C13×#418C2212yes—
35C13×#407C2212yes—
36C13×#391C2211yescharacteristic
37C13×#391C2211yescharacteristic
38C13×#390C2211yescharacteristic
39C13×#390C2211yescharacteristic
40C13×#386—22no—
41C13×#380—22no—
42C13×#343C2211yescharacteristic
43C13×#343C2211yescharacteristic
44C13×#343C2212yes—
45C13×#339C2212yes—
46C13×#339C2212yes—
47C2×C13×#41—22no—
48C2×C13×#41—22no—
49C2×C13×#41—22no—
50C2×C13×#41—22no—
51C2×C13×#41—22no—
52C2×C13×#41—42no—
53C2×C13×#41C2312yes—
54C22×Q8×C13C2311yescharacteristic
55C22×D4×C13—21no—
56C22×D4×C13C2311yescharacteristic
57C23×C4×C13—21no—
58C23×C4×C13D412yes—
59C23×C4×C13C2311yescharacteristic
60C13×#137—24no—
61C13×#137—42no—
62C13×AGL(1,ℤ/8)—24no—
63C13×AGL(1,ℤ/8)—42no—
64C2×C13×Q16—22no—
65C2×C13×SD16—22no—
66C2×C13×SD16—22no—
67C2×C13×D8—22no—
68C2×C13×M16C2312yes—
69C2×C13×M16C2312yes—
70C13×C4⋊Q8—22no—
71C13×#126—24no—
72C13×#125—24no—
73C13×#125—22no—
74C13×#123—24no—
75C13×#123—24no—
76C13×#123—22no—
77C13×C22⋊Q8—22no—
78C13×C22⋊Q8—24no—
79C13×C22⋊Q8—22no—
80C13×C22⋊Q8—22no—
81C13×C22⋊Q8D412yes—
82C13×C22⋊Q8D412yes—
83C13×#121—22no—
84C13×#121—22no—
85C13×#121—22no—
86C13×#121D412yes—
87C13×#121D412yes—
88C13×#120—22no—
89C4×Q8×C13—22no—
90C4×D4×C13—24no—
91C4×D4×C13—22no—
92C4×D4×C13—24no—
93C4×D4×C13—22no—
94C4×D4×C13—22no—
95C13×#117—22no—
96C13×#117—22no—
97C13×#117—42no—
98C13×#117C2312yes—
99C2×C13×C4⋊C4—22no—
100C2×C13×C4⋊C4—22no—
101C2×C13×C4⋊C4—22no—
102C2×C13×C4⋊C4—21no—
103C2×C13×C4⋊C4D412yes—
104C2×C13×C4⋊C4C2311yescharacteristic
105C2×C13×C4⋊C4C2311yescharacteristic
106C2×C13×C22⋊C4—21no—
107C2×C13×C22⋊C4—22no—
108C2×C13×C22⋊C4—22no—
109C2×C42×C13C2311yescharacteristic
110C2×C42×C13C2311yescharacteristic
111C13×#104—42no—
112C13×#104—42no—
113C13×#103—22no—
114C13×#103—22no—
115C13×#102—22no—
116C13×#102—22no—
117C13×C22⋊C8—22no—
118C13×C22⋊C8—22no—
119C13×#95—22no—
120C13×#95—22no—
121#23951C1311yesmaximal, characteristic, direct product factor, Sylow
122C24×C13—21no—
123C24×C13C2×D411yescharacteristic
124C13×#41—22no—
125C13×#41—22no—
126C13×#41—22no—
127C13×#41—22no—
128C13×#41—44no—
129C13×#41—44no—
130C13×#41—44no—
131C13×#41—44no—
132C13×#41—84no—
133C2×Q8×C13—22no—
134C2×Q8×C13—21no—
135C2×Q8×C13—22no—
136C2×Q8×C13—22no—
137C2×Q8×C13C2×D412yes—
138C2×Q8×C13#4112yescomplemented
139C2×D4×C13—24no—
140C2×D4×C13—22no—
141C2×D4×C13—22no—
142C2×D4×C13—22no—
143C2×D4×C13—22no—
144C2×D4×C13—22no—
145C2×D4×C13—21no—
146C2×D4×C13—22no—
147C2×D4×C13—42no—
148C2×D4×C13—41no—
149C2×D4×C13—41no—
150C2×D4×C13C2×D412yes—
151C2×D4×C13#4112yescomplemented
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—22no—
155C22×C4×C13—24no—
156C22×C4×C13—22no—
157C22×C4×C13—21no—
158C22×C4×C13—24no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—42no—
164C22×C4×C13—42no—
165C22×C4×C13—82no—
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D412yes—
168C22×C4×C13C2×D412yes—
169C22×C4×C13C2×D412yes—
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2411yescharacteristic
172C13×Q16—44no—
173C13×SD16—44no—
174C13×SD16—44no—
175C13×D8—44no—
176C13×M16—22no—
177C13×M16—22no—
178C13×M16—22no—
179C13×M16—22no—
180C2×C8×C13—22no—
181C2×C8×C13—22no—
182C13×C4⋊C4—24no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—24no—
186C13×C4⋊C4—24no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—42no—
192C13×C4⋊C4C2×D412yes—
193C13×C4⋊C4C2×D412yes—
194C13×C22⋊C4—24no—
195C13×C22⋊C4—24no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—42no—
202C13×C22⋊C4—82no—
203C13×C22⋊C4—82no—
204C42×C13—24no—
205C42×C13—22no—
206C42×C13—22no—
207C42×C13—22no—
208#3492C2×C1311yescharacteristic, complemented
209#3005C2×C1312yescomplemented
210#2311C2×C1311yescharacteristic, complemented
211#2028C2×C1311yescharacteristic, complemented
212#2027C2×C1311yescharacteristic, complemented
213#2007C2×C1311yescharacteristic, complemented
214#2006C2×C1311yescharacteristic, complemented
215#1897C2×C1312yescomplemented
216#1883C2×C1312yescomplemented
217#1882C2×C1312yescomplemented
218#1821C2×C1311yescharacteristic, complemented
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—42no—
226C23×C13—42no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13#12011yescharacteristic
230C23×C13#12011yescharacteristic
231C23×C13C22×D411yescharacteristic
232Q8×C13—22no—
233Q8×C13—24no—
234Q8×C13—22no—
235Q8×C13—42no—
236Q8×C13—82no—
237D4×C13—22no—
238D4×C13—24no—
239D4×C13—22no—
240D4×C13—44no—
241D4×C13—44no—
242D4×C13—44no—
243D4×C13—44no—
244D4×C13—42no—
245D4×C13—42no—
246D4×C13—42no—
247D4×C13—82no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—48no—
261C2×C4×C13—44no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13—42no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—82no—
275C2×C4×C13—84no—
276C2×C4×C13#12012yes—
277C2×C4×C13C22×D412yes—
278C2×C4×C13C2×#4111yescharacteristic
279C2×C4×C13C2×#4111yescharacteristic
280C2×C4×C13H(5,𝔽2)12yes—
281C8×C13—42no—
282C8×C13—42no—
283C22×#41C22×C1311yescharacteristic
284C2×#137C22×C1312yes—
285C2×AGL(1,ℤ/8)C22×C1312yes—
286#554—22no—
287#553—22no—
288#552—22no—
289#547—22no—
290#544C22×C1311yescharacteristic
291#539—22no—
292#537C22×C1311yescharacteristic
293#525—22no—
294#525C22×C1312yes—
295#520C22×C1312yes—
296C2×#117C22×C1311yescharacteristic
297C22×C4⋊C4C22×C1311yescharacteristic
298#452—22no—
299#452—22no—
300#449—22no—
301#449—22no—
302C2×#104C22×C1312yes—
303C2×#104C22×C1312yes—
304#419C22×C1312yes—
305#418C22×C1312yes—
306#407C22×C1312yes—
307#391C22×C1311yescharacteristic
308#391C22×C1311yescharacteristic
309#390C22×C1311yescharacteristic
310#390C22×C1311yescharacteristic
311#386—22no—
312#380—22no—
313#343C22×C1312yes—
314#343C22×C1311yescharacteristic
315#343C22×C1311yescharacteristic
316#339C22×C1312yes—
317#339C22×C1312yes—
318C22×C13—21no—
319C22×C13—21no—
320C22×C13—21no—
321C22×C13—21no—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13—42no—
327C22×C13—42no—
328C22×C13—44no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13—42no—
332C22×C13—42no—
333C22×C13—82no—
334C22×C13—81no—
335C22×C13—81no—
336C22×C13C2×#12011yescharacteristic
337C22×C13#52511yescharacteristic
338C22×C13#53511yescharacteristic
339C4×C13—22no—
340C4×C13—42no—
341C4×C13—42no—
342C4×C13—42no—
343C4×C13—42no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13—81no—
347C4×C13—81no—
348C4×C13#54612yes—
349C4×C13#54612yes—
350C2×#41—22no—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41—22no—
355C2×#41—42no—
356C2×#41C23×C1312yes—
357C22×Q8C23×C1311yescharacteristic
358C22×D4—21no—
359C22×D4C23×C1311yescharacteristic
360C23×C4—21no—
361C23×C4D4×C1312yes—
362C23×C4C23×C1311yescharacteristic
363#137—24no—
364#137—42no—
365AGL(1,ℤ/8)—24no—
366AGL(1,ℤ/8)—42no—
367C2×Q16—22no—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×D8—22no—
371C2×M16C23×C1312yes—
372C2×M16C23×C1312yes—
373C4⋊Q8—22no—
374#126—24no—
375#125—24no—
376#125—22no—
377#123—24no—
378#123—24no—
379#123—22no—
380C22⋊Q8—22no—
381C22⋊Q8—24no—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8D4×C1312yes—
385C22⋊Q8D4×C1312yes—
386#121—22no—
387#121—22no—
388#121—22no—
389#121D4×C1312yes—
390#121D4×C1312yes—
391#120—22no—
392C4×Q8—22no—
393C4×D4—24no—
394C4×D4—22no—
395C4×D4—24no—
396C4×D4—22no—
397C4×D4—22no—
398#117—22no—
399#117—22no—
400#117—42no—
401#117C23×C1312yes—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4D4×C1312yes—
407C2×C4⋊C4C23×C1311yescharacteristic
408C2×C4⋊C4C23×C1311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C42C23×C1311yescharacteristic
413C2×C42C23×C1311yescharacteristic
414#104—42no—
415#104—42no—
416#103—22no—
417#103—22no—
418#102—22no—
419#102—22no—
420C22⋊C8—22no—
421C22⋊C8—22no—
422#95—22no—
423#95—22no—
424C2×C13—21no—
425C2×C13—21no—
426C2×C13—41no—
427C2×C13—41no—
428C2×C13—82no—
429C2×C13—82no—
430C2×C13#240411yescharacteristic
431C2×C13#301911yescharacteristic
432C2×C13#302011yescharacteristic
433C24—21no—
434C24C2×D4×C1311yescharacteristic
435#41—22no—
436#41—22no—
437#41—22no—
438#41—22no—
439#41—44no—
440#41—44no—
441#41—44no—
442#41—44no—
443#41—84no—
444C2×Q8—22no—
445C2×Q8—21no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8C2×D4×C1312yes—
449C2×Q8C13×#4112yescomplemented
450C2×D4—24no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—22no—
458C2×D4—42no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4C2×D4×C1312yes—
462C2×D4C13×#4112yescomplemented
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—82no—
477C22×C4C2×D4×C1311yescharacteristic
478C22×C4C2×D4×C1312yes—
479C22×C4C2×D4×C1312yes—
480C22×C4C2×D4×C1312yes—
481C22×C4C2×D4×C1312yes—
482C22×C4C24×C1311yescharacteristic
483Q16—44no—
484SD16—44no—
485SD16—44no—
486D8—44no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—22no—
491C2×C8—22no—
492C2×C8—22no—
493C4⋊C4—24no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—42no—
503C4⋊C4C2×D4×C1312yes—
504C4⋊C4C2×D4×C1312yes—
505C22⋊C4—24no—
506C22⋊C4—24no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—42no—
513C22⋊C4—82no—
514C22⋊C4—82no—
515C42—24no—
516C42—22no—
517C42—22no—
518C42—22no—
519C13#2395111yescharacteristic, direct product factor, Sylow
520C23—21no—
521C23—21no—
522C23—22no—
523C23—22no—
524C23—41no—
525C23—41no—
526C23—42no—
527C23—42no—
528C23—41no—
529C23—41no—
530C23C13×#12011yescharacteristic
531C23C13×#12011yescharacteristic
532C23C22×D4×C1311yescharacteristic
533Q8—22no—
534Q8—24no—
535Q8—22no—
536Q8—42no—
537Q8—82no—
538D4—22no—
539D4—24no—
540D4—22no—
541D4—44no—
542D4—44no—
543D4—44no—
544D4—44no—
545D4—42no—
546D4—42no—
547D4—42no—
548D4—82no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—48no—
562C2×C4—44no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—82no—
576C2×C4—84no—
577C2×C4C13×#12012yes—
578C2×C4C22×D4×C1312yes—
579C2×C4C2×C13×#4111yescharacteristic
580C2×C4C2×C13×#4111yescharacteristic
581C2×C4C13×H(5,𝔽2)12yes—
582C8—42no—
583C8—42no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—42no—
593C22—42no—
594C22—44no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—82no—
600C22—81no—
601C22—81no—
602C22C2×C13×#12011yescharacteristic
603C22C13×#52511yescharacteristic
604C22C13×#53511yescharacteristic
605C4—22no—
606C4—42no—
607C4—42no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—42no—
612C4—81no—
613C4—81no—
614C4C13×#54612yes—
615C4C13×#54612yes—
616C2—21no—
617C2—21no—
618C2—41no—
619C2—41no—
620C2—82no—
621C2—82no—
622C2C13×#240411yescharacteristic
623C2C13×#301911yescharacteristic
624C2C13×#302011yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3492C2semidirect
2. C13×#3005C2semidirect
3. C13×#2311C2semidirect
4. C13×#2028C2semidirect
5. C13×#2027C2semidirect
6. C13×#2007C2semidirect
7. C13×#2006C2semidirect
8. C13×#1897C2semidirect
9. C13×#1883C2semidirect
10. C13×#1882C2semidirect
11. C13×#1821C2semidirect
121. #23951C13direct (N × H)
138. C2×Q8×C13#41semidirect
151. C2×D4×C13#41semidirect
208. #3492C2×C13semidirect
209. #3005C2×C13semidirect
210. #2311C2×C13semidirect
211. #2028C2×C13semidirect
212. #2027C2×C13semidirect
213. #2007C2×C13semidirect
214. #2006C2×C13semidirect
215. #1897C2×C13semidirect
216. #1883C2×C13semidirect
217. #1882C2×C13semidirect
218. #1821C2×C13semidirect
449. C2×Q8C13×#41semidirect
462. C2×D4C13×#41semidirect
519. C13#23951direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34922
C13×#30052
C13×#23112
C13×#20282
C13×#20272
C13×#20072
C13×#20062
C13×#18972
C13×#18832
C13×#18822
C13×#18212
#2395113