Finite Group Databasebeta

← C13×#24112 #15710451

Subgroups — C13×#24112 #15710451

Order 3328.

1518 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3490C211yesmaximal, characteristic
2C13×#2849C212yesmaximal, complemented
3C2×C13×#385C211yesmaximal, characteristic, complemented
4C13×#2062C212yesmaximal, complemented
5C13×#2044C212yesmaximal, complemented
6C13×#1898C212yesmaximal, complemented
7C13×#1867C214yesmaximal, complemented
8C13×#1819C211yesmaximal, characteristic, complemented
9C24×C4×C13C2211yescharacteristic
10C13×#551—22no—
11C13×#551—22no—
12C13×#546—22no—
13C13×#546—22no—
14C13×#543C2211yescharacteristic
15C13×#538—21no—
16C13×#538—21no—
17C13×#534C2211yescharacteristic
18C13×#525—21no—
19C13×#525—21no—
20C2×C13×#123—22no—
21C2×C13×#120C2212yes—
22C13×#518C2212yes—
23C22×C13×C4⋊C4—21no—
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C2×C13×#99C2214yes—
27C13×#386—22no—
28C13×#386C2214yes—
29C13×#385—21no—
30C13×#385—21no—
31C13×#385—22no—
32C13×#385C2212yes—
33C13×#385C2212yes—
34C13×#385C2214yes—
35C13×#381—22no—
36C13×#379C2212yes—
37C2×C13×#95—21no—
38C13×#342C2212yes—
39C13×#342C2214yes—
40C13×#342C2212yes—
41C25×C13C2311yescharacteristic
42C2×C13×#41—21no—
43C2×C13×#41—21no—
44C22×D4×C13D412yes—
45C22×D4×C13D412yes—
46C22×D4×C13C2312yes—
47C23×C4×C13—22no—
48C23×C4×C13—21no—
49C23×C4×C13—21no—
50C23×C4×C13—21no—
51C23×C4×C13—22no—
52C23×C4×C13—44no—
53C23×C4×C13D411yescharacteristic
54C23×C4×C13D411yescharacteristic
55C23×C4×C13C2312yes—
56C13×#126—22no—
57C13×#126—22no—
58C13×#124—22no—
59C13×#124—22no—
60C13×#123—22no—
61C13×#123—22no—
62C13×#123—22no—
63C13×#123—22no—
64C13×#123—22no—
65C13×#123—48no—
66C13×C22⋊Q8—21no—
67C13×C22⋊Q8—21no—
68C13×C22⋊Q8—21no—
69C13×C22⋊Q8—21no—
70C13×C22⋊Q8—22no—
71C13×C22⋊Q8—22no—
72C13×#121—21no—
73C13×#121—21no—
74C13×#121—22no—
75C13×#121—22no—
76C13×#121—21no—
77C13×#121—21no—
78C13×#120—22no—
79C13×#120—22no—
80C13×#120—22no—
81C13×#120—22no—
82C13×#120—22no—
83C4×D4×C13—22no—
84C4×D4×C13—22no—
85C4×D4×C13—22no—
86C4×D4×C13—22no—
87C4×D4×C13—22no—
88C4×D4×C13—22no—
89C13×#117—21no—
90C13×#117—21no—
91C13×#117—22no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—24no—
95C2×C13×C4⋊C4—44no—
96C2×C13×C22⋊C4—21no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—24no—
101C2×C13×C22⋊C4—22no—
102C2×C13×C22⋊C4—22no—
103C2×C13×C22⋊C4—24no—
104C2×C13×C22⋊C4D412yes—
105C2×C13×C22⋊C4D411yescharacteristic
106C2×C13×C22⋊C4D411yescharacteristic
107C2×C13×C22⋊C4D412yes—
108C2×C13×C22⋊C4C2314yes—
109C2×C13×C22⋊C4C2311yescharacteristic
110C2×C13×C22⋊C4C2311yescharacteristic
111C2×C13×C22⋊C4C2312yes—
112C2×C13×C22⋊C4C2312yes—
113C13×#99—28no—
114C13×#95—24no—
115C13×#95—24no—
116C13×#95—22no—
117C13×#95—22no—
118#24112C1311yesmaximal, characteristic, direct product factor, Sylow
119C24×C13—22no—
120C24×C13—22no—
121C24×C13—42no—
122C24×C13—42no—
123C24×C13C2×D411yescharacteristic
124C24×C13C2×D412yes—
125C24×C13C2×D412yes—
126C24×C13C2×D412yes—
127C24×C13C2×D411yescharacteristic
128C24×C13C2411yescharacteristic
129C13×#41—82no—
130C13×#41—82no—
131C2×Q8×C13—21no—
132C2×Q8×C13—21no—
133C2×D4×C13—22no—
134C2×D4×C13—22no—
135C2×D4×C13—22no—
136C2×D4×C13—22no—
137C2×D4×C13—24no—
138C2×D4×C13—24no—
139C2×D4×C13—21no—
140C2×D4×C13—21no—
141C2×D4×C13—22no—
142C2×D4×C13—22no—
143C2×D4×C13—44no—
144C2×D4×C13—44no—
145C22×C4×C13—24no—
146C22×C4×C13—24no—
147C22×C4×C13—28no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—22no—
151C22×C4×C13—24no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—24no—
158C22×C4×C13—44no—
159C22×C4×C13—48no—
160C22×C4×C13—44no—
161C22×C4×C13—42no—
162C22×C4×C13—42no—
163C22×C4×C13—42no—
164C22×C4×C13—44no—
165C22×C4×C13—42no—
166C22×C4×C13—41no—
167C22×C4×C13—41no—
168C22×C4×C13—42no—
169C22×C4×C13—42no—
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D412yes—
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D412yes—
176C22×C4×C13C2×D411yescharacteristic
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—44no—
186C13×C4⋊C4—44no—
187C13×C4⋊C4—48no—
188C13×C22⋊C4—24no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—24no—
205C13×C22⋊C4—24no—
206C13×C22⋊C4—48no—
207C13×C22⋊C4—44no—
208C13×C22⋊C4—44no—
209C13×C22⋊C4#4114yescomplemented
210C42×C13—22no—
211C42×C13—22no—
212#3490C2×C1311yescharacteristic
213#2849C2×C1312yescomplemented
214C2×#385C2×C1311yescharacteristic, complemented
215#2062C2×C1312yescomplemented
216#2044C2×C1312yescomplemented
217#1898C2×C1312yescomplemented
218#1867C2×C1314yescomplemented
219#1819C2×C1311yescharacteristic, complemented
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—24no—
227C23×C13—24no—
228C23×C13—24no—
229C23×C13—24no—
230C23×C13—22no—
231C23×C13—24no—
232C23×C13—41no—
233C23×C13—42no—
234C23×C13—41no—
235C23×C13—41no—
236C23×C13—42no—
237C23×C13—41no—
238C23×C13—48no—
239C23×C13—48no—
240C23×C13—42no—
241C23×C13—42no—
242C23×C13#12012yes—
243C23×C13#12011yescharacteristic
244C23×C13#12011yescharacteristic
245C23×C13C22×D411yescharacteristic
246C23×C13C22×D412yes—
247C23×C13C2×#4112yes—
248C23×C132−1+412yes—
249Q8×C13—81no—
250Q8×C13—81no—
251D4×C13—42no—
252D4×C13—42no—
253D4×C13—44no—
254D4×C13—44no—
255D4×C13—44no—
256D4×C13—82no—
257D4×C13—82no—
258D4×C13—81no—
259D4×C13—81no—
260C2×C4×C13—28no—
261C2×C4×C13—24no—
262C2×C4×C13—22no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—24no—
270C2×C4×C13—24no—
271C2×C4×C13—42no—
272C2×C4×C13—48no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—44no—
276C2×C4×C13—44no—
277C2×C4×C13—48no—
278C2×C4×C13—42no—
279C2×C4×C13—44no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—42no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—42no—
288C2×C4×C13—44no—
289C2×C4×C13—44no—
290C2×C4×C13—44no—
291C2×C4×C13—81no—
292C2×C4×C13—81no—
293C2×C4×C13—82no—
294C2×C4×C13—82no—
295C24×C4C22×C1311yescharacteristic
296#551—22no—
297#551—22no—
298#546—22no—
299#546—22no—
300#543C22×C1311yescharacteristic
301#538—21no—
302#538—21no—
303#534C22×C1311yescharacteristic
304#525—21no—
305#525—21no—
306C2×#123—22no—
307C2×#120C22×C1312yes—
308#518C22×C1312yes—
309C22×C4⋊C4—21no—
310C22×C22⋊C4C22×C1311yescharacteristic
311C22×C22⋊C4C22×C1311yescharacteristic
312C2×#99C22×C1314yes—
313#386—22no—
314#386C22×C1314yes—
315#385—22no—
316#385—21no—
317#385—21no—
318#385C22×C1314yes—
319#385C22×C1312yes—
320#385C22×C1312yes—
321#381—22no—
322#379C22×C1312yes—
323C2×#95—21no—
324#342C22×C1312yes—
325#342C22×C1314yes—
326#342C22×C1312yes—
327C22×C13—24no—
328C22×C13—24no—
329C22×C13—21no—
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—22no—
333C22×C13—21no—
334C22×C13—21no—
335C22×C13—22no—
336C22×C13—21no—
337C22×C13—22no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—42no—
341C22×C13—42no—
342C22×C13—48no—
343C22×C13—48no—
344C22×C13—42no—
345C22×C13—42no—
346C22×C13—42no—
347C22×C13—42no—
348C22×C13—42no—
349C22×C13—84no—
350C22×C13B(4,𝔽2)12yes—
351C22×C13#45812yes—
352C22×C13C2×#12011yescharacteristic
353C22×C13#52511yescharacteristic
354C22×C13#53611yescharacteristic
355C22×C13#54714yes—
356C4×C13—44no—
357C4×C13—42no—
358C4×C13—44no—
359C4×C13—41no—
360C4×C13—41no—
361C4×C13—42no—
362C4×C13—41no—
363C4×C13—41no—
364C4×C13—42no—
365C4×C13—84no—
366C25C23×C1311yescharacteristic
367C2×#41—21no—
368C2×#41—21no—
369C22×D4D4×C1312yes—
370C22×D4D4×C1312yes—
371C22×D4C23×C1312yes—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—22no—
375C23×C4—21no—
376C23×C4—22no—
377C23×C4—44no—
378C23×C4D4×C1311yescharacteristic
379C23×C4D4×C1311yescharacteristic
380C23×C4C23×C1312yes—
381#126—22no—
382#126—22no—
383#124—22no—
384#124—22no—
385#123—22no—
386#123—22no—
387#123—22no—
388#123—22no—
389#123—22no—
390#123—48no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397#121—21no—
398#121—21no—
399#121—22no—
400#121—22no—
401#121—21no—
402#121—21no—
403#120—22no—
404#120—22no—
405#120—22no—
406#120—22no—
407#120—22no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—22no—
413C4×D4—22no—
414#117—21no—
415#117—21no—
416#117—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—44no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4D4×C1311yescharacteristic
430C2×C22⋊C4D4×C1311yescharacteristic
431C2×C22⋊C4D4×C1312yes—
432C2×C22⋊C4D4×C1312yes—
433C2×C22⋊C4C23×C1314yes—
434C2×C22⋊C4C23×C1311yescharacteristic
435C2×C22⋊C4C23×C1311yescharacteristic
436C2×C22⋊C4C23×C1312yes—
437C2×C22⋊C4C23×C1312yes—
438#99—28no—
439#95—22no—
440#95—22no—
441#95—24no—
442#95—24no—
443C2×C13—21no—
444C2×C13—24no—
445C2×C13—21no—
446C2×C13—22no—
447C2×C13—22no—
448C2×C13—42no—
449C2×C13—82no—
450C2×C13#240611yescharacteristic
451C2×C13C2×B(4,𝔽2)11yescharacteristic
452C2×C13C2×#45811yescharacteristic
453C24—22no—
454C24—22no—
455C24—42no—
456C24—42no—
457C24C2×D4×C1311yescharacteristic
458C24C2×D4×C1312yes—
459C24C2×D4×C1312yes—
460C24C2×D4×C1312yes—
461C24C2×D4×C1311yescharacteristic
462C24C24×C1311yescharacteristic
463#41—82no—
464#41—82no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—24no—
472C2×D4—24no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—44no—
478C2×D4—44no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—28no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—44no—
493C22×C4—48no—
494C22×C4—44no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—44no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4C2×D4×C1312yes—
505C22×C4C2×D4×C1311yescharacteristic
506C22×C4C2×D4×C1312yes—
507C22×C4C2×D4×C1311yescharacteristic
508C22×C4C2×D4×C1311yescharacteristic
509C22×C4C2×D4×C1312yes—
510C22×C4C2×D4×C1311yescharacteristic
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—44no—
520C4⋊C4—44no—
521C4⋊C4—48no—
522C22⋊C4—24no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—24no—
539C22⋊C4—24no—
540C22⋊C4—48no—
541C22⋊C4—44no—
542C22⋊C4—44no—
543C22⋊C4C13×#4114yescomplemented
544C42—22no—
545C42—22no—
546C13#2411211yescharacteristic, direct product factor, Sylow
547C23—22no—
548C23—22no—
549C23—21no—
550C23—21no—
551C23—24no—
552C23—24no—
553C23—21no—
554C23—21no—
555C23—24no—
556C23—24no—
557C23—22no—
558C23—24no—
559C23—41no—
560C23—42no—
561C23—41no—
562C23—41no—
563C23—42no—
564C23—41no—
565C23—48no—
566C23—48no—
567C23—42no—
568C23—42no—
569C23C13×#12012yes—
570C23C13×#12011yescharacteristic
571C23C13×#12011yescharacteristic
572C23C22×D4×C1311yescharacteristic
573C23C22×D4×C1312yes—
574C23C2×C13×#4112yes—
575C23C13×2−1+412yes—
576Q8—81no—
577Q8—81no—
578D4—44no—
579D4—44no—
580D4—42no—
581D4—42no—
582D4—44no—
583D4—82no—
584D4—82no—
585D4—81no—
586D4—81no—
587C2×C4—28no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—48no—
603C2×C4—48no—
604C2×C4—42no—
605C2×C4—44no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—81no—
619C2×C4—81no—
620C2×C4—82no—
621C2×C4—82no—
622C22—24no—
623C22—24no—
624C22—21no—
625C22—22no—
626C22—21no—
627C22—21no—
628C22—22no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—42no—
636C22—42no—
637C22—48no—
638C22—48no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—84no—
645C22C13×B(4,𝔽2)12yes—
646C22C13×#45812yes—
647C22C2×C13×#12011yescharacteristic
648C22C13×#52511yescharacteristic
649C22C13×#53611yescharacteristic
650C22C13×#54714yes—
651C4—44no—
652C4—44no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—41no—
657C4—41no—
658C4—42no—
659C4—42no—
660C4—84no—
661C2—21no—
662C2—24no—
663C2—22no—
664C2—22no—
665C2—21no—
666C2—42no—
667C2—82no—
668C2C13×#240611yescharacteristic
669C2C2×C13×B(4,𝔽2)11yescharacteristic
670C2C2×C13×#45811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC13×#3490C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C25×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2849C2semidirect
3. C2×C13×#385C2semidirect
4. C13×#2062C2semidirect
5. C13×#2044C2semidirect
6. C13×#1898C2semidirect
7. C13×#1867C2semidirect
8. C13×#1819C2semidirect
118. #24112C13direct (N × H)
209. C13×C22⋊C4#41semidirect
213. #2849C2×C13semidirect
214. C2×#385C2×C13semidirect
215. #2062C2×C13semidirect
216. #2044C2×C13semidirect
217. #1898C2×C13semidirect
218. #1867C2×C13semidirect
219. #1819C2×C13semidirect
543. C22⋊C4C13×#41semidirect
546. C13#24112direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34902
C13×#28492
C2×C13×#3852
C13×#20622
C13×#20442
C13×#18982
C13×#18672
C13×#18192
#2411213