Finite Group Databasebeta

← C13×#9922 #15696261

Subgroups — C13×#9922 #15696261

Order 3328.

1278 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#450C211yesmaximal, characteristic, complemented
2C13×#2626C211yesmaximal, characteristic, complemented
3C2×C13×#392C211yesmaximal, characteristic
4C13×#1786C211yesmaximal, characteristic, complemented
5C2×C13×#328C211yesmaximal, characteristic, complemented
6C2×C13×#323C211yesmaximal, characteristic, complemented
7C13×#1294C211yesmaximal, characteristic, complemented
8C23×D4×C13—21no—
9C23×D4×C13C2211yescharacteristic
10C22×C13×SD16—21no—
11C2×C13×C22⋊Q8C2211yescharacteristic
12C22×C13×C22⋊C4—21no—
13C22×C13×C22⋊C4C2211yescharacteristic
14C13×#450—22no—
15C13×#450—22no—
16C2×C13×#102—21no—
17C2×C13×#102—22no—
18C2×C13×C22⋊C8C2211yescharacteristic
19C2×C13×C22⋊C8C2211yescharacteristic
20C13×#399—21no—
21C13×#396—22no—
22C13×#393—21no—
23C13×#392—22no—
24C13×#392—22no—
25C13×#385—21no—
26C13×#380C2211yescharacteristic
27C13×#379—21no—
28C2×C13×#95C2211yescharacteristic
29C13×#328—22no—
30C13×#323—22no—
31C25×C13—21no—
32C25×C13D411yescharacteristic
33C22×Q8×C13D411yescharacteristic, complemented
34C22×D4×C13—24no—
35C22×D4×C13—21no—
36C22×D4×C13—21no—
37C22×D4×C13—21no—
38C22×D4×C13—21no—
39C22×D4×C13—21no—
40C22×D4×C13—44no—
41C22×D4×C13—44no—
42C22×D4×C13—44no—
43C22×D4×C13—42no—
44C22×D4×C13—42no—
45C22×D4×C13D412yes—
46C23×C4×C13—21no—
47C23×C4×C13D411yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C2×C13×SD16—24no—
50C2×C13×SD16—44no—
51C22×C8×C13—21no—
52C22×C8×C13—21no—
53C13×C22⋊Q8—21no—
54C13×C22⋊Q8—21no—
55C13×C22⋊Q8—21no—
56C13×C22⋊Q8—21no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4D411yescharacteristic, complemented
60C2×C13×C4⋊C4D412yescomplemented
61C2×C13×C22⋊C4—24no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4—21no—
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4—21no—
68C2×C13×C22⋊C4—21no—
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4—44no—
73C13×#102—24no—
74C13×#102—44no—
75C13×C22⋊C8—21no—
76C13×C22⋊C8—21no—
77C13×C22⋊C8—21no—
78C13×C22⋊C8D412yescomplemented
79C13×#95—22no—
80C13×#95—21no—
81C13×#95—21no—
82C13×#95D412yes—
83#9922C1311yesmaximal, characteristic, direct product factor, Sylow
84C24×C13—24no—
85C24×C13—21no—
86C24×C13—22no—
87C24×C13—21no—
88C24×C13—21no—
89C24×C13—21no—
90C24×C13—21no—
91C24×C13—21no—
92C24×C13—42no—
93C24×C13—42no—
94C24×C13—42no—
95C24×C13—42no—
96C24×C13—42no—
97C24×C13—41no—
98C24×C13—41no—
99C24×C13—41no—
100C24×C13—41no—
101C24×C13—41no—
102C24×C13—41no—
103C24×C13SD1612yescomplemented
104C24×C13C2×D411yescharacteristic
105C2×Q8×C13—21no—
106C2×Q8×C13—21no—
107C2×Q8×C13—42no—
108C2×D4×C13—24no—
109C2×D4×C13—24no—
110C2×D4×C13—22no—
111C2×D4×C13—22no—
112C2×D4×C13—42no—
113C2×D4×C13—42no—
114C2×D4×C13—48no—
115C2×D4×C13—44no—
116C2×D4×C13—44no—
117C2×D4×C13—44no—
118C2×D4×C13—44no—
119C2×D4×C13—48no—
120C2×D4×C13—48no—
121C2×D4×C13—416no—
122C2×D4×C13—416no—
123C2×D4×C13—41no—
124C2×D4×C13—41no—
125C22×C4×C13—24no—
126C22×C4×C13—22no—
127C22×C4×C13—21no—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13—41no—
136C22×C4×C13—41no—
137C22×C4×C13—42no—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13#4111yescharacteristic
144C13×SD16—48no—
145C2×C8×C13—22no—
146C2×C8×C13—42no—
147C2×C8×C13—42no—
148C2×C8×C13—41no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—42no—
152C13×C4⋊C4—41no—
153C13×C4⋊C4—41no—
154C13×C4⋊C4—82no—
155C13×C22⋊C4—48no—
156C13×C22⋊C4—41no—
157C13×C22⋊C4—41no—
158C13×C22⋊C4—41no—
159C13×C22⋊C4—41no—
160C13×C22⋊C4—41no—
161C13×C22⋊C4—41no—
162C13×C22⋊C4—41no—
163C13×C22⋊C4—41no—
164C13×C22⋊C4—82no—
165C13×C22⋊C4—82no—
166C2×#450C2×C1311yescharacteristic, complemented
167#2626C2×C1311yescharacteristic, complemented
168C2×#392C2×C1311yescharacteristic
169#1786C2×C1311yescharacteristic, complemented
170C2×#328C2×C1311yescharacteristic, complemented
171C2×#323C2×C1311yescharacteristic, complemented
172#1294C2×C1311yescharacteristic, complemented
173C23×C13—22no—
174C23×C13—22no—
175C23×C13—24no—
176C23×C13—22no—
177C23×C13—22no—
178C23×C13—22no—
179C23×C13—44no—
180C23×C13—42no—
181C23×C13—44no—
182C23×C13—44no—
183C23×C13—44no—
184C23×C13—42no—
185C23×C13—42no—
186C23×C13—42no—
187C23×C13—42no—
188C23×C13—44no—
189C23×C13—44no—
190C23×C13—44no—
191C23×C13—41no—
192C23×C13—42no—
193C23×C13—41no—
194C23×C13—42no—
195C23×C13—41no—
196C23×C13—42no—
197C23×C13—42no—
198C23×C13—42no—
199C23×C13—44no—
200C23×C13—41no—
201C23×C13—82no—
202C23×C13—82no—
203C23×C13—82no—
204C23×C13—82no—
205C23×C13—82no—
206C23×C13—82no—
207C23×C13—82no—
208C23×C13—81no—
209C23×C13—81no—
210C23×C13—81no—
211C23×C13—81no—
212C23×C13—82no—
213C23×C13—81no—
214C23×C13—81no—
215C23×C13#12011yescharacteristic
216C23×C13#12011yescharacteristic
217C23×C13#12111yescharacteristic
218C23×C13C2×SD1611yescharacteristic
219C23×C13#13511yescharacteristic
220C23×C13AGL(1,ℤ/8)11yescharacteristic
221C23×C13#13711yescharacteristic
222Q8×C13—42no—
223Q8×C13—81no—
224D4×C13—24no—
225D4×C13—24no—
226D4×C13—42no—
227D4×C13—44no—
228D4×C13—42no—
229D4×C13—44no—
230D4×C13—432no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—24no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—44no—
239C2×C4×C13—44no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—81no—
253C2×C4×C13#12011yescharacteristic
254C2×C4×C13#12111yescharacteristic
255C2×C4×C13#12111yescharacteristic
256C2×C4×C13#12711yescharacteristic
257C8×C13—42no—
258C8×C13—81no—
259C23×D4—21no—
260C23×D4C22×C1311yescharacteristic
261C22×SD16—21no—
262C2×C22⋊Q8C22×C1311yescharacteristic
263C22×C22⋊C4—21no—
264C22×C22⋊C4C22×C1311yescharacteristic
265#450—22no—
266#450—22no—
267C2×#102—21no—
268C2×#102—22no—
269C2×C22⋊C8C22×C1311yescharacteristic
270C2×C22⋊C8C22×C1311yescharacteristic
271#399—21no—
272#396—22no—
273#393—21no—
274#392—22no—
275#392—22no—
276#385—21no—
277#380C22×C1311yescharacteristic
278#379—21no—
279C2×#95C22×C1311yescharacteristic
280#328—22no—
281#323—22no—
282C22×C13—22no—
283C22×C13—22no—
284C22×C13—22no—
285C22×C13—22no—
286C22×C13—21no—
287C22×C13—21no—
288C22×C13—21no—
289C22×C13—21no—
290C22×C13—44no—
291C22×C13—44no—
292C22×C13—44no—
293C22×C13—44no—
294C22×C13—42no—
295C22×C13—44no—
296C22×C13—82no—
297C22×C13—82no—
298C22×C13—82no—
299C22×C13—82no—
300C22×C13—84no—
301C22×C13—82no—
302C22×C13—84no—
303C22×C13—84no—
304C22×C13—82no—
305C22×C13—84no—
306C22×C13—82no—
307C22×C13—81no—
308C22×C13—82no—
309C22×C13—81no—
310C22×C13#39211yescharacteristic
311C22×C13#44811yescharacteristic
312C22×C13#44911yescharacteristic
313C22×C13#45011yescharacteristic
314C22×C13#45211yescharacteristic
315C22×C13#45312yes—
316C22×C13B(4,𝔽2)12yes—
317C22×C13#46511yescharacteristic
318C22×C13#46811yescharacteristic
319C4×C13—21no—
320C4×C13—21no—
321C4×C13—21no—
322C4×C13—21no—
323C4×C13—44no—
324C4×C13—82no—
325C4×C13—81no—
326C4×C13—81no—
327C4×C13—81no—
328C25—21no—
329C25D4×C1311yescharacteristic
330C22×Q8D4×C1311yescharacteristic, complemented
331C22×D4—24no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4—44no—
338C22×D4—44no—
339C22×D4—44no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4D4×C1312yes—
343C23×C4—21no—
344C23×C4D4×C1311yescharacteristic
345C23×C4C23×C1311yescharacteristic
346C2×SD16—24no—
347C2×SD16—44no—
348C22×C8—21no—
349C22×C8—21no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C1311yescharacteristic, complemented
357C2×C4⋊C4D4×C1312yescomplemented
358C2×C22⋊C4—24no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—44no—
370#102—24no—
371#102—44no—
372C22⋊C8—21no—
373C22⋊C8—21no—
374C22⋊C8—21no—
375C22⋊C8D4×C1312yescomplemented
376#95—22no—
377#95—21no—
378#95—21no—
379#95D4×C1312yes—
380C2×C13—21no—
381C2×C13—21no—
382C2×C13—21no—
383C2×C13—21no—
384C2×C13—82no—
385C2×C13—84no—
386C2×C13#159612yes—
387C2×C13#160012yes—
388C2×C13#200011yescharacteristic
389C2×C13#200211yescharacteristic
390C2×C13#202111yescharacteristic
391C24—24no—
392C24—21no—
393C24—21no—
394C24—22no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—42no—
400C24—42no—
401C24—42no—
402C24—42no—
403C24—42no—
404C24—41no—
405C24—41no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24C13×SD1612yescomplemented
411C24C2×D4×C1311yescharacteristic
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—42no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—48no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—48no—
427C2×D4—48no—
428C2×D4—416no—
429C2×D4—416no—
430C2×D4—41no—
431C2×D4—41no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—42no—
445C22×C4C2×D4×C1311yescharacteristic
446C22×C4C2×D4×C1311yescharacteristic
447C22×C4C2×D4×C1311yescharacteristic
448C22×C4C2×D4×C1311yescharacteristic
449C22×C4C2×D4×C1311yescharacteristic
450C22×C4C13×#4111yescharacteristic
451SD16—48no—
452C2×C8—22no—
453C2×C8—42no—
454C2×C8—42no—
455C2×C8—41no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—42no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—82no—
462C22⋊C4—48no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—82no—
472C22⋊C4—82no—
473C13#992211yescharacteristic, direct product factor, Sylow
474C23—22no—
475C23—22no—
476C23—24no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—44no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—44no—
487C23—44no—
488C23—44no—
489C23—44no—
490C23—44no—
491C23—44no—
492C23—41no—
493C23—42no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—44no—
501C23—41no—
502C23—82no—
503C23—81no—
504C23—81no—
505C23—82no—
506C23—82no—
507C23—82no—
508C23—82no—
509C23—82no—
510C23—82no—
511C23—81no—
512C23—81no—
513C23—82no—
514C23—81no—
515C23—81no—
516C23C13×#12011yescharacteristic
517C23C13×#12011yescharacteristic
518C23C13×#12111yescharacteristic
519C23C2×C13×SD1611yescharacteristic
520C23C13×#13511yescharacteristic
521C23C13×AGL(1,ℤ/8)11yescharacteristic
522C23C13×#13711yescharacteristic
523Q8—42no—
524Q8—81no—
525D4—24no—
526D4—24no—
527D4—42no—
528D4—44no—
529D4—42no—
530D4—44no—
531D4—432no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—81no—
554C2×C4C13×#12011yescharacteristic
555C2×C4C13×#12111yescharacteristic
556C2×C4C13×#12111yescharacteristic
557C2×C4C13×#12711yescharacteristic
558C8—42no—
559C8—81no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—44no—
569C22—44no—
570C22—44no—
571C22—42no—
572C22—44no—
573C22—44no—
574C22—82no—
575C22—82no—
576C22—82no—
577C22—82no—
578C22—84no—
579C22—82no—
580C22—84no—
581C22—82no—
582C22—81no—
583C22—82no—
584C22—81no—
585C22—84no—
586C22—82no—
587C22—84no—
588C22C13×#39211yescharacteristic
589C22C13×#44811yescharacteristic
590C22C13×#44911yescharacteristic
591C22C13×#45011yescharacteristic
592C22C13×#45211yescharacteristic
593C22C13×#45312yes—
594C22C13×B(4,𝔽2)12yes—
595C22C13×#46511yescharacteristic
596C22C13×#46811yescharacteristic
597C4—21no—
598C4—21no—
599C4—21no—
600C4—21no—
601C4—44no—
602C4—81no—
603C4—81no—
604C4—81no—
605C4—82no—
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—82no—
611C2—84no—
612C2C13×#159612yes—
613C2C13×#160012yes—
614C2C13×#200011yescharacteristic
615C2C13×#200211yescharacteristic
616C2C13×#202111yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#392C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#450C2semidirect
2. C13×#2626C2semidirect
4. C13×#1786C2semidirect
5. C2×C13×#328C2semidirect
6. C2×C13×#323C2semidirect
7. C13×#1294C2semidirect
33. C22×Q8×C13D4semidirect
59. C2×C13×C4⋊C4D4semidirect
60. C2×C13×C4⋊C4D4semidirect
78. C13×C22⋊C8D4semidirect
83. #9922C13direct (N × H)
103. C24×C13SD16semidirect
166. C2×#450C2×C13semidirect
167. #2626C2×C13semidirect
169. #1786C2×C13semidirect
170. C2×#328C2×C13semidirect
171. C2×#323C2×C13semidirect
172. #1294C2×C13semidirect
330. C22×Q8D4×C13semidirect
356. C2×C4⋊C4D4×C13semidirect
357. C2×C4⋊C4D4×C13semidirect
375. C22⋊C8D4×C13semidirect
410. C24C13×SD16semidirect
473. C13#9922direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4502
C13×#26262
C2×C13×#3922
C13×#17862
C2×C13×#3282
C2×C13×#3232
C13×#12942
#992213