Finite Group Databasebeta

← C13×#18428 #15704767

Subgroups — C13×#18428 #15704767

Order 3328.

1104 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3561C211yesmaximal, characteristic, complemented
2C13×#3217C211yesmaximal, characteristic, complemented
3C13×#3208C211yesmaximal, characteristic, complemented
4C13×#2657C211yesmaximal, characteristic, complemented
5C13×#1600C214yesmaximal, complemented
6C13×#1596C214yesmaximal, complemented
7C13×#1506C211yesmaximal, characteristic, complemented
8C13×#1500C211yesmaximal, characteristic, complemented
9C13×#1469C211yesmaximal, characteristic, complemented
10C13×#563—21no—
11C13×#562—21no—
12C13×#556—21no—
13C13×#551—22no—
14D4×Q8×C13—21no—
15C13×#548—21no—
16C13×#546—21no—
17C13×#543C2212yes—
18C13×#542—21no—
19C13×#542—22no—
20C13×#538C2212yes—
21C13×#536—21no—
22C13×#533C2211yescharacteristic
23C2×C13×#127—21no—
24C2×C13×#127C2211yescharacteristic
25C13×#529C2211yescharacteristic
26C2×C13×#124—21no—
27C2×C13×#124C2211yescharacteristic
28C13×#496—21no—
29C13×#492—21no—
30C13×#490—21no—
31C13×#486—21no—
32C13×#460—22no—
33C13×#460—21no—
34C13×#459—21no—
35C13×#450C2212yes—
36C13×#450C2214yes—
37C13×#447C2212yes—
38C13×#432C2211yescharacteristic
39C13×#431C2211yescharacteristic
40C13×#392—22no—
41C13×#392C2214yes—
42C13×#376C2211yescharacteristic
43C13×#328C2212yes—
44C13×#328C2214yes—
45C13×#327C2212yes—
46C13×#323C2214yes—
47C2×C13×#41—21no—
48C22×Q8×C13—21no—
49C22×Q8×C13D411yescharacteristic
50C22×D4×C13—24no—
51C22×D4×C13—21no—
52C22×D4×C13—21no—
53C22×D4×C13D411yescharacteristic
54C22×D4×C13C2312yes—
55C2×C13×SD16—24no—
56C2×C13×SD16—22no—
57C2×C13×D8—22no—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8—22no—
60C13×C4⋊Q8D411yescharacteristic, complemented
61C13×C4⋊Q8D411yescharacteristic, complemented
62C13×#127—21no—
63C13×#127—21no—
64C13×#127—21no—
65C13×#127—21no—
66C13×#127—44no—
67C13×#126—22no—
68C13×#126—22no—
69C13×#126—22no—
70C13×#126—21no—
71C13×#125—21no—
72C13×#125D411yescharacteristic, complemented
73C13×#124—21no—
74C13×#124—22no—
75C13×#124—22no—
76C13×#124—21no—
77C13×#124—21no—
78C13×#124—21no—
79C13×#124—21no—
80C13×#124—44no—
81C13×#124D411yescharacteristic, complemented
82C13×#123—22no—
83C13×#123—22no—
84C13×#123—22no—
85C13×#123—21no—
86C13×#123—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8—21no—
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8—22no—
96C13×C22⋊Q8C2311yescharacteristic
97C13×C22⋊Q8C2312yes—
98C13×#121—21no—
99C13×#121—22no—
100C13×#121—22no—
101C13×#121C2311yescharacteristic
102C13×#120—22no—
103C4×Q8×C13—21no—
104C4×Q8×C13—21no—
105C4×Q8×C13D411yescharacteristic, complemented
106C4×Q8×C13D412yescomplemented
107C4×D4×C13—21no—
108C4×D4×C13—22no—
109C4×D4×C13—21no—
110C4×D4×C13—22no—
111C4×D4×C13D411yescharacteristic, complemented
112C13×#117—22no—
113C13×#117—21no—
114C13×#117—21no—
115C2×C13×C22⋊C4—22no—
116C2×C13×C22⋊C4—24no—
117C2×C13×C22⋊C4D412yes—
118C2×C13×C22⋊C4C2312yes—
119C2×C42×C13—21no—
120C2×C42×C13C2311yescharacteristic
121C13×C4⋊C8—21no—
122C13×C4⋊C8—21no—
123C13×#102—22no—
124C13×#102—22no—
125C13×#102—24no—
126C13×C22⋊C8C2312yes—
127C13×C22⋊C8C2312yes—
128C13×#97—21no—
129C4×C8×C13—21no—
130C13×#95—21no—
131C13×#95C2312yes—
132#18428C1311yesmaximal, characteristic, direct product factor, Sylow
133C24×C13—22no—
134C24×C13C2×D412yes—
135C13×#41—82no—
136C2×Q8×C13—22no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13—42no—
141C2×Q8×C13—82no—
142C2×Q8×C13C2×D411yescharacteristic
143C2×Q8×C13C2×D412yes—
144C2×D4×C13—21no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—21no—
148C2×D4×C13—21no—
149C2×D4×C13—22no—
150C2×D4×C13—22no—
151C2×D4×C13—42no—
152C2×D4×C13—42no—
153C2×D4×C13—42no—
154C2×D4×C13—48no—
155C2×D4×C13—41no—
156C2×D4×C13—41no—
157C2×D4×C13—41no—
158C2×D4×C13—41no—
159C2×D4×C13—82no—
160C2×D4×C13—82no—
161C2×D4×C13—84no—
162C2×D4×C13—84no—
163C2×D4×C13C2×D411yescharacteristic
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—21no—
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D412yes—
172C22×C4×C13C2411yescharacteristic
173C13×SD16—82no—
174C13×SD16—84no—
175C13×D8—82no—
176C2×C8×C13—22no—
177C2×C8×C13—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4C2×D411yescharacteristic
192C13×C4⋊C4C2×D411yescharacteristic
193C13×C4⋊C4C2×D412yes—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—21no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—21no—
204C13×C22⋊C4—21no—
205C13×C22⋊C4—21no—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—22no—
208C13×C22⋊C4—21no—
209C13×C22⋊C4—48no—
210C42×C13—24no—
211C42×C13—22no—
212C42×C13—22no—
213C42×C13—21no—
214C42×C13C2×D411yescharacteristic
215C42×C13C2×D411yescharacteristic
216C42×C13C2×D411yescharacteristic
217C42×C13C2×D411yescharacteristic
218#3561C2×C1311yescharacteristic, complemented
219#3217C2×C1311yescharacteristic, complemented
220#3208C2×C1311yescharacteristic, complemented
221#2657C2×C1311yescharacteristic, complemented
222#1600C2×C1314yescomplemented
223#1596C2×C1314yescomplemented
224#1506C2×C1311yescharacteristic, complemented
225#1500C2×C1311yescharacteristic, complemented
226#1469C2×C1311yescharacteristic, complemented
227C23×C13—22no—
228C23×C13—21no—
229C23×C13—24no—
230C23×C13—42no—
231C23×C13—42no—
232C23×C13—42no—
233C23×C13—42no—
234C23×C13—44no—
235C23×C13—42no—
236C23×C13—44no—
237C23×C13C22×D411yescharacteristic
238Q8×C13—41no—
239Q8×C13—42no—
240Q8×C13—42no—
241Q8×C13—42no—
242Q8×C13—81no—
243Q8×C13—82no—
244D4×C13—41no—
245D4×C13—42no—
246D4×C13—42no—
247D4×C13—44no—
248D4×C13—42no—
249D4×C13—42no—
250D4×C13—81no—
251D4×C13—82no—
252D4×C13—82no—
253D4×C13—82no—
254D4×C13—82no—
255D4×C13—82no—
256D4×C13—816no—
257D4×C13—82no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—24no—
261C2×C4×C13—21no—
262C2×C4×C13—22no—
263C2×C4×C13—21no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—21no—
267C2×C4×C13—41no—
268C2×C4×C13—42no—
269C2×C4×C13—42no—
270C2×C4×C13—42no—
271C2×C4×C13—42no—
272C2×C4×C13—82no—
273C2×C4×C13—82no—
274C2×C4×C13—82no—
275C2×C4×C13#12011yescharacteristic
276C2×C4×C13#12011yescharacteristic
277C2×C4×C13#12011yescharacteristic
278C2×C4×C13#12011yescharacteristic
279C2×C4×C13C22×D411yescharacteristic
280C2×C4×C13C22×D411yescharacteristic
281C8×C13—42no—
282C8×C13—42no—
283#563—21no—
284#562—21no—
285#556—21no—
286#551—22no—
287D4×Q8—21no—
288#548—21no—
289#546—21no—
290#543C22×C1312yes—
291#542—21no—
292#542—22no—
293#538C22×C1312yes—
294#536—21no—
295#533C22×C1311yescharacteristic
296C2×#127—21no—
297C2×#127C22×C1311yescharacteristic
298#529C22×C1311yescharacteristic
299C2×#124—21no—
300C2×#124C22×C1311yescharacteristic
301#496—21no—
302#492—21no—
303#490—21no—
304#486—21no—
305#460—22no—
306#460—21no—
307#459—21no—
308#450C22×C1312yes—
309#450C22×C1314yes—
310#447C22×C1312yes—
311#432C22×C1311yescharacteristic
312#431C22×C1311yescharacteristic
313#392—22no—
314#392C22×C1314yes—
315#376C22×C1311yescharacteristic
316#328C22×C1312yes—
317#328C22×C1314yes—
318#327C22×C1312yes—
319#323C22×C1314yes—
320C22×C13—21no—
321C22×C13—21no—
322C22×C13—41no—
323C22×C13—42no—
324C22×C13—41no—
325C22×C13—42no—
326C22×C13—42no—
327C22×C13—41no—
328C22×C13—84no—
329C22×C13—84no—
330C22×C13—84no—
331C22×C13—82no—
332C22×C13—82no—
333C22×C13—82no—
334C22×C13C2×#12011yescharacteristic
335C22×C13#57712yes—
336C4×C13—21no—
337C4×C13—21no—
338C4×C13—21no—
339C4×C13—21no—
340C4×C13—21no—
341C4×C13—44no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13—41no—
347C4×C13—42no—
348C4×C13#45312yes—
349C2×#41—21no—
350C22×Q8—21no—
351C22×Q8D4×C1311yescharacteristic
352C22×D4—24no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4D4×C1311yescharacteristic
356C22×D4C23×C1312yes—
357C2×SD16—24no—
358C2×SD16—22no—
359C2×D8—22no—
360C4⋊Q8—21no—
361C4⋊Q8—22no—
362C4⋊Q8D4×C1311yescharacteristic, complemented
363C4⋊Q8D4×C1311yescharacteristic, complemented
364#127—21no—
365#127—21no—
366#127—21no—
367#127—21no—
368#127—44no—
369#126—22no—
370#126—22no—
371#126—22no—
372#126—21no—
373#125—21no—
374#125D4×C1311yescharacteristic, complemented
375#124—21no—
376#124—22no—
377#124—22no—
378#124—21no—
379#124—21no—
380#124—21no—
381#124—21no—
382#124—44no—
383#124D4×C1311yescharacteristic, complemented
384#123—22no—
385#123—22no—
386#123—22no—
387#123—21no—
388#123—22no—
389C22⋊Q8—22no—
390C22⋊Q8—21no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—21no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8C23×C1311yescharacteristic
399C22⋊Q8C23×C1312yes—
400#121—21no—
401#121—22no—
402#121—22no—
403#121C23×C1311yescharacteristic
404#120—22no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8D4×C1311yescharacteristic, complemented
408C4×Q8D4×C1312yescomplemented
409C4×D4—21no—
410C4×D4—22no—
411C4×D4—21no—
412C4×D4—22no—
413C4×D4D4×C1311yescharacteristic, complemented
414#117—22no—
415#117—21no—
416#117—21no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4D4×C1312yes—
420C2×C22⋊C4C23×C1312yes—
421C2×C42—21no—
422C2×C42C23×C1311yescharacteristic
423C4⋊C8—21no—
424C4⋊C8—21no—
425#102—22no—
426#102—22no—
427#102—24no—
428C22⋊C8C23×C1312yes—
429C22⋊C8C23×C1312yes—
430#97—21no—
431C4×C8—21no—
432#95—21no—
433#95C23×C1312yes—
434C2×C13—22no—
435C2×C13—81no—
436C2×C13—82no—
437C2×C13—162no—
438C2×C13#301011yescharacteristic
439C2×C13C2×#45311yescharacteristic
440C2×C13#302711yescharacteristic
441C24—22no—
442C24C2×D4×C1312yes—
443#41—82no—
444C2×Q8—22no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—42no—
449C2×Q8—82no—
450C2×Q8C2×D4×C1311yescharacteristic
451C2×Q8C2×D4×C1312yes—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—48no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—82no—
468C2×D4—82no—
469C2×D4—84no—
470C2×D4—84no—
471C2×D4C2×D4×C1311yescharacteristic
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4C2×D4×C1311yescharacteristic
478C22×C4C2×D4×C1311yescharacteristic
479C22×C4C2×D4×C1312yes—
480C22×C4C24×C1311yescharacteristic
481SD16—82no—
482SD16—84no—
483D8—82no—
484C2×C8—22no—
485C2×C8—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4C2×D4×C1311yescharacteristic
500C4⋊C4C2×D4×C1311yescharacteristic
501C4⋊C4C2×D4×C1312yes—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—21no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—21no—
517C22⋊C4—48no—
518C42—24no—
519C42—22no—
520C42—22no—
521C42—21no—
522C42C2×D4×C1311yescharacteristic
523C42C2×D4×C1311yescharacteristic
524C42C2×D4×C1311yescharacteristic
525C42C2×D4×C1311yescharacteristic
526C13#1842811yescharacteristic, direct product factor, Sylow
527C23—22no—
528C23—21no—
529C23—24no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—44no—
535C23—42no—
536C23—44no—
537C23C22×D4×C1311yescharacteristic
538Q8—41no—
539Q8—42no—
540Q8—42no—
541Q8—42no—
542Q8—81no—
543Q8—82no—
544D4—41no—
545D4—42no—
546D4—42no—
547D4—44no—
548D4—42no—
549D4—42no—
550D4—81no—
551D4—82no—
552D4—82no—
553D4—82no—
554D4—82no—
555D4—82no—
556D4—816no—
557D4—82no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4C13×#12011yescharacteristic
576C2×C4C13×#12011yescharacteristic
577C2×C4C13×#12011yescharacteristic
578C2×C4C13×#12011yescharacteristic
579C2×C4C22×D4×C1311yescharacteristic
580C2×C4C22×D4×C1311yescharacteristic
581C8—42no—
582C8—42no—
583C22—21no—
584C22—21no—
585C22—41no—
586C22—42no—
587C22—41no—
588C22—42no—
589C22—42no—
590C22—41no—
591C22—84no—
592C22—84no—
593C22—84no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22C2×C13×#12011yescharacteristic
598C22C13×#57712yes—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—44no—
605C4—41no—
606C4—41no—
607C4—42no—
608C4—42no—
609C4—41no—
610C4—42no—
611C4C13×#45312yes—
612C2—22no—
613C2—82no—
614C2—81no—
615C2—162no—
616C2C13×#301011yescharacteristic
617C2C2×C13×#45311yescharacteristic
618C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3561C2semidirect
2. C13×#3217C2semidirect
3. C13×#3208C2semidirect
4. C13×#2657C2semidirect
5. C13×#1600C2semidirect
6. C13×#1596C2semidirect
7. C13×#1506C2semidirect
8. C13×#1500C2semidirect
9. C13×#1469C2semidirect
60. C13×C4⋊Q8D4semidirect
61. C13×C4⋊Q8D4semidirect
72. C13×#125D4semidirect
81. C13×#124D4semidirect
105. C4×Q8×C13D4semidirect
106. C4×Q8×C13D4semidirect
111. C4×D4×C13D4semidirect
132. #18428C13direct (N × H)
218. #3561C2×C13semidirect
219. #3217C2×C13semidirect
220. #3208C2×C13semidirect
221. #2657C2×C13semidirect
222. #1600C2×C13semidirect
223. #1596C2×C13semidirect
224. #1506C2×C13semidirect
225. #1500C2×C13semidirect
226. #1469C2×C13semidirect
362. C4⋊Q8D4×C13semidirect
363. C4⋊Q8D4×C13semidirect
374. #125D4×C13semidirect
383. #124D4×C13semidirect
407. C4×Q8D4×C13semidirect
408. C4×Q8D4×C13semidirect
413. C4×D4D4×C13semidirect
526. C13#18428direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35612
C13×#32172
C13×#32082
C13×#26572
C13×#16002
C13×#15962
C13×#15062
C13×#15002
C13×#14692
#1842813