Finite Group Databasebeta

← C13×#18437 #15704776

Subgroups — C13×#18437 #15704776

Order 3328.

1028 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3558C211yesmaximal, characteristic
2C13×#3239C211yesmaximal, characteristic, complemented
3C13×#3227C211yesmaximal, characteristic, complemented
4C13×#2658C211yesmaximal, characteristic, complemented
5C13×#1618C214yesmaximal, complemented
6C13×#1613C214yesmaximal, complemented
7C13×#1505C211yesmaximal, characteristic, complemented
8C13×#1500C211yesmaximal, characteristic, complemented
9C13×#1469C211yesmaximal, characteristic, complemented
10C13×#562—21no—
11C13×H(3,𝔽4)—21no—
12C13×#559—21no—
13C13×#548—21no—
14C13×#546—21no—
15C13×#546—22no—
16D42×C13—21no—
17C13×#542—21no—
18C13×#538—22no—
19C13×#538C2212yes—
20C13×#535—21no—
21C13×#534C2212yes—
22C13×#532C2211yescharacteristic
23C2×C13×C4⋊Q8—21no—
24C2×C13×C4⋊Q8C2211yescharacteristic, complemented
25C13×#529C2211yescharacteristic
26C2×C13×#124—21no—
27C2×C13×#124C2211yescharacteristic
28C13×#501—21no—
29C13×#498—21no—
30C13×#489—21no—
31C13×#486—21no—
32C13×#484C2212yescomplemented
33C13×#481C2212yes—
34C13×#481C2214yescomplemented
35C13×#476—22no—
36C13×#475—21no—
37C13×#474—21no—
38C13×#432C2211yescharacteristic, complemented
39C13×#431C2211yescharacteristic, complemented
40C13×#399—22no—
41C13×#399C2214yescomplemented
42C13×#376C2211yescharacteristic, complemented
43C13×#328C2212yescomplemented
44C13×#327C2212yes—
45C13×#327C2214yescomplemented
46C13×#323C2214yescomplemented
47C2×C13×#41—21no—
48C2×C13×#41—21no—
49C22×Q8×C13—21no—
50C22×Q8×C13D411yescharacteristic
51C22×D4×C13—21no—
52C22×D4×C13—22no—
53C22×D4×C13D411yescharacteristic
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—21no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8—44no—
59C13×C4⋊Q8D411yescharacteristic
60C13×#127—21no—
61C13×#127D411yescharacteristic
62C13×#126—22no—
63C13×#126—21no—
64C13×#125D411yescharacteristic
65C13×#124—21no—
66C13×#124—22no—
67C13×#124—22no—
68C13×#124—22no—
69C13×#124—21no—
70C13×#124—21no—
71C13×#124—21no—
72C13×#124—21no—
73C13×#124—21no—
74C13×#124—44no—
75C13×#124D411yescharacteristic
76C13×#123—22no—
77C13×#123—21no—
78C13×#123—22no—
79C13×#123—22no—
80C13×#123—22no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—21no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8C2311yescharacteristic
85C13×#121—22no—
86C13×#121—22no—
87C13×#121—22no—
88C13×#121—21no—
89C13×#121—22no—
90C13×#121—21no—
91C13×#121—22no—
92C13×#121C2311yescharacteristic
93C13×#121C2312yes—
94C13×#120—22no—
95C13×#120—22no—
96C13×#120—22no—
97C13×#120—22no—
98C13×#120—22no—
99C4×Q8×C13—21no—
100C4×Q8×C13D411yescharacteristic
101C4×D4×C13—22no—
102C4×D4×C13—21no—
103C4×D4×C13—21no—
104C4×D4×C13—22no—
105C4×D4×C13—21no—
106C4×D4×C13D411yescharacteristic
107C4×D4×C13D412yes—
108C13×#117—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—24no—
111C2×C13×C4⋊C4C2312yes—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—24no—
114C2×C13×C22⋊C4D412yes—
115C2×C13×C22⋊C4C2312yes—
116C2×C42×C13—21no—
117C2×C42×C13C2311yescharacteristic
118C13×#107—22no—
119C13×#106—22no—
120C13×#106—24no—
121C13×C4⋊C8—21no—
122C13×C4⋊C8—21no—
123C13×#103—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#18437C1311yesmaximal, characteristic, direct product factor, Sylow
133C24×C13—22no—
134C24×C13C2×D412yes—
135C13×#41—82no—
136C13×#41—82no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13—42no—
141C2×Q8×C13—42no—
142C2×Q8×C13—42no—
143C2×Q8×C13—41no—
144C2×Q8×C13—41no—
145C2×Q8×C13C2×D411yescharacteristic
146C2×D4×C13—22no—
147C2×D4×C13—21no—
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—22no—
151C2×D4×C13—22no—
152C2×D4×C13—22no—
153C2×D4×C13—21no—
154C2×D4×C13—21no—
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C2×D4×C13—42no—
158C2×D4×C13—82no—
159C2×D4×C13—84no—
160C2×D4×C13C2×D411yescharacteristic
161C2×D4×C13C2×D412yes—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—21no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2411yescharacteristic
172C2×C8×C13—22no—
173C2×C8×C13—22no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—48no—
184C13×C4⋊C4—41no—
185C13×C4⋊C4—41no—
186C13×C4⋊C4C2×D412yes—
187C13×C4⋊C4C2×D411yescharacteristic
188C13×C4⋊C4C2×D411yescharacteristic
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—21no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—21no—
199C13×C22⋊C4—21no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—21no—
204C13×C22⋊C4—22no—
205C13×C22⋊C4—48no—
206C42×C13—24no—
207C42×C13—22no—
208C42×C13—21no—
209C42×C13C2×D411yescharacteristic
210C42×C13C2×D411yescharacteristic
211C42×C13C2×D411yescharacteristic
212C42×C13C2×D411yescharacteristic
213#3558C2×C1311yescharacteristic
214#3239C2×C1311yescharacteristic, complemented
215#3227C2×C1311yescharacteristic, complemented
216#2658C2×C1311yescharacteristic, complemented
217#1618C2×C1314yescomplemented
218#1613C2×C1314yescomplemented
219#1505C2×C1311yescharacteristic, complemented
220#1500C2×C1311yescharacteristic, complemented
221#1469C2×C1311yescharacteristic, complemented
222C23×C13—22no—
223C23×C13—21no—
224C23×C13—22no—
225C23×C13—24no—
226C23×C13—42no—
227C23×C13—42no—
228C23×C13—82no—
229C23×C13—82no—
230C23×C13—82no—
231C23×C13C22×D411yescharacteristic
232Q8×C13—41no—
233Q8×C13—42no—
234Q8×C13—81no—
235Q8×C13—81no—
236Q8×C13—82no—
237Q8×C13—82no—
238D4×C13—42no—
239D4×C13—41no—
240D4×C13—42no—
241D4×C13—44no—
242D4×C13—42no—
243D4×C13—42no—
244D4×C13—81no—
245D4×C13—81no—
246D4×C13—82no—
247D4×C13—82no—
248D4×C13—82no—
249D4×C13—82no—
250D4×C13—82no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—24no—
254C2×C4×C13—21no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—41no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13—82no—
268C2×C4×C13—82no—
269C2×C4×C13—82no—
270C2×C4×C13#12011yescharacteristic
271C2×C4×C13#12011yescharacteristic
272C2×C4×C13#12011yescharacteristic
273C2×C4×C13#12011yescharacteristic
274C2×C4×C13C22×D411yescharacteristic
275C2×C4×C13C22×D411yescharacteristic
276C8×C13—42no—
277C8×C13—42no—
278#562—21no—
279H(3,𝔽4)—21no—
280#559—21no—
281#548—21no—
282#546—21no—
283#546—22no—
284D42—21no—
285#542—21no—
286#538—22no—
287#538C22×C1312yes—
288#535—21no—
289#534C22×C1312yes—
290#532C22×C1311yescharacteristic
291C2×C4⋊Q8—21no—
292C2×C4⋊Q8C22×C1311yescharacteristic, complemented
293#529C22×C1311yescharacteristic
294C2×#124—21no—
295C2×#124C22×C1311yescharacteristic
296#501—21no—
297#498—21no—
298#489—21no—
299#486—21no—
300#484C22×C1312yescomplemented
301#481C22×C1312yes—
302#481C22×C1314yescomplemented
303#476—22no—
304#475—21no—
305#474—21no—
306#432C22×C1311yescharacteristic, complemented
307#431C22×C1311yescharacteristic, complemented
308#399—22no—
309#399C22×C1314yescomplemented
310#376C22×C1311yescharacteristic, complemented
311#328C22×C1312yescomplemented
312#327C22×C1312yes—
313#327C22×C1314yescomplemented
314#323C22×C1314yescomplemented
315C22×C13—21no—
316C22×C13—21no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—41no—
320C22×C13—41no—
321C22×C13—42no—
322C22×C13—42no—
323C22×C13—42no—
324C22×C13—41no—
325C22×C13—42no—
326C22×C13—84no—
327C22×C13—164no—
328C22×C13C2×#12011yescharacteristic
329C22×C13#57712yes—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13—44no—
336C4×C13—41no—
337C4×C13—42no—
338C4×C13—41no—
339C4×C13—42no—
340C4×C13—41no—
341C4×C13—82no—
342C4×C13#45312yes—
343C2×#41—21no—
344C2×#41—21no—
345C22×Q8—21no—
346C22×Q8D4×C1311yescharacteristic
347C22×D4—21no—
348C22×D4—22no—
349C22×D4D4×C1311yescharacteristic
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—44no—
355C4⋊Q8D4×C1311yescharacteristic
356#127—21no—
357#127D4×C1311yescharacteristic
358#126—22no—
359#126—21no—
360#125D4×C1311yescharacteristic
361#124—21no—
362#124—22no—
363#124—22no—
364#124—22no—
365#124—21no—
366#124—21no—
367#124—21no—
368#124—21no—
369#124—21no—
370#124—44no—
371#124D4×C1311yescharacteristic
372#123—22no—
373#123—21no—
374#123—22no—
375#123—22no—
376#123—22no—
377C22⋊Q8—22no—
378C22⋊Q8—21no—
379C22⋊Q8—22no—
380C22⋊Q8C23×C1311yescharacteristic
381#121—22no—
382#121—22no—
383#121—22no—
384#121—21no—
385#121—22no—
386#121—21no—
387#121—22no—
388#121C23×C1311yescharacteristic
389#121C23×C1312yes—
390#120—22no—
391#120—22no—
392#120—22no—
393#120—22no—
394#120—22no—
395C4×Q8—21no—
396C4×Q8D4×C1311yescharacteristic
397C4×D4—22no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—22no—
401C4×D4—21no—
402C4×D4D4×C1311yescharacteristic
403C4×D4D4×C1312yes—
404#117—21no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4C23×C1312yes—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4D4×C1312yes—
411C2×C22⋊C4C23×C1312yes—
412C2×C42—21no—
413C2×C42C23×C1311yescharacteristic
414#107—22no—
415#106—22no—
416#106—24no—
417C4⋊C8—21no—
418C4⋊C8—21no—
419#103—22no—
420#102—22no—
421#102—24no—
422C22⋊C8C23×C1312yes—
423C22⋊C8C23×C1312yes—
424#97—21no—
425C4×C8—21no—
426#95—21no—
427#95C23×C1312yes—
428C2×C13—22no—
429C2×C13—82no—
430C2×C13—82no—
431C2×C13—81no—
432C2×C13#300911yescharacteristic
433C2×C13C2×#45311yescharacteristic
434C2×C13#302811yescharacteristic
435C24—22no—
436C24C2×D4×C1312yes—
437#41—82no—
438#41—82no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—42no—
443C2×Q8—42no—
444C2×Q8—42no—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8C2×D4×C1311yescharacteristic
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—42no—
460C2×D4—82no—
461C2×D4—84no—
462C2×D4C2×D4×C1311yescharacteristic
463C2×D4C2×D4×C1312yes—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4C2×D4×C1311yescharacteristic
471C22×C4C2×D4×C1311yescharacteristic
472C22×C4C2×D4×C1312yes—
473C22×C4C24×C1311yescharacteristic
474C2×C8—22no—
475C2×C8—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—48no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C1312yes—
489C4⋊C4C2×D4×C1311yescharacteristic
490C4⋊C4C2×D4×C1311yescharacteristic
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—21no—
506C22⋊C4—22no—
507C22⋊C4—48no—
508C42—24no—
509C42—22no—
510C42—21no—
511C42C2×D4×C1311yescharacteristic
512C42C2×D4×C1311yescharacteristic
513C42C2×D4×C1311yescharacteristic
514C42C2×D4×C1311yescharacteristic
515C13#1843711yescharacteristic, direct product factor, Sylow
516C23—22no—
517C23—21no—
518C23—22no—
519C23—24no—
520C23—42no—
521C23—42no—
522C23—82no—
523C23—82no—
524C23—82no—
525C23C22×D4×C1311yescharacteristic
526Q8—41no—
527Q8—42no—
528Q8—81no—
529Q8—81no—
530Q8—82no—
531Q8—82no—
532D4—42no—
533D4—41no—
534D4—42no—
535D4—44no—
536D4—42no—
537D4—42no—
538D4—81no—
539D4—81no—
540D4—82no—
541D4—82no—
542D4—82no—
543D4—82no—
544D4—82no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—82no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4C13×#12011yescharacteristic
565C2×C4C13×#12011yescharacteristic
566C2×C4C13×#12011yescharacteristic
567C2×C4C13×#12011yescharacteristic
568C2×C4C22×D4×C1311yescharacteristic
569C2×C4C22×D4×C1311yescharacteristic
570C8—42no—
571C8—42no—
572C22—21no—
573C22—21no—
574C22—42no—
575C22—42no—
576C22—41no—
577C22—41no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—41no—
582C22—42no—
583C22—84no—
584C22—164no—
585C22C2×C13×#12011yescharacteristic
586C22C13×#57712yes—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—21no—
592C4—44no—
593C4—41no—
594C4—42no—
595C4—41no—
596C4—42no—
597C4—41no—
598C4—82no—
599C4C13×#45312yes—
600C2—22no—
601C2—82no—
602C2—81no—
603C2—82no—
604C2C13×#300911yescharacteristic
605C2C2×C13×#45311yescharacteristic
606C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3558C2
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
2. C13×#3239C2semidirect
3. C13×#3227C2semidirect
4. C13×#2658C2semidirect
5. C13×#1618C2semidirect
6. C13×#1613C2semidirect
7. C13×#1505C2semidirect
8. C13×#1500C2semidirect
9. C13×#1469C2semidirect
24. C2×C13×C4⋊Q8C22semidirect
32. C13×#484C22semidirect
34. C13×#481C22semidirect
38. C13×#432C22semidirect
39. C13×#431C22semidirect
41. C13×#399C22semidirect
42. C13×#376C22semidirect
43. C13×#328C22semidirect
45. C13×#327C22semidirect
46. C13×#323C22semidirect
132. #18437C13direct (N × H)
214. #3239C2×C13semidirect
215. #3227C2×C13semidirect
216. #2658C2×C13semidirect
217. #1618C2×C13semidirect
218. #1613C2×C13semidirect
219. #1505C2×C13semidirect
220. #1500C2×C13semidirect
221. #1469C2×C13semidirect
292. C2×C4⋊Q8C22×C13semidirect
300. #484C22×C13semidirect
302. #481C22×C13semidirect
306. #432C22×C13semidirect
307. #431C22×C13semidirect
309. #399C22×C13semidirect
310. #376C22×C13semidirect
311. #328C22×C13semidirect
313. #327C22×C13semidirect
314. #323C22×C13semidirect
515. C13#18437direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35582
C13×#32392
C13×#32272
C13×#26582
C13×#16182
C13×#16132
C13×#15052
C13×#15002
C13×#14692
#1843713