Finite Group Databasebeta

← C13×#18427 #15704766

Subgroups — C13×#18427 #15704766

Order 3328.

996 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3558C211yesmaximal, characteristic
2C13×#3218C211yesmaximal, characteristic, complemented
3C13×#3206C211yesmaximal, characteristic, complemented
4C13×#2640C211yesmaximal, characteristic, complemented
5C13×#1606C214yesmaximal, complemented
6C13×#1601C214yesmaximal, 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⋊Q8C2211yescharacteristic, complemented
24C13×#529C2211yescharacteristic
25C2×C13×#124C2211yescharacteristic
26C13×#497—21no—
27C13×#492—21no—
28C13×#491—21no—
29C13×#487—21no—
30C13×#462—21no—
31C13×#461—22no—
32C13×#461—21no—
33C13×#451C2212yescomplemented
34C13×#448C2212yes—
35C13×#448C2214yescomplemented
36C13×#432C2211yescharacteristic, complemented
37C13×#431C2211yescharacteristic, complemented
38C13×#397—22no—
39C13×#393C2214yescomplemented
40C13×#391—21no—
41C13×#390—21no—
42C13×#376C2211yescharacteristic, complemented
43C13×#328C2212yescomplemented
44C13×#327C2212yes—
45C13×#327C2214yescomplemented
46C13×#323C2214yescomplemented
47C2×C13×#41—21no—
48C2×C13×#41—21no—
49C22×Q8×C13D411yescharacteristic
50C22×Q8×C13C2312yes—
51C22×D4×C13—21no—
52C22×D4×C13—22no—
53C22×D4×C13D411yescharacteristic
54C2×C13×Q16—22no—
55C2×C13×SD16—22no—
56C2×C13×SD16—24no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8—21no—
61C13×C4⋊Q8D411yescharacteristic
62C13×#127—21no—
63C13×#127D411yescharacteristic
64C13×#126—22no—
65C13×#126—21no—
66C13×#125D411yescharacteristic
67C13×#124—21no—
68C13×#124—22no—
69C13×#124—22no—
70C13×#124—22no—
71C13×#124—21no—
72C13×#124—21no—
73C13×#124—21no—
74C13×#124—21no—
75C13×#124—21no—
76C13×#124D411yescharacteristic
77C13×#123—22no—
78C13×#123—21no—
79C13×#123—22no—
80C13×#123—22no—
81C13×#123—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—21no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8C2311yescharacteristic
86C13×#121—22no—
87C13×#121—22no—
88C13×#121—22no—
89C13×#121—21no—
90C13×#121—22no—
91C13×#121—21no—
92C13×#121—22no—
93C13×#121C2311yescharacteristic
94C13×#121C2312yes—
95C13×#120—22no—
96C13×#120—22no—
97C13×#120—22no—
98C13×#120—22no—
99C13×#120—22no—
100C4×Q8×C13—21no—
101C4×Q8×C13D411yescharacteristic
102C4×D4×C13—22no—
103C4×D4×C13—21no—
104C4×D4×C13—21no—
105C4×D4×C13—22no—
106C4×D4×C13—21no—
107C4×D4×C13D411yescharacteristic
108C4×D4×C13D412yes—
109C13×#117—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—21no—
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×C4⋊C8—21no—
119C13×C4⋊C8—21no—
120C13×#103—22no—
121C13×#103—24no—
122C13×#103—22no—
123C13×C22⋊C8C2312yes—
124C13×C22⋊C8C2312yes—
125C13×#97—21no—
126C4×C8×C13—21no—
127C13×#95—24no—
128C13×#95—21no—
129C13×#95C2312yes—
130#18427C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13—22no—
132C24×C13C2×D412yes—
133C13×#41—82no—
134C13×#41—82no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—22no—
139C2×Q8×C13—22no—
140C2×Q8×C13—42no—
141C2×Q8×C13—82no—
142C2×Q8×C13C2×D411yescharacteristic
143C2×D4×C13—22no—
144C2×D4×C13—21no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—22no—
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13—42no—
155C2×D4×C13—82no—
156C2×D4×C13—84no—
157C2×D4×C13C2×D411yescharacteristic
158C2×D4×C13C2×D412yes—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—21no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D412yes—
168C22×C4×C13C2411yescharacteristic
169C13×Q16—82no—
170C13×SD16—84no—
171C13×SD16—82no—
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—41no—
182C13×C4⋊C4—41no—
183C13×C4⋊C4—41no—
184C13×C4⋊C4—41no—
185C13×C4⋊C4C2×D412yes—
186C13×C4⋊C4C2×D411yescharacteristic
187C13×C4⋊C4C2×D411yescharacteristic
188C13×C22⋊C4—22no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—21no—
194C13×C22⋊C4—21no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—21no—
198C13×C22⋊C4—21no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—21no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—84no—
205C42×C13—22no—
206C42×C13—21no—
207C42×C13—42no—
208C42×C13C2×D411yescharacteristic
209C42×C13C2×D411yescharacteristic
210C42×C13C2×D411yescharacteristic
211C42×C13C2×D411yescharacteristic
212#3558C2×C1311yescharacteristic
213#3218C2×C1311yescharacteristic, complemented
214#3206C2×C1311yescharacteristic, complemented
215#2640C2×C1311yescharacteristic, complemented
216#1606C2×C1314yescomplemented
217#1601C2×C1314yescomplemented
218#1505C2×C1311yescharacteristic, complemented
219#1500C2×C1311yescharacteristic, complemented
220#1469C2×C1311yescharacteristic, complemented
221C23×C13—22no—
222C23×C13—21no—
223C23×C13—22no—
224C23×C13—24no—
225C23×C13—42no—
226C23×C13—42no—
227C23×C13—82no—
228C23×C13—82no—
229C23×C13—82no—
230C23×C13C22×D411yescharacteristic
231Q8×C13—41no—
232Q8×C13—44no—
233Q8×C13—42no—
234Q8×C13—42no—
235Q8×C13—42no—
236Q8×C13—81no—
237Q8×C13—81no—
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—21no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—41no—
259C2×C4×C13—42no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13—44no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—82no—
267C2×C4×C13—82no—
268C2×C4×C13—82no—
269C2×C4×C13#12011yescharacteristic
270C2×C4×C13#12011yescharacteristic
271C2×C4×C13#12011yescharacteristic
272C2×C4×C13#12011yescharacteristic
273C2×C4×C13C22×D411yescharacteristic
274C2×C4×C13C22×D411yescharacteristic
275C8×C13—42no—
276C8×C13—42no—
277#562—21no—
278H(3,𝔽4)—21no—
279#559—21no—
280#548—21no—
281#546—21no—
282#546—22no—
283D42—21no—
284#542—21no—
285#538—22no—
286#538C22×C1312yes—
287#535—21no—
288#534C22×C1312yes—
289#532C22×C1311yescharacteristic
290C2×C4⋊Q8C22×C1311yescharacteristic, complemented
291#529C22×C1311yescharacteristic
292C2×#124C22×C1311yescharacteristic
293#497—21no—
294#492—21no—
295#491—21no—
296#487—21no—
297#462—21no—
298#461—22no—
299#461—21no—
300#451C22×C1312yescomplemented
301#448C22×C1312yes—
302#448C22×C1314yescomplemented
303#432C22×C1311yescharacteristic, complemented
304#431C22×C1311yescharacteristic, complemented
305#397—22no—
306#393C22×C1314yescomplemented
307#391—21no—
308#390—21no—
309#376C22×C1311yescharacteristic, complemented
310#328C22×C1312yescomplemented
311#327C22×C1312yes—
312#327C22×C1314yescomplemented
313#323C22×C1314yescomplemented
314C22×C13—21no—
315C22×C13—21no—
316C22×C13—42no—
317C22×C13—42no—
318C22×C13—41no—
319C22×C13—41no—
320C22×C13—42no—
321C22×C13—42no—
322C22×C13—42no—
323C22×C13—41no—
324C22×C13—42no—
325C22×C13—84no—
326C22×C13—164no—
327C22×C13C2×#12011yescharacteristic
328C22×C13#57712yes—
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—41no—
335C4×C13—42no—
336C4×C13—41no—
337C4×C13—42no—
338C4×C13—41no—
339C4×C13—82no—
340C4×C13—82no—
341C4×C13#45512yes—
342C2×#41—21no—
343C2×#41—21no—
344C22×Q8D4×C1311yescharacteristic
345C22×Q8C23×C1312yes—
346C22×D4—21no—
347C22×D4—22no—
348C22×D4D4×C1311yescharacteristic
349C2×Q16—22no—
350C2×SD16—22no—
351C2×SD16—24no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8—21no—
356C4⋊Q8D4×C1311yescharacteristic
357#127—21no—
358#127D4×C1311yescharacteristic
359#126—22no—
360#126—21no—
361#125D4×C1311yescharacteristic
362#124—21no—
363#124—22no—
364#124—22no—
365#124—22no—
366#124—21no—
367#124—21no—
368#124—21no—
369#124—21no—
370#124—21no—
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—21no—
406C2×C4⋊C4—21no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4D4×C1312yes—
410C2×C22⋊C4C23×C1312yes—
411C2×C42—21no—
412C2×C42C23×C1311yescharacteristic
413C4⋊C8—21no—
414C4⋊C8—21no—
415#103—22no—
416#103—24no—
417#103—22no—
418C22⋊C8C23×C1312yes—
419C22⋊C8C23×C1312yes—
420#97—21no—
421C4×C8—21no—
422#95—21no—
423#95—24no—
424#95C23×C1312yes—
425C2×C13—22no—
426C2×C13—82no—
427C2×C13—82no—
428C2×C13—81no—
429C2×C13#300911yescharacteristic
430C2×C13C2×#45511yescharacteristic
431C2×C13#302711yescharacteristic
432C24—22no—
433C24C2×D4×C1312yes—
434#41—82no—
435#41—82no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—42no—
442C2×Q8—82no—
443C2×Q8C2×D4×C1311yescharacteristic
444C2×D4—22no—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—42no—
456C2×D4—82no—
457C2×D4—84no—
458C2×D4C2×D4×C1311yescharacteristic
459C2×D4C2×D4×C1312yes—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4C2×D4×C1311yescharacteristic
467C22×C4C2×D4×C1311yescharacteristic
468C22×C4C2×D4×C1312yes—
469C22×C4C24×C1311yescharacteristic
470Q16—82no—
471SD16—84no—
472SD16—82no—
473C2×C8—22no—
474C2×C8—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4C2×D4×C1312yes—
487C4⋊C4C2×D4×C1311yescharacteristic
488C4⋊C4C2×D4×C1311yescharacteristic
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—21no—
504C22⋊C4—22no—
505C22⋊C4—84no—
506C42—22no—
507C42—21no—
508C42—42no—
509C42C2×D4×C1311yescharacteristic
510C42C2×D4×C1311yescharacteristic
511C42C2×D4×C1311yescharacteristic
512C42C2×D4×C1311yescharacteristic
513C13#1842711yescharacteristic, direct product factor, Sylow
514C23—22no—
515C23—21no—
516C23—22no—
517C23—24no—
518C23—42no—
519C23—42no—
520C23—82no—
521C23—82no—
522C23—82no—
523C23C22×D4×C1311yescharacteristic
524Q8—41no—
525Q8—44no—
526Q8—42no—
527Q8—42no—
528Q8—42no—
529Q8—81no—
530Q8—81no—
531D4—42no—
532D4—41no—
533D4—42no—
534D4—44no—
535D4—42no—
536D4—42no—
537D4—81no—
538D4—81no—
539D4—82no—
540D4—82no—
541D4—82no—
542D4—82no—
543D4—82no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—44no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4C13×#12011yescharacteristic
563C2×C4C13×#12011yescharacteristic
564C2×C4C13×#12011yescharacteristic
565C2×C4C13×#12011yescharacteristic
566C2×C4C22×D4×C1311yescharacteristic
567C2×C4C22×D4×C1311yescharacteristic
568C8—42no—
569C8—42no—
570C22—21no—
571C22—21no—
572C22—42no—
573C22—42no—
574C22—41no—
575C22—41no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—41no—
580C22—42no—
581C22—84no—
582C22—164no—
583C22C2×C13×#12011yescharacteristic
584C22C13×#57712yes—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—42no—
594C4—41no—
595C4—82no—
596C4—82no—
597C4C13×#45512yes—
598C2—22no—
599C2—82no—
600C2—81no—
601C2—82no—
602C2C13×#300911yescharacteristic
603C2C2×C13×#45511yescharacteristic
604C2C13×#302711yescharacteristic
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×#3218C2semidirect
3. C13×#3206C2semidirect
4. C13×#2640C2semidirect
5. C13×#1606C2semidirect
6. C13×#1601C2semidirect
7. C13×#1505C2semidirect
8. C13×#1500C2semidirect
9. C13×#1469C2semidirect
23. C2×C13×C4⋊Q8C22semidirect
33. C13×#451C22semidirect
35. C13×#448C22semidirect
36. C13×#432C22semidirect
37. C13×#431C22semidirect
39. C13×#393C22semidirect
42. C13×#376C22semidirect
43. C13×#328C22semidirect
45. C13×#327C22semidirect
46. C13×#323C22semidirect
130. #18427C13direct (N × H)
213. #3218C2×C13semidirect
214. #3206C2×C13semidirect
215. #2640C2×C13semidirect
216. #1606C2×C13semidirect
217. #1601C2×C13semidirect
218. #1505C2×C13semidirect
219. #1500C2×C13semidirect
220. #1469C2×C13semidirect
290. C2×C4⋊Q8C22×C13semidirect
300. #451C22×C13semidirect
302. #448C22×C13semidirect
303. #432C22×C13semidirect
304. #431C22×C13semidirect
306. #393C22×C13semidirect
309. #376C22×C13semidirect
310. #328C22×C13semidirect
312. #327C22×C13semidirect
313. #323C22×C13semidirect
513. C13#18427direct (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×#32182
C13×#32062
C13×#26402
C13×#16062
C13×#16012
C13×#15052
C13×#15002
C13×#14692
#1842713