Finite Group Databasebeta

← C13×#18356 #15704695

Subgroups — C13×#18356 #15704695

Order 3328.

1054 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3491C211yesmaximal, characteristic, complemented
2C13×#3217C212yesmaximal, complemented
3C13×#2619C211yesmaximal, characteristic, complemented
4C13×#1597C214yesmaximal, complemented
5C13×#1596C212yesmaximal, complemented
6C13×#1595C212yesmaximal, complemented
7C13×#1512C212yesmaximal, complemented
8C13×#1464C211yesmaximal, characteristic, complemented
9C13×#552—22no—
10C13×#552—22no—
11C13×#551—22no—
12C13×#551—22no—
13C13×#543C2211yescharacteristic
14C13×#539—21no—
15C13×#539C2212yes—
16C13×#534C2211yescharacteristic
17C2×C13×#127C2211yescharacteristic, complemented
18C13×#529—21no—
19C13×#529C2212yes—
20C2×C13×#123—21no—
21C2×C13×#121—21no—
22C13×#518—21no—
23C2×C13×#117C2211yescharacteristic
24C13×#496—22no—
25C13×#490—22no—
26C13×#460—22no—
27C13×#459—22no—
28C13×#450C2214yescomplemented
29C13×#447C2214yes—
30C13×#432C2212yescomplemented
31C13×#394—21no—
32C13×#394C2212yescomplemented
33C13×#392—21no—
34C13×#392C2212yes—
35C13×#390—21no—
36C13×#382C2211yescharacteristic, complemented
37C13×#328C2214yescomplemented
38C13×#327C2214yes—
39C13×#324C2212yescomplemented
40C13×#323C2212yes—
41C22×D4×C13—21no—
42C22×D4×C13—22no—
43C22×D4×C13—21no—
44C22×D4×C13—21no—
45C22×D4×C13C2312yes—
46C23×C4×C13D411yescharacteristic
47C2×C13×SD16—24no—
48C2×C13×D8—24no—
49C13×#127—22no—
50C13×#127—22no—
51C13×#126—22no—
52C13×#126—22no—
53C13×#126—22no—
54C13×#126—22no—
55C13×#125—21no—
56C13×#125—22no—
57C13×#125—22no—
58C13×#125D412yescomplemented
59C13×#124—21no—
60C13×#124D412yescomplemented
61C13×#123—22no—
62C13×#123—22no—
63C13×#123—22no—
64C13×#123—22no—
65C13×#123—22no—
66C13×#123—22no—
67C13×#123—22no—
68C13×C22⋊Q8—22no—
69C13×C22⋊Q8—22no—
70C13×C22⋊Q8—22no—
71C13×C22⋊Q8—21no—
72C13×C22⋊Q8—22no—
73C13×C22⋊Q8C2312yes—
74C13×#121—21no—
75C13×#121—44no—
76C13×#121C2312yes—
77C13×#120—22no—
78C4×Q8×C13—21no—
79C4×Q8×C13D412yescomplemented
80C4×D4×C13—22no—
81C4×D4×C13—22no—
82C4×D4×C13—21no—
83C4×D4×C13—22no—
84C4×D4×C13—22no—
85C4×D4×C13D412yescomplemented
86C13×#117—22no—
87C13×#117—22no—
88C13×#117—22no—
89C13×#117—22no—
90C13×#117—22no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4—21no—
93C2×C13×C4⋊C4—21no—
94C2×C13×C4⋊C4D411yescharacteristic
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—21no—
98C2×C13×C22⋊C4—21no—
99C2×C13×C22⋊C4—21no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4—22no—
102C2×C13×C22⋊C4—22no—
103C2×C13×C22⋊C4D411yescharacteristic
104C2×C13×C22⋊C4C2311yescharacteristic
105C2×C42×C13D411yescharacteristic
106C2×C42×C13C2311yescharacteristic
107C13×C4⋊C8—22no—
108C13×#102—24no—
109C13×#102—24no—
110C13×C22⋊C8C2314yes—
111C13×#97—22no—
112C13×#95—21no—
113C13×#95C2312yes—
114#18356C1311yesmaximal, characteristic, direct product factor, Sylow
115C24×C13—21no—
116C24×C13—22no—
117C24×C13C2×D411yescharacteristic
118C2×Q8×C13—21no—
119C2×Q8×C13C2×D412yes—
120C2×D4×C13—22no—
121C2×D4×C13—22no—
122C2×D4×C13—21no—
123C2×D4×C13—24no—
124C2×D4×C13—42no—
125C2×D4×C13—42no—
126C2×D4×C13—42no—
127C2×D4×C13—42no—
128C2×D4×C13—44no—
129C2×D4×C13—41no—
130C2×D4×C13—41no—
131C2×D4×C13—42no—
132C2×D4×C13—82no—
133C2×D4×C13—82no—
134C2×D4×C13—82no—
135C2×D4×C13—82no—
136C2×D4×C13C2×D412yes—
137C22×C4×C13—21no—
138C22×C4×C13—22no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—41no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2411yescharacteristic
153C13×SD16—84no—
154C13×D8—84no—
155C2×C8×C13—24no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—42no—
169C13×C4⋊C4C2×D412yes—
170C13×C4⋊C4C2×D412yes—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—22no—
178C13×C22⋊C4—22no—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—22no—
181C13×C22⋊C4—22no—
182C13×C22⋊C4—22no—
183C13×C22⋊C4—44no—
184C13×C22⋊C4—82no—
185C13×C22⋊C4—82no—
186C42×C13—22no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—22no—
190C42×C13C2×D412yes—
191C42×C13C2×D412yes—
192#3491C2×C1311yescharacteristic, complemented
193#3217C2×C1312yescomplemented
194#2619C2×C1311yescharacteristic, complemented
195#1597C2×C1314yescomplemented
196#1596C2×C1312yescomplemented
197#1595C2×C1312yescomplemented
198#1512C2×C1312yescomplemented
199#1464C2×C1311yescharacteristic, complemented
200C23×C13—21no—
201C23×C13—21no—
202C23×C13—22no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13—42no—
213C23×C13—81no—
214C23×C13—81no—
215C23×C13AGL(1,ℤ/8)12yes—
216C23×C13C22×D411yescharacteristic
217Q8×C13—42no—
218Q8×C13—81no—
219D4×C13—42no—
220D4×C13—44no—
221D4×C13—44no—
222D4×C13—44no—
223D4×C13—42no—
224D4×C13—42no—
225D4×C13—82no—
226D4×C13—82no—
227D4×C13—84no—
228D4×C13—81no—
229D4×C13—88no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—82no—
251C2×C4×C13—81no—
252C2×C4×C13—82no—
253C2×C4×C13—81no—
254C2×C4×C13#12011yescharacteristic
255C2×C4×C13#12011yescharacteristic
256C2×C4×C13#12012yes—
257C2×C4×C13C22×D412yes—
258C8×C13—44no—
259#552—22no—
260#552—22no—
261#551—22no—
262#551—22no—
263#543C22×C1311yescharacteristic
264#539—21no—
265#539C22×C1312yes—
266#534C22×C1311yescharacteristic
267C2×#127C22×C1311yescharacteristic, complemented
268#529—21no—
269#529C22×C1312yes—
270C2×#123—21no—
271C2×#121—21no—
272#518—21no—
273C2×#117C22×C1311yescharacteristic
274#496—22no—
275#490—22no—
276#460—22no—
277#459—22no—
278#450C22×C1314yescomplemented
279#447C22×C1314yes—
280#432C22×C1312yescomplemented
281#394—21no—
282#394C22×C1312yescomplemented
283#392—21no—
284#392C22×C1312yes—
285#390—21no—
286#382C22×C1311yescharacteristic, complemented
287#328C22×C1314yescomplemented
288#327C22×C1314yes—
289#324C22×C1312yescomplemented
290#323C22×C1312yes—
291C22×C13—21no—
292C22×C13—21no—
293C22×C13—22no—
294C22×C13—42no—
295C22×C13—41no—
296C22×C13—41no—
297C22×C13—42no—
298C22×C13—42no—
299C22×C13—42no—
300C22×C13—81no—
301C22×C13—82no—
302C22×C13—82no—
303C22×C13—82no—
304C22×C13—82no—
305C22×C13—82no—
306C22×C13—82no—
307C22×C13—82no—
308C22×C13—162no—
309C22×C13C2×#12011yescharacteristic
310C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
311C22×C13#57511yescharacteristic
312C4×C13—21no—
313C4×C13—21no—
314C4×C13—22no—
315C4×C13—22no—
316C4×C13—41no—
317C4×C13—42no—
318C4×C13—41no—
319C4×C13—42no—
320C4×C13—41no—
321C4×C13—42no—
322C4×C13—82no—
323C22×D4—21no—
324C22×D4—22no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4C23×C1312yes—
328C23×C4D4×C1311yescharacteristic
329C2×SD16—24no—
330C2×D8—24no—
331#127—22no—
332#127—22no—
333#126—22no—
334#126—22no—
335#126—22no—
336#126—22no—
337#125—21no—
338#125—22no—
339#125—22no—
340#125D4×C1312yescomplemented
341#124—21no—
342#124D4×C1312yescomplemented
343#123—22no—
344#123—22no—
345#123—22no—
346#123—22no—
347#123—22no—
348#123—22no—
349#123—22no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—21no—
354C22⋊Q8—22no—
355C22⋊Q8C23×C1312yes—
356#121—21no—
357#121—44no—
358#121C23×C1312yes—
359#120—22no—
360C4×Q8—21no—
361C4×Q8D4×C1312yescomplemented
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—21no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4D4×C1312yescomplemented
368#117—22no—
369#117—22no—
370#117—22no—
371#117—22no—
372#117—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4D4×C1311yescharacteristic
377C2×C4⋊C4C23×C1311yescharacteristic
378C2×C22⋊C4—22no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4D4×C1311yescharacteristic
386C2×C22⋊C4C23×C1311yescharacteristic
387C2×C42D4×C1311yescharacteristic
388C2×C42C23×C1311yescharacteristic
389C4⋊C8—22no—
390#102—24no—
391#102—24no—
392C22⋊C8C23×C1314yes—
393#97—22no—
394#95—21no—
395#95C23×C1312yes—
396C2×C13—21no—
397C2×C13—21no—
398C2×C13—42no—
399C2×C13—82no—
400C2×C13—162no—
401C2×C13#300611yescharacteristic
402C2×C13#302111yescharacteristic
403C2×C13#302711yescharacteristic
404C24—21no—
405C24—22no—
406C24C2×D4×C1311yescharacteristic
407C2×Q8—21no—
408C2×Q8C2×D4×C1312yes—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—21no—
412C2×D4—24no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—44no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—42no—
421C2×D4—82no—
422C2×D4—82no—
423C2×D4—82no—
424C2×D4—82no—
425C2×D4C2×D4×C1312yes—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—41no—
436C22×C4C2×D4×C1311yescharacteristic
437C22×C4C2×D4×C1311yescharacteristic
438C22×C4C2×D4×C1311yescharacteristic
439C22×C4C2×D4×C1311yescharacteristic
440C22×C4C2×D4×C1311yescharacteristic
441C22×C4C24×C1311yescharacteristic
442SD16—84no—
443D8—84no—
444C2×C8—24no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—42no—
458C4⋊C4C2×D4×C1312yes—
459C4⋊C4C2×D4×C1312yes—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—44no—
473C22⋊C4—82no—
474C22⋊C4—82no—
475C42—22no—
476C42—21no—
477C42—21no—
478C42—22no—
479C42C2×D4×C1312yes—
480C42C2×D4×C1312yes—
481C13#1835611yescharacteristic, direct product factor, Sylow
482C23—21no—
483C23—21no—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—81no—
496C23—81no—
497C23C13×AGL(1,ℤ/8)12yes—
498C23C22×D4×C1311yescharacteristic
499Q8—42no—
500Q8—81no—
501D4—42no—
502D4—44no—
503D4—44no—
504D4—44no—
505D4—42no—
506D4—42no—
507D4—82no—
508D4—82no—
509D4—84no—
510D4—81no—
511D4—88no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—82no—
533C2×C4—81no—
534C2×C4—82no—
535C2×C4—81no—
536C2×C4C13×#12011yescharacteristic
537C2×C4C13×#12011yescharacteristic
538C2×C4C13×#12012yes—
539C2×C4C22×D4×C1312yes—
540C8—44no—
541C22—21no—
542C22—21no—
543C22—22no—
544C22—42no—
545C22—41no—
546C22—41no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—81no—
551C22—82no—
552C22—82no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—162no—
559C22C2×C13×#12011yescharacteristic
560C22C2×C13×AGL(1,ℤ/8)11yescharacteristic
561C22C13×#57511yescharacteristic
562C4—21no—
563C4—21no—
564C4—22no—
565C4—22no—
566C4—41no—
567C4—42no—
568C4—41no—
569C4—42no—
570C4—41no—
571C4—42no—
572C4—82no—
573C2—21no—
574C2—21no—
575C2—42no—
576C2—82no—
577C2—162no—
578C2C13×#300611yescharacteristic
579C2C13×#302111yescharacteristic
580C2C13×#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×#3491C2semidirect
2. C13×#3217C2semidirect
3. C13×#2619C2semidirect
4. C13×#1597C2semidirect
5. C13×#1596C2semidirect
6. C13×#1595C2semidirect
7. C13×#1512C2semidirect
8. C13×#1464C2semidirect
17. C2×C13×#127C22semidirect
28. C13×#450C22semidirect
30. C13×#432C22semidirect
32. C13×#394C22semidirect
36. C13×#382C22semidirect
37. C13×#328C22semidirect
39. C13×#324C22semidirect
58. C13×#125D4semidirect
60. C13×#124D4semidirect
79. C4×Q8×C13D4semidirect
85. C4×D4×C13D4semidirect
114. #18356C13direct (N × H)
192. #3491C2×C13semidirect
193. #3217C2×C13semidirect
194. #2619C2×C13semidirect
195. #1597C2×C13semidirect
196. #1596C2×C13semidirect
197. #1595C2×C13semidirect
198. #1512C2×C13semidirect
199. #1464C2×C13semidirect
267. C2×#127C22×C13semidirect
278. #450C22×C13semidirect
280. #432C22×C13semidirect
282. #394C22×C13semidirect
286. #382C22×C13semidirect
287. #328C22×C13semidirect
289. #324C22×C13semidirect
340. #125D4×C13semidirect
342. #124D4×C13semidirect
361. C4×Q8D4×C13semidirect
367. C4×D4D4×C13semidirect
481. C13#18356direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34912
C13×#32172
C13×#26192
C13×#15972
C13×#15962
C13×#15952
C13×#15122
C13×#14642
#1835613