Finite Group Databasebeta

← C13×#18271 #15704610

Subgroups — C13×#18271 #15704610

Order 3328.

984 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3536C211yesmaximal, characteristic
2C13×#3092C211yesmaximal, characteristic, complemented
3C2×C13×#481C211yesmaximal, characteristic, complemented
4C13×#2503C211yesmaximal, characteristic, complemented
5C13×#1616C214yesmaximal, complemented
6C13×#1615C214yesmaximal, complemented
7C13×#1507C211yesmaximal, characteristic, complemented
8C13×#1501C211yesmaximal, characteristic, complemented
9C13×#1472C211yesmaximal, characteristic, complemented
10C13×#562—22no—
11C13×#554—21no—
12C13×#548—21no—
13C13×#547—21no—
14C13×#546—21no—
15C13×#546—22no—
16C13×#543—21no—
17C13×#542—21no—
18C13×#539C2212yes—
19C13×#538—21no—
20C13×#537—21no—
21C13×#537C2212yes—
22C13×#525C2211yescharacteristic
23C2×C13×C22⋊Q8C2211yescharacteristic
24C2×C13×#121C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C13×#484C2212yescomplemented
27C13×#483—21no—
28C13×#481—22no—
29C13×#481C2214yes—
30C13×#481C2212yescomplemented
31C13×#480—21no—
32C13×#428—21no—
33C2×C13×#106—21no—
34C13×#417—21no—
35C2×C13×#102—21no—
36C13×#407C2211yescharacteristic
37C2×C13×C22⋊C8C2211yescharacteristic
38C13×#400C2214yescomplemented
39C13×#391—21no—
40C13×#382—21no—
41C13×#381—22no—
42C4×C13×C22⋊C4C2211yescharacteristic
43C13×#328C2212yescomplemented
44C13×#327C2214yes—
45C13×#327C2212yescomplemented
46C13×#324C2214yescomplemented
47C2×C13×#41—21no—
48C2×C13×#41—22no—
49C2×C13×#41D411yescharacteristic
50C22×Q8×C13D411yescharacteristic
51C22×D4×C13—21no—
52C22×D4×C13D411yescharacteristic
53C23×C4×C13—21no—
54C23×C4×C13C2311yescharacteristic
55C2×C13×M16—21no—
56C22×C8×C13—21no—
57C13×C4⋊Q8—21no—
58C13×#126—22no—
59C13×#125—22no—
60C13×#124—22no—
61C13×#124—21no—
62C13×#124—22no—
63C13×#123—22no—
64C13×#123—22no—
65C13×#123—22no—
66C13×#123—21no—
67C13×#123—22no—
68C13×C22⋊Q8—21no—
69C13×C22⋊Q8—22no—
70C13×C22⋊Q8—22no—
71C13×C22⋊Q8—22no—
72C13×C22⋊Q8—22no—
73C13×C22⋊Q8—21no—
74C13×C22⋊Q8—21no—
75C13×C22⋊Q8—21no—
76C13×C22⋊Q8—21no—
77C13×C22⋊Q8—22no—
78C13×C22⋊Q8—22no—
79C13×C22⋊Q8D411yescharacteristic
80C13×C22⋊Q8C2311yescharacteristic
81C13×#121—21no—
82C13×#121—22no—
83C13×#121—22no—
84C13×#121—22no—
85C13×#121—22no—
86C13×#121—21no—
87C13×#121—21no—
88C13×#121—22no—
89C13×#121D411yescharacteristic
90C13×#121D412yes—
91C13×#121C2312yes—
92C13×#121C2311yescharacteristic
93C13×#120—22no—
94C13×#120—21no—
95C4×Q8×C13—21no—
96C4×D4×C13—22no—
97C4×D4×C13—21no—
98C4×D4×C13—21no—
99C4×D4×C13—21no—
100C4×D4×C13—22no—
101C13×#117D411yescharacteristic
102C2×C13×C4⋊C4—21no—
103C2×C13×C4⋊C4—21no—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4D411yescharacteristic
109C2×C13×C4⋊C4D411yescharacteristic
110C2×C13×C4⋊C4C2312yes—
111C2×C13×C4⋊C4C2312yes—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4D412yes—
116C2×C42×C13—21no—
117C13×#107—22no—
118C13×#106—24no—
119C13×#106—22no—
120C13×#103—22no—
121C13×#102—24no—
122C13×#102—22no—
123C13×C22⋊C8—21no—
124C13×C22⋊C8—21no—
125C13×C22⋊C8C2312yes—
126C13×C22⋊C8C2312yes—
127C13×#95—24no—
128C13×#95—24no—
129C13×#95C2312yes—
130#18271C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13—21no—
132C24×C13C2×D411yescharacteristic
133C13×#41—42no—
134C13×#41—84no—
135C13×#41—82no—
136C2×Q8×C13—22no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—42no—
140C2×Q8×C13C2×D411yescharacteristic
141C2×D4×C13—21no—
142C2×D4×C13—21no—
143C2×D4×C13—22no—
144C2×D4×C13—22no—
145C2×D4×C13—22no—
146C2×D4×C13—21no—
147C2×D4×C13—22no—
148C2×D4×C13—21no—
149C2×D4×C13—42no—
150C2×D4×C13—82no—
151C2×D4×C13C2×D411yescharacteristic
152C2×D4×C13C2×D412yes—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—42no—
161C22×C4×C13—44no—
162C22×C4×C13—41no—
163C22×C4×C13—41no—
164C22×C4×C13C2×D412yes—
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D412yes—
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2411yescharacteristic
172C13×M16—42no—
173C2×C8×C13—22no—
174C2×C8×C13—22no—
175C2×C8×C13—42no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—41no—
190C13×C4⋊C4—41no—
191C13×C4⋊C4C2×D412yes—
192C13×C4⋊C4C2×D411yescharacteristic
193C13×C4⋊C4C2×D411yescharacteristic
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—21no—
203C13×C22⋊C4—21no—
204C13×C22⋊C4—22no—
205C13×C22⋊C4—21no—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—21no—
208C13×C22⋊C4—42no—
209C42×C13—22no—
210C42×C13—21no—
211C42×C13—42no—
212#3536C2×C1311yescharacteristic
213#3092C2×C1311yescharacteristic, complemented
214C2×#481C2×C1311yescharacteristic, complemented
215#2503C2×C1311yescharacteristic, complemented
216#1616C2×C1314yescomplemented
217#1615C2×C1314yescomplemented
218#1507C2×C1311yescharacteristic, complemented
219#1501C2×C1311yescharacteristic, complemented
220#1472C2×C1311yescharacteristic, complemented
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—21no—
225C23×C13—41no—
226C23×C13—42no—
227C23×C13—81no—
228C23×C13—81no—
229C23×C13#12011yescharacteristic
230C23×C13#12011yescharacteristic
231C23×C13C22×D411yescharacteristic
232Q8×C13—41no—
233Q8×C13—42no—
234Q8×C13—81no—
235Q8×C13—82no—
236D4×C13—42no—
237D4×C13—41no—
238D4×C13—44no—
239D4×C13—42no—
240D4×C13—42no—
241D4×C13—42no—
242D4×C13—82no—
243D4×C13—81no—
244D4×C13—82no—
245D4×C13—82no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—21no—
250C2×C4×C13—22no—
251C2×C4×C13—21no—
252C2×C4×C13—22no—
253C2×C4×C13—21no—
254C2×C4×C13—22no—
255C2×C4×C13—24no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
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—81no—
267C2×C4×C13—82no—
268C2×C4×C13—82no—
269C2×C4×C13—82no—
270C2×C4×C13—82no—
271C2×C4×C13—82no—
272C2×C4×C13#12011yescharacteristic
273C2×C4×C13#12011yescharacteristic
274C2×C4×C13C22×D411yescharacteristic
275C2×C4×C13C22×D411yescharacteristic
276C8×C13—42no—
277C8×C13—42no—
278#562—22no—
279#554—21no—
280#548—21no—
281#547—21no—
282#546—21no—
283#546—22no—
284#543—21no—
285#542—21no—
286#539C22×C1312yes—
287#538—21no—
288#537—21no—
289#537C22×C1312yes—
290#525C22×C1311yescharacteristic
291C2×C22⋊Q8C22×C1311yescharacteristic
292C2×#121C22×C1311yescharacteristic
293C22×C4⋊C4C22×C1311yescharacteristic
294#484C22×C1312yescomplemented
295#483—21no—
296#481—22no—
297#481C22×C1314yes—
298#481C22×C1312yescomplemented
299#480—21no—
300#428—21no—
301C2×#106—21no—
302#417—21no—
303C2×#102—21no—
304#407C22×C1311yescharacteristic
305C2×C22⋊C8C22×C1311yescharacteristic
306#400C22×C1314yescomplemented
307#391—21no—
308#382—21no—
309#381—22no—
310C4×C22⋊C4C22×C1311yescharacteristic
311#328C22×C1312yescomplemented
312#327C22×C1314yes—
313#327C22×C1312yescomplemented
314#324C22×C1314yescomplemented
315C22×C13—21no—
316C22×C13—21no—
317C22×C13—21no—
318C22×C13—21no—
319C22×C13—21no—
320C22×C13—21no—
321C22×C13—21no—
322C22×C13—44no—
323C22×C13—41no—
324C22×C13—42no—
325C22×C13—41no—
326C22×C13—42no—
327C22×C13—41no—
328C22×C13—42no—
329C22×C13—162no—
330C22×C13#45412yes—
331C22×C13C2×#12011yescharacteristic
332C22×C13#57712yes—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13—21no—
336C4×C13—42no—
337C4×C13—42no—
338C4×C13—41no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13—42no—
342C4×C13—82no—
343C4×C13—82no—
344C4×C13#45812yes—
345C2×#41—21no—
346C2×#41—22no—
347C2×#41D4×C1311yescharacteristic
348C22×Q8D4×C1311yescharacteristic
349C22×D4—21no—
350C22×D4D4×C1311yescharacteristic
351C23×C4—21no—
352C23×C4C23×C1311yescharacteristic
353C2×M16—21no—
354C22×C8—21no—
355C4⋊Q8—21no—
356#126—22no—
357#125—22no—
358#124—22no—
359#124—21no—
360#124—22no—
361#123—22no—
362#123—22no—
363#123—22no—
364#123—21no—
365#123—22no—
366C22⋊Q8—21no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8D4×C1311yescharacteristic
378C22⋊Q8C23×C1311yescharacteristic
379#121—21no—
380#121—22no—
381#121—22no—
382#121—22no—
383#121—22no—
384#121—21no—
385#121—21no—
386#121—22no—
387#121D4×C1312yes—
388#121D4×C1311yescharacteristic
389#121C23×C1312yes—
390#121C23×C1311yescharacteristic
391#120—22no—
392#120—21no—
393C4×Q8—21no—
394C4×D4—22no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—22no—
399#117D4×C1311yescharacteristic
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4D4×C1311yescharacteristic
407C2×C4⋊C4D4×C1311yescharacteristic
408C2×C4⋊C4C23×C1312yes—
409C2×C4⋊C4C23×C1312yes—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4D4×C1312yes—
414C2×C42—21no—
415#107—22no—
416#106—24no—
417#106—22no—
418#103—22no—
419#102—24no—
420#102—22no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8C23×C1312yes—
424C22⋊C8C23×C1312yes—
425#95—24no—
426#95—24no—
427#95C23×C1312yes—
428C2×C13—22no—
429C2×C13—22no—
430C2×C13—41no—
431C2×C13—81no—
432C2×C13—82no—
433C2×C13#300911yescharacteristic
434C2×C13C2×#45411yescharacteristic
435C2×C13C2×#45811yescharacteristic
436C24—21no—
437C24C2×D4×C1311yescharacteristic
438#41—42no—
439#41—84no—
440#41—82no—
441C2×Q8—22no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—42no—
445C2×Q8C2×D4×C1311yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—42no—
455C2×D4—82no—
456C2×D4C2×D4×C1311yescharacteristic
457C2×D4C2×D4×C1312yes—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—42no—
466C22×C4—44no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4C2×D4×C1312yes—
470C22×C4C2×D4×C1311yescharacteristic
471C22×C4C2×D4×C1311yescharacteristic
472C22×C4C2×D4×C1311yescharacteristic
473C22×C4C2×D4×C1312yes—
474C22×C4C2×D4×C1311yescharacteristic
475C22×C4C2×D4×C1311yescharacteristic
476C22×C4C24×C1311yescharacteristic
477M16—42no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—42no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4C2×D4×C1312yes—
497C4⋊C4C2×D4×C1311yescharacteristic
498C4⋊C4C2×D4×C1311yescharacteristic
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—21no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—22no—
510C22⋊C4—21no—
511C22⋊C4—22no—
512C22⋊C4—21no—
513C22⋊C4—42no—
514C42—22no—
515C42—21no—
516C42—42no—
517C13#1827111yescharacteristic, direct product factor, Sylow
518C23—22no—
519C23—22no—
520C23—22no—
521C23—21no—
522C23—41no—
523C23—42no—
524C23—81no—
525C23—81no—
526C23C13×#12011yescharacteristic
527C23C13×#12011yescharacteristic
528C23C22×D4×C1311yescharacteristic
529Q8—41no—
530Q8—42no—
531Q8—81no—
532Q8—82no—
533D4—42no—
534D4—41no—
535D4—42no—
536D4—44no—
537D4—42no—
538D4—42no—
539D4—82no—
540D4—81no—
541D4—82no—
542D4—82no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—44no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—81no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4—82no—
569C2×C4C13×#12011yescharacteristic
570C2×C4C13×#12011yescharacteristic
571C2×C4C22×D4×C1311yescharacteristic
572C2×C4C22×D4×C1311yescharacteristic
573C8—42no—
574C8—42no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—44no—
583C22—41no—
584C22—42no—
585C22—41no—
586C22—42no—
587C22—41no—
588C22—42no—
589C22—162no—
590C22C13×#45412yes—
591C22C2×C13×#12011yescharacteristic
592C22C13×#57712yes—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—42no—
597C4—42no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—42no—
602C4—82no—
603C4—82no—
604C4C13×#45812yes—
605C2—22no—
606C2—22no—
607C2—41no—
608C2—82no—
609C2—81no—
610C2C13×#300911yescharacteristic
611C2C2×C13×#45411yescharacteristic
612C2C2×C13×#45811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3536C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3092C2semidirect
3. C2×C13×#481C2semidirect
4. C13×#2503C2semidirect
5. C13×#1616C2semidirect
6. C13×#1615C2semidirect
7. C13×#1507C2semidirect
8. C13×#1501C2semidirect
9. C13×#1472C2semidirect
26. C13×#484C22semidirect
30. C13×#481C22semidirect
38. C13×#400C22semidirect
43. C13×#328C22semidirect
45. C13×#327C22semidirect
46. C13×#324C22semidirect
130. #18271C13direct (N × H)
213. #3092C2×C13semidirect
214. C2×#481C2×C13semidirect
215. #2503C2×C13semidirect
216. #1616C2×C13semidirect
217. #1615C2×C13semidirect
218. #1507C2×C13semidirect
219. #1501C2×C13semidirect
220. #1472C2×C13semidirect
294. #484C22×C13semidirect
298. #481C22×C13semidirect
306. #400C22×C13semidirect
311. #328C22×C13semidirect
313. #327C22×C13semidirect
314. #324C22×C13semidirect
517. C13#18271direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35362
C13×#30922
C2×C13×#4812
C13×#25032
C13×#16162
C13×#16152
C13×#15072
C13×#15012
C13×#14722
#1827113