Finite Group Databasebeta

← C13×#18266 #15704605

Subgroups — C13×#18266 #15704605

Order 3328.

1000 conjugacy classes of subgroups.

The subgroup lattice has 616 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×#483C211yesmaximal, characteristic, complemented
4C13×#2504C211yesmaximal, characteristic, complemented
5C13×#1612C214yesmaximal, complemented
6C13×#1608C214yesmaximal, complemented
7C13×#1508C211yesmaximal, characteristic, complemented
8C13×#1501C211yesmaximal, characteristic, complemented
9C13×#1471C211yesmaximal, characteristic, complemented
10C13×#562—22no—
11C13×#554—21no—
12C13×#548—21no—
13C13×#547—21no—
14C13×#546—22no—
15C13×#546—21no—
16C13×#543C2212yes—
17C13×#542—21no—
18C13×#539—21no—
19C13×#538C2212yes—
20C13×#537—21no—
21C13×#537—21no—
22C13×#525C2211yescharacteristic
23C2×C13×C22⋊Q8C2211yescharacteristic
24C2×C13×#121C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C13×#484—21no—
27C13×#483—22no—
28C13×#483C2214yes—
29C13×#483C2212yes—
30C13×#481—21no—
31C13×#480C2212yes—
32C13×#428—21no—
33C2×C13×#106—21no—
34C13×#417—21no—
35C2×C13×#103—21no—
36C13×#407C2211yescharacteristic
37C2×C13×C22⋊C8C2211yescharacteristic
38C13×#397C2214yes—
39C13×#390—21no—
40C13×#386—22no—
41C13×#382—21no—
42C4×C13×C22⋊C4C2211yescharacteristic
43C13×#328C2212yes—
44C13×#328C2214yes—
45C13×#327C2212yes—
46C13×#323C2214yes—
47C2×C13×#41—22no—
48C2×C13×#41—21no—
49C2×C13×#41D411yescharacteristic
50C22×Q8×C13D411yescharacteristic
51C22×D4×C13D412yes—
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—21no—
61C13×#124—22no—
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—21no—
73C13×C22⋊Q8—21no—
74C13×C22⋊Q8—22no—
75C13×C22⋊Q8—22no—
76C13×C22⋊Q8—22no—
77C13×C22⋊Q8D412yes—
78C13×C22⋊Q8D411yescharacteristic
79C13×C22⋊Q8C2312yes—
80C13×C22⋊Q8C2311yescharacteristic
81C13×#121—21no—
82C13×#121—22no—
83C13×#121—22no—
84C13×#121—22no—
85C13×#121—22no—
86C13×#121—22no—
87C13×#121—21no—
88C13×#121—21no—
89C13×#121—21no—
90C13×#121—21no—
91C13×#121D411yescharacteristic
92C13×#121C2311yescharacteristic
93C13×#120—21no—
94C13×#120—22no—
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⋊C4—21no—
109C2×C13×C4⋊C4D411yescharacteristic
110C2×C13×C4⋊C4D411yescharacteristic
111C2×C13×C4⋊C4C2312yes—
112C2×C13×C22⋊C4—21no—
113C2×C13×C22⋊C4—22no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—24no—
116C2×C13×C22⋊C4C2312yes—
117C2×C42×C13—21no—
118C13×#107—22no—
119C13×#106—24no—
120C13×#106—22no—
121C13×#103—24no—
122C13×#103—22no—
123C13×#102—22no—
124C13×C22⋊C8—21no—
125C13×C22⋊C8—21no—
126C13×C22⋊C8C2312yes—
127C13×C22⋊C8C2312yes—
128C13×#95—24no—
129C13×#95C2312yes—
130#18266C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13C2×D411yescharacteristic
132C24×C13C2×D412yes—
133C13×#41—42no—
134C13×#41—84no—
135C13×#41—82no—
136C2×Q8×C13—22no—
137C2×Q8×C13—21no—
138C2×Q8×C13—42no—
139C2×Q8×C13C2×D411yescharacteristic
140C2×Q8×C13C2×D412yes—
141C2×D4×C13—21no—
142C2×D4×C13—22no—
143C2×D4×C13—21no—
144C2×D4×C13—22no—
145C2×D4×C13—22no—
146C2×D4×C13—21no—
147C2×D4×C13—22no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—42no—
151C2×D4×C13—44no—
152C2×D4×C13C2×D411yescharacteristic
153C22×C4×C13—21no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—42no—
162C22×C4×C13—41no—
163C22×C4×C13—41no—
164C22×C4×C13—82no—
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—22no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
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—22no—
200C13×C22⋊C4—21no—
201C13×C22⋊C4—21no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—21no—
204C13×C22⋊C4—21no—
205C13×C22⋊C4—22no—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—21no—
208C13×C22⋊C4—42no—
209C13×C22⋊C4—84no—
210C42×C13—22no—
211C42×C13—21no—
212C42×C13—42no—
213#3536C2×C1311yescharacteristic
214#3092C2×C1311yescharacteristic, complemented
215C2×#483C2×C1311yescharacteristic, complemented
216#2504C2×C1311yescharacteristic, complemented
217#1612C2×C1314yescomplemented
218#1608C2×C1314yescomplemented
219#1508C2×C1311yescharacteristic, complemented
220#1501C2×C1311yescharacteristic, complemented
221#1471C2×C1311yescharacteristic, complemented
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—21no—
226C23×C13—24no—
227C23×C13—41no—
228C23×C13—42no—
229C23×C13—42no—
230C23×C13#12011yescharacteristic
231C23×C13#12011yescharacteristic
232C23×C13C22×D411yescharacteristic
233Q8×C13—42no—
234Q8×C13—41no—
235Q8×C13—42no—
236Q8×C13—82no—
237D4×C13—41no—
238D4×C13—42no—
239D4×C13—44no—
240D4×C13—42no—
241D4×C13—42no—
242D4×C13—81no—
243D4×C13—82no—
244D4×C13—81no—
245D4×C13—82no—
246D4×C13—82no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—21no—
251C2×C4×C13—22no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—21no—
255C2×C4×C13—22no—
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—42no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—44no—
267C2×C4×C13—81no—
268C2×C4×C13—82no—
269C2×C4×C13—82no—
270C2×C4×C13—82no—
271C2×C4×C13—82no—
272C2×C4×C13—82no—
273C2×C4×C13#12011yescharacteristic
274C2×C4×C13#12011yescharacteristic
275C2×C4×C13C22×D411yescharacteristic
276C2×C4×C13C22×D411yescharacteristic
277C8×C13—42no—
278C8×C13—42no—
279#562—22no—
280#554—21no—
281#548—21no—
282#547—21no—
283#546—22no—
284#546—21no—
285#543C22×C1312yes—
286#542—21no—
287#539—21no—
288#538C22×C1312yes—
289#537—21no—
290#537—21no—
291#525C22×C1311yescharacteristic
292C2×C22⋊Q8C22×C1311yescharacteristic
293C2×#121C22×C1311yescharacteristic
294C22×C4⋊C4C22×C1311yescharacteristic
295#484—21no—
296#483—22no—
297#483C22×C1314yes—
298#483C22×C1312yes—
299#481—21no—
300#480C22×C1312yes—
301#428—21no—
302C2×#106—21no—
303#417—21no—
304C2×#103—21no—
305#407C22×C1311yescharacteristic
306C2×C22⋊C8C22×C1311yescharacteristic
307#397C22×C1314yes—
308#390—21no—
309#386—22no—
310#382—21no—
311C4×C22⋊C4C22×C1311yescharacteristic
312#328C22×C1312yes—
313#328C22×C1314yes—
314#327C22×C1312yes—
315#323C22×C1314yes—
316C22×C13—21no—
317C22×C13—21no—
318C22×C13—21no—
319C22×C13—21no—
320C22×C13—21no—
321C22×C13—21no—
322C22×C13—21no—
323C22×C13—44no—
324C22×C13—41no—
325C22×C13—42no—
326C22×C13—41no—
327C22×C13—42no—
328C22×C13—41no—
329C22×C13—42no—
330C22×C13—84no—
331C22×C13#45512yes—
332C22×C13C2×#12011yescharacteristic
333C22×C13#57712yes—
334C4×C13—21no—
335C4×C13—21no—
336C4×C13—21no—
337C4×C13—41no—
338C4×C13—42no—
339C4×C13—42no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13—42no—
343C4×C13—82no—
344C4×C13—82no—
345C4×C13#45812yes—
346C2×#41—22no—
347C2×#41—21no—
348C2×#41D4×C1311yescharacteristic
349C22×Q8D4×C1311yescharacteristic
350C22×D4D4×C1312yes—
351C22×D4D4×C1311yescharacteristic
352C23×C4—21no—
353C23×C4C23×C1311yescharacteristic
354C2×M16—21no—
355C22×C8—21no—
356C4⋊Q8—21no—
357#126—22no—
358#125—22no—
359#124—21no—
360#124—22no—
361#124—22no—
362#123—22no—
363#123—22no—
364#123—22no—
365#123—21no—
366#123—22no—
367C22⋊Q8—21no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8D4×C1312yes—
377C22⋊Q8D4×C1311yescharacteristic
378C22⋊Q8C23×C1312yes—
379C22⋊Q8C23×C1311yescharacteristic
380#121—21no—
381#121—22no—
382#121—22no—
383#121—22no—
384#121—22no—
385#121—22no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121—21no—
390#121D4×C1311yescharacteristic
391#121C23×C1311yescharacteristic
392#120—21no—
393#120—22no—
394C4×Q8—21no—
395C4×D4—22no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—22no—
400#117D4×C1311yescharacteristic
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4D4×C1311yescharacteristic
409C2×C4⋊C4D4×C1311yescharacteristic
410C2×C4⋊C4C23×C1312yes—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4C23×C1312yes—
416C2×C42—21no—
417#107—22no—
418#106—24no—
419#106—22no—
420#103—24no—
421#103—22no—
422#102—22no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8C23×C1312yes—
426C22⋊C8C23×C1312yes—
427#95—24no—
428#95C23×C1312yes—
429C2×C13—22no—
430C2×C13—22no—
431C2×C13—41no—
432C2×C13—81no—
433C2×C13—82no—
434C2×C13#301011yescharacteristic
435C2×C13C2×#45511yescharacteristic
436C2×C13C2×#45811yescharacteristic
437C24C2×D4×C1311yescharacteristic
438C24C2×D4×C1312yes—
439#41—42no—
440#41—84no—
441#41—82no—
442C2×Q8—22no—
443C2×Q8—21no—
444C2×Q8—42no—
445C2×Q8C2×D4×C1311yescharacteristic
446C2×Q8C2×D4×C1312yes—
447C2×D4—21no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—42no—
457C2×D4—44no—
458C2×D4C2×D4×C1311yescharacteristic
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—42no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—82no—
471C22×C4C2×D4×C1311yescharacteristic
472C22×C4C2×D4×C1311yescharacteristic
473C22×C4C2×D4×C1311yescharacteristic
474C22×C4C2×D4×C1312yes—
475C22×C4C2×D4×C1311yescharacteristic
476C22×C4C2×D4×C1311yescharacteristic
477C22×C4C24×C1311yescharacteristic
478M16—42no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—42no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4C2×D4×C1312yes—
498C4⋊C4C2×D4×C1311yescharacteristic
499C4⋊C4C2×D4×C1311yescharacteristic
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—22no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—21no—
514C22⋊C4—42no—
515C22⋊C4—84no—
516C42—22no—
517C42—21no—
518C42—42no—
519C13#1826611yescharacteristic, direct product factor, Sylow
520C23—22no—
521C23—22no—
522C23—22no—
523C23—21no—
524C23—24no—
525C23—41no—
526C23—42no—
527C23—42no—
528C23C13×#12011yescharacteristic
529C23C13×#12011yescharacteristic
530C23C22×D4×C1311yescharacteristic
531Q8—42no—
532Q8—41no—
533Q8—42no—
534Q8—82no—
535D4—41no—
536D4—44no—
537D4—42no—
538D4—42no—
539D4—42no—
540D4—81no—
541D4—82no—
542D4—81no—
543D4—82no—
544D4—82no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—44no—
565C2×C4—81no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4C13×#12011yescharacteristic
572C2×C4C13×#12011yescharacteristic
573C2×C4C22×D4×C1311yescharacteristic
574C2×C4C22×D4×C1311yescharacteristic
575C8—42no—
576C8—42no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—44no—
585C22—41no—
586C22—42no—
587C22—41no—
588C22—42no—
589C22—41no—
590C22—42no—
591C22—84no—
592C22C13×#45512yes—
593C22C2×C13×#12011yescharacteristic
594C22C13×#57712yes—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—41no—
599C4—42no—
600C4—42no—
601C4—41no—
602C4—41no—
603C4—42no—
604C4—82no—
605C4—82no—
606C4C13×#45812yes—
607C2—22no—
608C2—22no—
609C2—41no—
610C2—82no—
611C2—81no—
612C2C13×#301011yescharacteristic
613C2C2×C13×#45511yescharacteristic
614C2C2×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×#483C2semidirect
4. C13×#2504C2semidirect
5. C13×#1612C2semidirect
6. C13×#1608C2semidirect
7. C13×#1508C2semidirect
8. C13×#1501C2semidirect
9. C13×#1471C2semidirect
130. #18266C13direct (N × H)
214. #3092C2×C13semidirect
215. C2×#483C2×C13semidirect
216. #2504C2×C13semidirect
217. #1612C2×C13semidirect
218. #1608C2×C13semidirect
219. #1508C2×C13semidirect
220. #1501C2×C13semidirect
221. #1471C2×C13semidirect
519. C13#18266direct (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×#4832
C13×#25042
C13×#16122
C13×#16082
C13×#15082
C13×#15012
C13×#14712
#1826613