Finite Group Databasebeta

← C13×#32527 #15718866

Subgroups — C13×#32527 #15718866

Order 3328.

630 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2514C211yesmaximal, characteristic, complemented
2C13×#2513C211yesmaximal, characteristic
3C13×#2097C211yesmaximal, characteristic, complemented
4C13×#2092C211yesmaximal, characteristic
5C13×#2068C211yesmaximal, characteristic, complemented
6C13×#2067C211yesmaximal, characteristic
7C13×#2055C211yesmaximal, characteristic
8C13×#2055C211yesmaximal, characteristic
9C13×#1968C211yesmaximal, characteristic
10C13×#1949C211yesmaximal, characteristic, complemented
11C13×#1949C211yesmaximal, characteristic, complemented
12C13×#1941C211yesmaximal, characteristic, complemented
13C13×#1939C211yesmaximal, characteristic, complemented
14C13×#1927C211yesmaximal, characteristic, complemented
15C13×#1926C211yesmaximal, characteristic
16C22×C13×SD16C2211yescharacteristic
17C2×C13×#107C2211yescharacteristic
18C2×C13×#107C2211yescharacteristic
19C2×C13×#106C2211yescharacteristic
20C2×C13×#106C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×#103C2211yescharacteristic
26C2×C13×#103C2211yescharacteristic
27C2×C13×#103C2211yescharacteristic
28C2×C13×#102C2211yescharacteristic
29C2×C13×#102C2211yescharacteristic
30C2×C13×#102C2211yescharacteristic
31C2×C4×C8×C13C2211yescharacteristic
32C13×#401—21no—
33C13×#400—21no—
34C13×#397—21no—
35C13×#397—21no—
36C13×#391C2211yescharacteristic
37C13×#391C2211yescharacteristic
38C13×#391C2211yescharacteristic
39C13×#390C2211yescharacteristic
40C13×#390C2211yescharacteristic
41C13×#390C2211yescharacteristic
42C13×#389C2211yescharacteristic
43C13×#389C2211yescharacteristic
44C13×#388—21no—
45C13×#388—21no—
46C13×#387—21no—
47C13×#383—21no—
48C13×#382C2211yescharacteristic
49C13×#382C2211yescharacteristic
50C4×C13×C4⋊C4C2211yescharacteristic
51C4×C13×C4⋊C4C2211yescharacteristic
52C4×C13×C4⋊C4C2211yescharacteristic
53C13×#340C2211yescharacteristic
54C13×#340C2211yescharacteristic
55C13×#340C2211yescharacteristic
56C13×#340C2211yescharacteristic
57C13×#336C2211yescharacteristic
58C13×#336C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C2×C13×SD16—22no—
62C2×C13×SD16—41no—
63C2×C13×SD16—41no—
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4D411yescharacteristic
71C2×C13×C4⋊C4D411yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C42×C13—21no—
85C2×C42×C13—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C13×#107—41no—
90C13×#107—41no—
91C13×#106—22no—
92C13×#106—41no—
93C13×#106—41no—
94C13×C4⋊C8—22no—
95C13×C4⋊C8—22no—
96C13×C4⋊C8—41no—
97C13×#103—22no—
98C13×#103—41no—
99C13×#103—41no—
100C13×#102—22no—
101C13×#102—41no—
102C13×#102—41no—
103C4×C8×C13—41no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95—21no—
116C13×#95—21no—
117C13×#95—21no—
118C13×#95D411yescharacteristic
119C13×#95D411yescharacteristic
120#32527C1311yesmaximal, characteristic, direct product factor, Sylow
121C24×C13—21no—
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—21no—
125C2×Q8×C13—21no—
126C2×Q8×C13—21no—
127C2×Q8×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2411yescharacteristic
148C13×SD16—44no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13#4112yes—
160C2×C8×C13#4112yes—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—41no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4—81no—
177C13×C22⋊C4—42no—
178C13×C22⋊C4—42no—
179C13×C22⋊C4—81no—
180C13×C22⋊C4—81no—
181C13×C22⋊C4—81no—
182C13×C22⋊C4—81no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—42no—
190C42×C13—81no—
191#2514C2×C1311yescharacteristic, complemented
192#2513C2×C1311yescharacteristic
193#2097C2×C1311yescharacteristic, complemented
194#2092C2×C1311yescharacteristic
195#2068C2×C1311yescharacteristic, complemented
196#2067C2×C1311yescharacteristic
197#2055C2×C1311yescharacteristic
198#2055C2×C1311yescharacteristic
199#1968C2×C1311yescharacteristic
200#1949C2×C1311yescharacteristic, complemented
201#1949C2×C1311yescharacteristic, complemented
202#1941C2×C1311yescharacteristic, complemented
203#1939C2×C1311yescharacteristic, complemented
204#1927C2×C1311yescharacteristic, complemented
205#1926C2×C1311yescharacteristic
206C23×C13—41no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13—41no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13C22×D411yescharacteristic
214Q8×C13—41no—
215Q8×C13—41no—
216Q8×C13—41no—
217Q8×C13—41no—
218D4×C13—41no—
219D4×C13—41no—
220D4×C13—41no—
221D4×C13—41no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13#13512yes—
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13H(5,𝔽2)11yescharacteristic
264C2×C4×C13H(5,𝔽2)11yescharacteristic
265C2×C4×C132−1+411yescharacteristic
266C2×C4×C132−1+411yescharacteristic
267C8×C13—22no—
268C8×C13—22no—
269C8×C13—41no—
270C8×C13—41no—
271C22×SD16C22×C1311yescharacteristic
272C2×#107C22×C1311yescharacteristic
273C2×#107C22×C1311yescharacteristic
274C2×#106C22×C1311yescharacteristic
275C2×#106C22×C1311yescharacteristic
276C2×#106C22×C1311yescharacteristic
277C2×C4⋊C8C22×C1311yescharacteristic
278C2×C4⋊C8C22×C1311yescharacteristic
279C2×C4⋊C8C22×C1311yescharacteristic
280C2×#103C22×C1311yescharacteristic
281C2×#103C22×C1311yescharacteristic
282C2×#103C22×C1311yescharacteristic
283C2×#102C22×C1311yescharacteristic
284C2×#102C22×C1311yescharacteristic
285C2×#102C22×C1311yescharacteristic
286C2×C4×C8C22×C1311yescharacteristic
287#401—21no—
288#400—21no—
289#397—21no—
290#397—21no—
291#391C22×C1311yescharacteristic
292#391C22×C1311yescharacteristic
293#391C22×C1311yescharacteristic
294#390C22×C1311yescharacteristic
295#390C22×C1311yescharacteristic
296#390C22×C1311yescharacteristic
297#389C22×C1311yescharacteristic
298#389C22×C1311yescharacteristic
299#388—21no—
300#388—21no—
301#387—21no—
302#383—21no—
303#382C22×C1311yescharacteristic
304#382C22×C1311yescharacteristic
305C4×C4⋊C4C22×C1311yescharacteristic
306C4×C4⋊C4C22×C1311yescharacteristic
307C4×C4⋊C4C22×C1311yescharacteristic
308#340C22×C1311yescharacteristic
309#340C22×C1311yescharacteristic
310#340C22×C1311yescharacteristic
311#340C22×C1311yescharacteristic
312#336C22×C1311yescharacteristic
313#336C22×C1311yescharacteristic
314C22×C13—81no—
315C22×C13—81no—
316C22×C13—81no—
317C22×C13—81no—
318C22×C13—81no—
319C22×C13—81no—
320C22×C13—81no—
321C22×C13#53711yescharacteristic
322C22×C13#54711yescharacteristic
323C22×C13#55011yescharacteristic
324C22×C13C2×#13511yescharacteristic
325C22×C13#57511yescharacteristic
326C22×C13#57711yescharacteristic
327C22×C13#57711yescharacteristic
328C4×C13—22no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—81no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13—81no—
339C4×C13—81no—
340C4×C13—81no—
341C4×C13#53811yescharacteristic
342C4×C13#53911yescharacteristic
343C4×C13#55611yescharacteristic
344C4×C13#56311yescharacteristic
345C22×Q8C23×C1311yescharacteristic
346C22×D4C23×C1311yescharacteristic
347C2×SD16—22no—
348C2×SD16—41no—
349C2×SD16—41no—
350C22×C8C23×C1311yescharacteristic
351C22×C8C23×C1311yescharacteristic
352C22×C8C23×C1311yescharacteristic
353C22×C8C23×C1311yescharacteristic
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4D4×C1311yescharacteristic
357C2×C4⋊C4D4×C1311yescharacteristic
358C2×C4⋊C4C23×C1311yescharacteristic
359C2×C4⋊C4C23×C1311yescharacteristic
360C2×C4⋊C4C23×C1311yescharacteristic
361C2×C4⋊C4C23×C1311yescharacteristic
362C2×C4⋊C4C23×C1311yescharacteristic
363C2×C4⋊C4C23×C1311yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42C23×C1311yescharacteristic
373C2×C42C23×C1311yescharacteristic
374C2×C42C23×C1311yescharacteristic
375#107—41no—
376#107—41no—
377#106—22no—
378#106—41no—
379#106—41no—
380C4⋊C8—22no—
381C4⋊C8—22no—
382C4⋊C8—41no—
383#103—22no—
384#103—41no—
385#103—41no—
386#102—22no—
387#102—41no—
388#102—41no—
389C4×C8—41no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95D4×C1311yescharacteristic
405#95D4×C1311yescharacteristic
406C2×C13—161no—
407C2×C13#272711yescharacteristic
408C2×C13#325011yescharacteristic
409C2×C13#326011yescharacteristic
410C2×C13#334011yescharacteristic
411C2×C13#335111yescharacteristic
412C2×C13#339411yescharacteristic
413C2×C13#340111yescharacteristic
414C24—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4C2×D4×C1311yescharacteristic
435C22×C4C2×D4×C1311yescharacteristic
436C22×C4C2×D4×C1311yescharacteristic
437C22×C4C2×D4×C1311yescharacteristic
438C22×C4C2×D4×C1311yescharacteristic
439C22×C4C2×D4×C1311yescharacteristic
440C22×C4C24×C1311yescharacteristic
441SD16—44no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8C13×#4112yes—
453C2×C8C13×#4112yes—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—42no—
469C4⋊C4—81no—
470C22⋊C4—42no—
471C22⋊C4—42no—
472C22⋊C4—81no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C22⋊C4—81no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—42no—
483C42—81no—
484C13#3252711yescharacteristic, direct product factor, Sylow
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23C22×D4×C1311yescharacteristic
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—41no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4C13×#13512yes—
540C2×C4C2×C13×#4111yescharacteristic
541C2×C4C2×C13×#4111yescharacteristic
542C2×C4C13×H(5,𝔽2)11yescharacteristic
543C2×C4C13×H(5,𝔽2)11yescharacteristic
544C2×C4C13×2−1+411yescharacteristic
545C2×C4C13×2−1+411yescharacteristic
546C8—22no—
547C8—22no—
548C8—41no—
549C8—41no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C13×#53711yescharacteristic
558C22C13×#54711yescharacteristic
559C22C13×#55011yescharacteristic
560C22C2×C13×#13511yescharacteristic
561C22C13×#57511yescharacteristic
562C22C13×#57711yescharacteristic
563C22C13×#57711yescharacteristic
564C4—22no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C13×#53811yescharacteristic
578C4C13×#53911yescharacteristic
579C4C13×#55611yescharacteristic
580C4C13×#56311yescharacteristic
581C2—161no—
582C2C13×#272711yescharacteristic
583C2C13×#325011yescharacteristic
584C2C13×#326011yescharacteristic
585C2C13×#334011yescharacteristic
586C2C13×#335111yescharacteristic
587C2C13×#339411yescharacteristic
588C2C13×#340111yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC22×D4×C13C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C4×C13×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2514C2semidirect
3. C13×#2097C2semidirect
5. C13×#2068C2semidirect
10. C13×#1949C2semidirect
11. C13×#1949C2semidirect
12. C13×#1941C2semidirect
13. C13×#1939C2semidirect
14. C13×#1927C2semidirect
120. #32527C13direct (N × H)
191. #2514C2×C13semidirect
193. #2097C2×C13semidirect
195. #2068C2×C13semidirect
200. #1949C2×C13semidirect
201. #1949C2×C13semidirect
202. #1941C2×C13semidirect
203. #1939C2×C13semidirect
204. #1927C2×C13semidirect
484. C13#32527direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25142
C13×#25132
C13×#20972
C13×#20922
C13×#20682
C13×#20672
C13×#20552
C13×#19682
C13×#19492
C13×#19412
C13×#19392
C13×#19272
C13×#19262
#3252713