Finite Group Databasebeta

← C13×#32751 #15719090

Subgroups — C13×#32751 #15719090

Order 3328.

656 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2628C211yesmaximal, characteristic, complemented
2C13×#2624C211yesmaximal, characteristic
3C13×#2088C211yesmaximal, characteristic, complemented
4C13×#2088C211yesmaximal, characteristic, complemented
5C13×#2085C211yesmaximal, characteristic, complemented
6C13×#2077C211yesmaximal, characteristic, complemented
7C13×#2075C211yesmaximal, characteristic, complemented
8C13×#2073C211yesmaximal, characteristic, complemented
9C13×#2067C211yesmaximal, characteristic, complemented
10C13×#2065C211yesmaximal, characteristic, complemented
11C13×#2058C211yesmaximal, characteristic, complemented
12C13×#2034C211yesmaximal, characteristic
13C13×#2034C211yesmaximal, characteristic
14C13×#2023C211yesmaximal, characteristic, complemented
15C13×#1798C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×#121C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C2×C13×#106C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C2×C13×#106C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×#102C2211yescharacteristic
26C2×C13×#102C2211yescharacteristic
27C2×C13×#102C2211yescharacteristic
28C2×C13×#102C2211yescharacteristic
29C2×C13×C22⋊C8C2211yescharacteristic
30C2×C13×C22⋊C8C2211yescharacteristic
31C13×#400—21no—
32C13×#399—21no—
33C13×#399—21no—
34C13×#397—21no—
35C13×#395—21no—
36C13×#394—21no—
37C13×#394—21no—
38C13×#393—21no—
39C13×#390C2211yescharacteristic
40C13×#390C2211yescharacteristic
41C13×#389C2211yescharacteristic
42C13×#389C2211yescharacteristic
43C13×#389C2211yescharacteristic
44C13×#389C2211yescharacteristic
45C13×#382C2211yescharacteristic
46C13×#380C2211yescharacteristic
47C13×#380C2211yescharacteristic
48C13×#380C2211yescharacteristic
49C13×#340C2211yescharacteristic
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54C13×#340C2211yescharacteristic
55C13×#340C2211yescharacteristic
56C13×#340C2211yescharacteristic
57C13×#336C2211yescharacteristic
58C13×#336C2211yescharacteristic
59C22×Q8×C13—21no—
60C22×D4×C13—21no—
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C13×C4⋊Q8—41no—
68C13×C4⋊Q8—41no—
69C13×#121—41no—
70C13×#121—41no—
71C13×#117—41no—
72C13×#117—41no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4D411yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C4⋊C4C2311yescharacteristic
86C2×C13×C4⋊C4C2311yescharacteristic
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4—21no—
90C2×C13×C22⋊C4—21no—
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4—21no—
93C2×C13×C22⋊C4—21no—
94C2×C13×C22⋊C4—21no—
95C2×C13×C22⋊C4D411yescharacteristic
96C2×C13×C22⋊C4D411yescharacteristic
97C2×C42×C13C2311yescharacteristic
98C2×C42×C13C2311yescharacteristic
99C13×#107—41no—
100C13×#106—41no—
101C13×#106—41no—
102C13×#106—41no—
103C13×C4⋊C8—41no—
104C13×C4⋊C8—41no—
105C13×#102—41no—
106C13×#102—41no—
107C13×#102—41no—
108C13×#102—41no—
109C13×C22⋊C8—41no—
110C13×C22⋊C8—41no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95—21no—
116C13×#95—21no—
117C13×#95—21no—
118C13×#95—21no—
119C13×#95—21no—
120#32751C1311yesmaximal, characteristic, direct product factor, Sylow
121C24×C13—21no—
122C24×C13C2×D411yescharacteristic
123C2×Q8×C13—42no—
124C2×Q8×C13—81no—
125C2×Q8×C13—81no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—42no—
133C2×D4×C13—81no—
134C2×D4×C13—81no—
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×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2411yescharacteristic
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—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—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—41no—
181C13×C4⋊C4—41no—
182C13×C4⋊C4—42no—
183C13×C4⋊C4—81no—
184C13×C4⋊C4—81no—
185C13×C4⋊C4—81no—
186C13×C4⋊C4—81no—
187C13×C22⋊C4—41no—
188C13×C22⋊C4—41no—
189C13×C22⋊C4—42no—
190C13×C22⋊C4—81no—
191C13×C22⋊C4—81no—
192C13×C22⋊C4—81no—
193C13×C22⋊C4—81no—
194C13×C22⋊C4—81no—
195C13×C22⋊C4—81no—
196C13×C22⋊C4—81no—
197C42×C13—21no—
198C42×C13—21no—
199C42×C13—21no—
200C42×C13—21no—
201#2628C2×C1311yescharacteristic, complemented
202#2624C2×C1311yescharacteristic
203#2088C2×C1311yescharacteristic, complemented
204#2088C2×C1311yescharacteristic, complemented
205#2085C2×C1311yescharacteristic, complemented
206#2077C2×C1311yescharacteristic, complemented
207#2075C2×C1311yescharacteristic, complemented
208#2073C2×C1311yescharacteristic, complemented
209#2067C2×C1311yescharacteristic, complemented
210#2065C2×C1311yescharacteristic, complemented
211#2058C2×C1311yescharacteristic, complemented
212#2034C2×C1311yescharacteristic
213#2034C2×C1311yescharacteristic
214#2023C2×C1311yescharacteristic, complemented
215#1798C2×C1311yescharacteristic, complemented
216C23×C13—21no—
217C23×C13—21no—
218C23×C13—21no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13C22×D411yescharacteristic
231Q8×C13—84no—
232D4×C13—41no—
233D4×C13—41no—
234D4×C13—41no—
235D4×C13—41no—
236D4×C13—84no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
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—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13H(5,𝔽2)11yescharacteristic
278C2×C4×C13H(5,𝔽2)11yescharacteristic
279C2×C4×C13H(5,𝔽2)11yescharacteristic
280C2×C4×C132−1+411yescharacteristic
281C2×C4×C132−1+411yescharacteristic
282C2×C4×C132−1+411yescharacteristic
283C8×C13—41no—
284C8×C13—41no—
285C8×C13—41no—
286C8×C13—41no—
287C2×C4⋊Q8C22×C1311yescharacteristic
288C2×#121C22×C1311yescharacteristic
289C2×#117C22×C1311yescharacteristic
290C2×#107C22×C1311yescharacteristic
291C2×#106C22×C1311yescharacteristic
292C2×#106C22×C1311yescharacteristic
293C2×#106C22×C1311yescharacteristic
294C2×C4⋊C8C22×C1311yescharacteristic
295C2×C4⋊C8C22×C1311yescharacteristic
296C2×#102C22×C1311yescharacteristic
297C2×#102C22×C1311yescharacteristic
298C2×#102C22×C1311yescharacteristic
299C2×#102C22×C1311yescharacteristic
300C2×C22⋊C8C22×C1311yescharacteristic
301C2×C22⋊C8C22×C1311yescharacteristic
302#400—21no—
303#399—21no—
304#399—21no—
305#397—21no—
306#395—21no—
307#394—21no—
308#394—21no—
309#393—21no—
310#390C22×C1311yescharacteristic
311#390C22×C1311yescharacteristic
312#389C22×C1311yescharacteristic
313#389C22×C1311yescharacteristic
314#389C22×C1311yescharacteristic
315#389C22×C1311yescharacteristic
316#382C22×C1311yescharacteristic
317#380C22×C1311yescharacteristic
318#380C22×C1311yescharacteristic
319#380C22×C1311yescharacteristic
320#340C22×C1311yescharacteristic
321#340C22×C1311yescharacteristic
322#340C22×C1311yescharacteristic
323#340C22×C1311yescharacteristic
324#340C22×C1311yescharacteristic
325#340C22×C1311yescharacteristic
326#340C22×C1311yescharacteristic
327#340C22×C1311yescharacteristic
328#336C22×C1311yescharacteristic
329#336C22×C1311yescharacteristic
330C22×C13—41no—
331C22×C13—41no—
332C22×C13—41no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—81no—
338C22×C13—81no—
339C22×C13—81no—
340C22×C13—81no—
341C22×C13—81no—
342C22×C13—81no—
343C22×C13—81no—
344C22×C13#53411yescharacteristic
345C22×C13#53611yescharacteristic
346C22×C13#53711yescharacteristic
347C22×C13#57611yescharacteristic
348C22×C13#57711yescharacteristic
349C22×C13#57711yescharacteristic
350C22×C13#57711yescharacteristic
351C4×C13—41no—
352C4×C13—41no—
353C4×C13—41no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13—81no—
357C4×C13—81no—
358C4×C13—81no—
359C4×C13—81no—
360C4×C13—81no—
361C4×C13—81no—
362C4×C13—81no—
363C4×C13#56211yescharacteristic
364C4×C13#56211yescharacteristic
365C4×C13#56311yescharacteristic
366C4×C13#56311yescharacteristic
367C22×Q8—21no—
368C22×D4—21no—
369C22×D4C23×C1311yescharacteristic
370C23×C4C23×C1311yescharacteristic
371C22×C8C23×C1311yescharacteristic
372C22×C8C23×C1311yescharacteristic
373C22×C8C23×C1311yescharacteristic
374C22×C8C23×C1311yescharacteristic
375C4⋊Q8—41no—
376C4⋊Q8—41no—
377#121—41no—
378#121—41no—
379#117—41no—
380#117—41no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4D4×C1311yescharacteristic
387C2×C4⋊C4D4×C1311yescharacteristic
388C2×C4⋊C4C23×C1311yescharacteristic
389C2×C4⋊C4C23×C1311yescharacteristic
390C2×C4⋊C4C23×C1311yescharacteristic
391C2×C4⋊C4C23×C1311yescharacteristic
392C2×C4⋊C4C23×C1311yescharacteristic
393C2×C4⋊C4C23×C1311yescharacteristic
394C2×C4⋊C4C23×C1311yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4D4×C1311yescharacteristic
404C2×C22⋊C4D4×C1311yescharacteristic
405C2×C42C23×C1311yescharacteristic
406C2×C42C23×C1311yescharacteristic
407#107—41no—
408#106—41no—
409#106—41no—
410#106—41no—
411C4⋊C8—41no—
412C4⋊C8—41no—
413#102—41no—
414#102—41no—
415#102—41no—
416#102—41no—
417C22⋊C8—41no—
418C22⋊C8—41no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428C2×C13—81no—
429C2×C13—161no—
430C2×C13#281411yescharacteristic
431C2×C13#319811yescharacteristic
432C2×C13#320011yescharacteristic
433C2×C13#324111yescharacteristic
434C2×C13#324411yescharacteristic
435C2×C13#325711yescharacteristic
436C2×C13#326311yescharacteristic
437C24—21no—
438C24C2×D4×C1311yescharacteristic
439C2×Q8—42no—
440C2×Q8—81no—
441C2×Q8—81no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—42no—
449C2×D4—81no—
450C2×D4—81no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4C2×D4×C1311yescharacteristic
465C22×C4C2×D4×C1311yescharacteristic
466C22×C4C2×D4×C1311yescharacteristic
467C22×C4C2×D4×C1311yescharacteristic
468C22×C4C2×D4×C1311yescharacteristic
469C22×C4C24×C1311yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—42no—
499C4⋊C4—81no—
500C4⋊C4—81no—
501C4⋊C4—81no—
502C4⋊C4—81no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—42no—
506C22⋊C4—81no—
507C22⋊C4—81no—
508C22⋊C4—81no—
509C22⋊C4—81no—
510C22⋊C4—81no—
511C22⋊C4—81no—
512C22⋊C4—81no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C13#3275111yescharacteristic, direct product factor, Sylow
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23C22×D4×C1311yescharacteristic
533Q8—84no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—84no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4C13×H(5,𝔽2)11yescharacteristic
580C2×C4C13×H(5,𝔽2)11yescharacteristic
581C2×C4C13×H(5,𝔽2)11yescharacteristic
582C2×C4C13×2−1+411yescharacteristic
583C2×C4C13×2−1+411yescharacteristic
584C2×C4C13×2−1+411yescharacteristic
585C8—41no—
586C8—41no—
587C8—41no—
588C8—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22C13×#53411yescharacteristic
604C22C13×#53611yescharacteristic
605C22C13×#53711yescharacteristic
606C22C13×#57611yescharacteristic
607C22C13×#57711yescharacteristic
608C22C13×#57711yescharacteristic
609C22C13×#57711yescharacteristic
610C4—41no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4C13×#56211yescharacteristic
623C4C13×#56211yescharacteristic
624C4C13×#56311yescharacteristic
625C4C13×#56311yescharacteristic
626C2—81no—
627C2—161no—
628C2C13×#281411yescharacteristic
629C2C13×#319811yescharacteristic
630C2C13×#320011yescharacteristic
631C2C13×#324111yescharacteristic
632C2C13×#324411yescharacteristic
633C2C13×#325711yescharacteristic
634C2C13×#326311yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC2×C13×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C13×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2628C2semidirect
3. C13×#2088C2semidirect
4. C13×#2088C2semidirect
5. C13×#2085C2semidirect
6. C13×#2077C2semidirect
7. C13×#2075C2semidirect
8. C13×#2073C2semidirect
9. C13×#2067C2semidirect
10. C13×#2065C2semidirect
11. C13×#2058C2semidirect
14. C13×#2023C2semidirect
15. C13×#1798C2semidirect
120. #32751C13direct (N × H)
201. #2628C2×C13semidirect
203. #2088C2×C13semidirect
204. #2088C2×C13semidirect
205. #2085C2×C13semidirect
206. #2077C2×C13semidirect
207. #2075C2×C13semidirect
208. #2073C2×C13semidirect
209. #2067C2×C13semidirect
210. #2065C2×C13semidirect
211. #2058C2×C13semidirect
214. #2023C2×C13semidirect
215. #1798C2×C13semidirect
517. C13#32751direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26282
C13×#26242
C13×#20882
C13×#20852
C13×#20772
C13×#20752
C13×#20732
C13×#20672
C13×#20652
C13×#20582
C13×#20342
C13×#20232
C13×#17982
#3275113