Finite Group Databasebeta

← C13×#14543 #15700882

Subgroups — C13×#14543 #15700882

Order 3328.

1490 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#399C211yesmaximal, characteristic
2C2×C13×#388C212yesmaximal
3C2×C13×#387C212yesmaximal, complemented
4C13×#1441C212yesmaximal, complemented
5C13×#1440C211yesmaximal, characteristic
6C13×#1439C212yesmaximal
7C13×#1437C211yesmaximal, characteristic
8C13×#1436C212yesmaximal, complemented
9C13×C4⋊#95C212yesmaximal, complemented
10C22×C13×C4⋊C4C2212yes—
11C22×C13×C4⋊C4C2212yes—
12C22×C13×C4⋊C4C2212yes—
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2212yes—
16C22×C13×C22⋊C4C2212yes—
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×C42×C13C2212yes—
21C13×#399C418yescomplemented
22C13×#388—28no—
23C13×#387—28no—
24C2×C13×#95C2212yes—
25C2×C13×#95C2212yes—
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×C13×#95C2212yes—
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2212yes—
34C25×C13C2311yescharacteristic
35C23×C4×C13C2312yes—
36C23×C4×C13C2311yescharacteristic
37C23×C4×C13C2312yes—
38C23×C4×C13C2311yescharacteristic
39C23×C4×C13C2312yes—
40C23×C4×C13C2312yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2312yes—
43C2×C13×C4⋊C4—24no—
44C2×C13×C4⋊C4—24no—
45C2×C13×C4⋊C4—24no—
46C2×C13×C4⋊C4—24no—
47C2×C13×C4⋊C4—24no—
48C2×C13×C4⋊C4—24no—
49C2×C13×C4⋊C4—41no—
50C2×C13×C4⋊C4—41no—
51C2×C13×C4⋊C4—42no—
52C2×C13×C4⋊C4—42no—
53C2×C13×C4⋊C4C2×C418yes—
54C2×C13×C4⋊C4C2×C414yes—
55C2×C13×C22⋊C4—24no—
56C2×C13×C22⋊C4—24no—
57C2×C13×C22⋊C4—24no—
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4—24no—
60C2×C13×C22⋊C4—41no—
61C2×C13×C22⋊C4—41no—
62C2×C13×C22⋊C4—42no—
63C2×C13×C22⋊C4—41no—
64C2×C13×C22⋊C4—41no—
65C2×C13×C22⋊C4—42no—
66C2×C13×C22⋊C4C2×C418yes—
67C2×C13×C22⋊C4C2×C414yes—
68C2×C42×C13—24no—
69C2×C42×C13—24no—
70C2×C42×C13—24no—
71C2×C42×C13—42no—
72C2×C42×C13—41no—
73C13×#95—24no—
74C13×#95—24no—
75C13×#95—24no—
76C13×#95—24no—
77C13×#95—41no—
78C13×#95—42no—
79C13×#95—42no—
80C13×#95—42no—
81C13×#95C2×C414yes—
82C13×#95D418yes—
83#14543C1311yesmaximal, characteristic, direct product factor, Sylow
84C24×C13—22no—
85C24×C13—22no—
86C24×C13—22no—
87C24×C13—21no—
88C24×C13—21no—
89C24×C13—22no—
90C24×C13—22no—
91C24×C13—22no—
92C24×C13C22×C412yes—
93C24×C13C2411yescharacteristic
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13C22×C412yes—
138C22×C4×C13C22×C414yes—
139C22×C4×C13C22×C412yes—
140C22×C4×C13C22×C414yes—
141C22×C4×C13C2×D414yes—
142C22×C4×C13C2×D414yes—
143C22×C4×C13C2×D414yes—
144C22×C4×C13#4114yes—
145C22×C4×C13#4114yes—
146C13×C4⋊C4—216no—
147C13×C4⋊C4—44no—
148C13×C4⋊C4—48no—
149C13×C4⋊C4—48no—
150C13×C22⋊C4—216no—
151C13×C22⋊C4—44no—
152C13×C22⋊C4—44no—
153C13×C22⋊C4—48no—
154C13×C22⋊C4—44no—
155C42×C13—48no—
156C42×C13—44no—
157C2×#399C2×C1311yescharacteristic
158C2×#388C2×C1312yes—
159C2×#387C2×C1312yescomplemented
160#1441C2×C1312yescomplemented
161#1440C2×C1311yescharacteristic
162#1439C2×C1312yes—
163#1437C2×C1311yescharacteristic
164#1436C2×C1312yescomplemented
165C4⋊#95C2×C1312yescomplemented
166C23×C13—24no—
167C23×C13—22no—
168C23×C13—22no—
169C23×C13—22no—
170C23×C13—24no—
171C23×C13—42no—
172C23×C13—42no—
173C23×C13—42no—
174C23×C13—42no—
175C23×C13—42no—
176C23×C13—42no—
177C23×C13—41no—
178C23×C13—42no—
179C23×C13—42no—
180C23×C13—42no—
181C23×C13—42no—
182C23×C13—42no—
183C23×C13—41no—
184C23×C13—41no—
185C23×C13—42no—
186C23×C13—41no—
187C23×C13C23×C411yescharacteristic
188C23×C13C22×D412yes—
189C23×C13C2×#4112yes—
190C23×C13C2×#4112yes—
191C23×C13H(5,𝔽2)11yescharacteristic
192C23×C13H(5,𝔽2)11yescharacteristic
193C23×C13H(5,𝔽2)12yes—
194C23×C132−1+412yes—
195C23×C132−1+412yes—
196C2×C4×C13—24no—
197C2×C4×C13—24no—
198C2×C4×C13—24no—
199C2×C4×C13—24no—
200C2×C4×C13—24no—
201C2×C4×C13—24no—
202C2×C4×C13—24no—
203C2×C4×C13—24no—
204C2×C4×C13—24no—
205C2×C4×C13—22no—
206C2×C4×C13—22no—
207C2×C4×C13—24no—
208C2×C4×C13—24no—
209C2×C4×C13—24no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—24no—
215C2×C4×C13—24no—
216C2×C4×C13—24no—
217C2×C4×C13—24no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—41no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—41no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13C4×D418yes—
248C22×C4⋊C4C22×C1312yes—
249C22×C4⋊C4C22×C1312yes—
250C22×C4⋊C4C22×C1312yes—
251C22×C4⋊C4C22×C1311yescharacteristic
252C22×C22⋊C4C22×C1312yes—
253C22×C22⋊C4C22×C1311yescharacteristic
254C22×C22⋊C4C22×C1312yes—
255C22×C22⋊C4C22×C1311yescharacteristic
256C22×C22⋊C4C22×C1311yescharacteristic
257C22×C42C22×C1312yes—
258C22×C42C22×C1311yescharacteristic
259#399C4×C1318yescomplemented
260#388—28no—
261#387—28no—
262C2×#95C22×C1312yes—
263C2×#95C22×C1312yes—
264C2×#95C22×C1312yes—
265C2×#95C22×C1312yes—
266C2×#95C22×C1311yescharacteristic
267C2×#95C22×C1312yes—
268C2×#95C22×C1312yes—
269C2×#95C22×C1312yes—
270C2×#95C22×C1311yescharacteristic
271C2×#95C22×C1312yes—
272C22×C13—44no—
273C22×C13—42no—
274C22×C13—44no—
275C22×C13—42no—
276C22×C13—42no—
277C22×C13—82no—
278C22×C13—82no—
279C22×C13—82no—
280C22×C13—82no—
281C22×C13C2×C4×D412yes—
282C22×C13C4×#4111yescharacteristic
283C22×C13#51811yescharacteristic
284C22×C13#51911yescharacteristic
285C22×C13#52012yes—
286C22×C13#53612yes—
287C22×C13#53712yes—
288C22×C13#53912yes—
289C22×C13#54112yes—
290C22×C13#54212yes—
291C22×C13#54212yes—
292C22×C13D4211yescharacteristic
293C22×C13#54612yes—
294C22×C13#54712yes—
295C22×C13#55012yes—
296C22×C13#55112yes—
297C22×C13#55212yes—
298C22×C13#55911yescharacteristic
299C22×C13#56011yescharacteristic
300C22×C13#56212yes—
301C22×C13#56311yescharacteristic
302C4×C13—28no—
303C4×C13—44no—
304C4×C13—42no—
305C4×C13—42no—
306C4×C13—44no—
307C4×C13—44no—
308C4×C13—44no—
309C4×C13—82no—
310C25C23×C1311yescharacteristic
311C23×C4C23×C1312yes—
312C23×C4C23×C1312yes—
313C23×C4C23×C1311yescharacteristic
314C23×C4C23×C1311yescharacteristic
315C23×C4C23×C1312yes—
316C23×C4C23×C1312yes—
317C23×C4C23×C1312yes—
318C23×C4C23×C1312yes—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—41no—
326C2×C4⋊C4—41no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4C2×C4×C1318yes—
330C2×C4⋊C4C2×C4×C1314yes—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—41no—
337C2×C22⋊C4—41no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4C2×C4×C1318yes—
343C2×C22⋊C4C2×C4×C1314yes—
344C2×C42—24no—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—42no—
348C2×C42—41no—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—41no—
354#95—42no—
355#95—42no—
356#95—42no—
357#95C2×C4×C1314yes—
358#95D4×C1318yes—
359C2×C13—82no—
360C2×C13#232312yes—
361C2×C13#233211yescharacteristic
362C2×C13#235912yes—
363C2×C13#236611yescharacteristic
364C2×C13#237611yescharacteristic
365C2×C13#267212yes—
366C2×C13#270512yes—
367C2×C13#272112yes—
368C2×C13#275412yes—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—21no—
373C24—21no—
374C24—22no—
375C24—22no—
376C24—22no—
377C24C22×C4×C1312yes—
378C24C24×C1311yescharacteristic
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4C22×C4×C1312yes—
423C22×C4C22×C4×C1314yes—
424C22×C4C22×C4×C1312yes—
425C22×C4C22×C4×C1314yes—
426C22×C4C2×D4×C1314yes—
427C22×C4C2×D4×C1314yes—
428C22×C4C2×D4×C1314yes—
429C22×C4C13×#4114yes—
430C22×C4C13×#4114yes—
431C4⋊C4—216no—
432C4⋊C4—44no—
433C4⋊C4—48no—
434C4⋊C4—48no—
435C22⋊C4—216no—
436C22⋊C4—44no—
437C22⋊C4—44no—
438C22⋊C4—48no—
439C22⋊C4—44no—
440C42—48no—
441C42—44no—
442C13#1454311yescharacteristic, direct product factor, Sylow
443C23—24no—
444C23—22no—
445C23—22no—
446C23—22no—
447C23—24no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23—41no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—41no—
461C23—41no—
462C23—42no—
463C23—41no—
464C23C23×C4×C1311yescharacteristic
465C23C22×D4×C1312yes—
466C23C2×C13×#4112yes—
467C23C2×C13×#4112yes—
468C23C13×H(5,𝔽2)11yescharacteristic
469C23C13×H(5,𝔽2)11yescharacteristic
470C23C13×H(5,𝔽2)12yes—
471C23C13×2−1+412yes—
472C23C13×2−1+412yes—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4C4×D4×C1318yes—
525C22—44no—
526C22—42no—
527C22—44no—
528C22—42no—
529C22—42no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22C2×C4×D4×C1312yes—
535C22C4×C13×#4111yescharacteristic
536C22C13×#51811yescharacteristic
537C22C13×#51911yescharacteristic
538C22C13×#52012yes—
539C22C13×#53612yes—
540C22C13×#53712yes—
541C22C13×#53912yes—
542C22C13×#54112yes—
543C22C13×#54212yes—
544C22C13×#54212yes—
545C22D42×C1311yescharacteristic
546C22C13×#54612yes—
547C22C13×#54712yes—
548C22C13×#55012yes—
549C22C13×#55112yes—
550C22C13×#55212yes—
551C22C13×#55911yescharacteristic
552C22C13×#56011yescharacteristic
553C22C13×#56212yes—
554C22C13×#56311yescharacteristic
555C4—28no—
556C4—44no—
557C4—42no—
558C4—42no—
559C4—44no—
560C4—44no—
561C4—44no—
562C4—82no—
563C2—82no—
564C2C13×#232312yes—
565C2C13×#233211yescharacteristic
566C2C13×#235912yes—
567C2C13×#236611yescharacteristic
568C2C13×#237611yescharacteristic
569C2C13×#267212yes—
570C2C13×#270512yes—
571C2C13×#272112yes—
572C2C13×#275412yes—
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C13×#387C2semidirect
4. C13×#1441C2semidirect
8. C13×#1436C2semidirect
9. C13×C4⋊#95C2semidirect
21. C13×#399C4semidirect
83. #14543C13direct (N × H)
159. C2×#387C2×C13semidirect
160. #1441C2×C13semidirect
164. #1436C2×C13semidirect
165. C4⋊#95C2×C13semidirect
259. #399C4×C13semidirect
442. C13#14543direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3992
C2×C13×#3882
C2×C13×#3872
C13×#14412
C13×#14402
C13×#14392
C13×#14372
C13×#14362
C13×C4⋊#952
#1454313