Finite Group Databasebeta

← C13×#14646 #15700985

Subgroups — C13×#14646 #15700985

Order 3328.

1226 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#399C211yesmaximal, characteristic
2C13×#1443C212yesmaximal, complemented
3C13×#1441C212yesmaximal, complemented
4C13×#1441C212yesmaximal, complemented
5C13×#1440C212yesmaximal
6C13×#1440C211yesmaximal, characteristic
7C13×#1439C212yesmaximal
8C13×#1437C211yesmaximal, characteristic
9C13×#1436C212yesmaximal, complemented
10C22×C13×C4⋊C4C2212yes—
11C22×C13×C4⋊C4C2212yes—
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C22⋊C4C2212yes—
14C22×C13×C22⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2211yescharacteristic
16C22×C13×C22⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2212yes—
18C22×C42×C13C2211yescharacteristic
19C13×#399C418yescomplemented
20C2×C13×#95C2212yes—
21C2×C13×#95C2212yes—
22C2×C13×#95C2212yes—
23C2×C13×#95C2212yes—
24C2×C13×#95C2212yes—
25C2×C13×#95C2211yescharacteristic
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×C13×#95C2211yescharacteristic
32C25×C13C2311yescharacteristic
33C23×C4×C13C2312yes—
34C23×C4×C13C2312yes—
35C23×C4×C13C2312yes—
36C23×C4×C13C2311yescharacteristic
37C23×C4×C13C2312yes—
38C23×C4×C13C2312yes—
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2312yes—
41C2×C13×C4⋊C4—42no—
42C2×C13×C4⋊C4—41no—
43C2×C13×C4⋊C4—42no—
44C2×C13×C4⋊C4—41no—
45C2×C13×C4⋊C4—42no—
46C2×C13×C4⋊C4—42no—
47C2×C13×C4⋊C4—42no—
48C2×C13×C4⋊C4C2×C418yes—
49C2×C13×C4⋊C4C2×C414yes—
50C2×C13×C22⋊C4—24no—
51C2×C13×C22⋊C4—41no—
52C2×C13×C22⋊C4—42no—
53C2×C13×C22⋊C4—41no—
54C2×C13×C22⋊C4—42no—
55C2×C13×C22⋊C4—42no—
56C2×C13×C22⋊C4—42no—
57C2×C13×C22⋊C4—42no—
58C2×C13×C22⋊C4—41no—
59C2×C13×C22⋊C4—42no—
60C2×C13×C22⋊C4—41no—
61C2×C13×C22⋊C4C2×C414yes—
62C2×C13×C22⋊C4C2×C418yes—
63C2×C42×C13—41no—
64C2×C42×C13—42no—
65C13×#95—24no—
66C13×#95—24no—
67C13×#95—42no—
68C13×#95—42no—
69C13×#95—42no—
70C13×#95—42no—
71C13×#95—42no—
72C13×#95—42no—
73C13×#95—41no—
74C13×#95—42no—
75C13×#95—42no—
76C13×#95C2×C414yes—
77#14646C1311yesmaximal, characteristic, direct product factor, Sylow
78C24×C13—22no—
79C24×C13—22no—
80C24×C13—21no—
81C24×C13—22no—
82C24×C13—21no—
83C24×C13—22no—
84C24×C13—22no—
85C24×C13—22no—
86C24×C13C22×C412yes—
87C24×C13C2411yescharacteristic
88C22×C4×C13—22no—
89C22×C4×C13—22no—
90C22×C4×C13—22no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13—21no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—21no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
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—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
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×C13C22×C414yes—
136C22×C4×C13C22×C412yes—
137C22×C4×C13C22×C412yes—
138C22×C4×C13C22×C414yes—
139C22×C4×C13#4114yes—
140C13×C4⋊C4—48no—
141C13×C4⋊C4—44no—
142C13×C4⋊C4—48no—
143C13×C22⋊C4—48no—
144C13×C22⋊C4—44no—
145C13×C22⋊C4—48no—
146C13×C22⋊C4—44no—
147C13×C22⋊C4—44no—
148C42×C13—44no—
149C2×#399C2×C1311yescharacteristic
150#1443C2×C1312yescomplemented
151#1441C2×C1312yescomplemented
152#1441C2×C1312yescomplemented
153#1440C2×C1312yes—
154#1440C2×C1311yescharacteristic
155#1439C2×C1312yes—
156#1437C2×C1311yescharacteristic
157#1436C2×C1312yescomplemented
158C23×C13—22no—
159C23×C13—22no—
160C23×C13—24no—
161C23×C13—22no—
162C23×C13—24no—
163C23×C13—42no—
164C23×C13—42no—
165C23×C13—42no—
166C23×C13—42no—
167C23×C13—42no—
168C23×C13—42no—
169C23×C13—41no—
170C23×C13—41no—
171C23×C13—41no—
172C23×C13—42no—
173C23×C13—42no—
174C23×C13—42no—
175C23×C13—42no—
176C23×C13—41no—
177C23×C13—42no—
178C23×C13—42no—
179C23×C13C23×C411yescharacteristic
180C23×C13C2×#4112yes—
181C23×C13H(5,𝔽2)12yes—
182C23×C13H(5,𝔽2)11yescharacteristic
183C23×C13H(5,𝔽2)12yes—
184C23×C13H(5,𝔽2)11yescharacteristic
185C23×C13H(5,𝔽2)12yes—
186C23×C132−1+412yes—
187C23×C132−1+412yes—
188C2×C4×C13—24no—
189C2×C4×C13—24no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—24no—
193C2×C4×C13—24no—
194C2×C4×C13—24no—
195C2×C4×C13—24no—
196C2×C4×C13—24no—
197C2×C4×C13—24no—
198C2×C4×C13—24no—
199C2×C4×C13—24no—
200C2×C4×C13—24no—
201C2×C4×C13—42no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13—42no—
206C2×C4×C13—41no—
207C2×C4×C13—42no—
208C2×C4×C13—41no—
209C2×C4×C13—42no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—41no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—41no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
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—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C22×C4⋊C4C22×C1312yes—
241C22×C4⋊C4C22×C1312yes—
242C22×C4⋊C4C22×C1311yescharacteristic
243C22×C22⋊C4C22×C1312yes—
244C22×C22⋊C4C22×C1311yescharacteristic
245C22×C22⋊C4C22×C1311yescharacteristic
246C22×C22⋊C4C22×C1311yescharacteristic
247C22×C22⋊C4C22×C1312yes—
248C22×C42C22×C1311yescharacteristic
249#399C4×C1318yescomplemented
250C2×#95C22×C1312yes—
251C2×#95C22×C1312yes—
252C2×#95C22×C1312yes—
253C2×#95C22×C1312yes—
254C2×#95C22×C1312yes—
255C2×#95C22×C1311yescharacteristic
256C2×#95C22×C1312yes—
257C2×#95C22×C1312yes—
258C2×#95C22×C1312yes—
259C2×#95C22×C1312yes—
260C2×#95C22×C1312yes—
261C2×#95C22×C1311yescharacteristic
262C22×C13—42no—
263C22×C13—44no—
264C22×C13—42no—
265C22×C13—44no—
266C22×C13—42no—
267C22×C13—82no—
268C22×C13—82no—
269C22×C13—82no—
270C22×C13—82no—
271C22×C13C4×#4111yescharacteristic
272C22×C13#51811yescharacteristic
273C22×C13#51812yes—
274C22×C13#51911yescharacteristic
275C22×C13#52012yes—
276C22×C13#53812yes—
277C22×C13#53912yes—
278C22×C13#53912yes—
279C22×C13#54012yes—
280C22×C13#54212yes—
281C22×C13#54212yes—
282C22×C13#56011yescharacteristic
283C22×C13#56011yescharacteristic
284C22×C13#56012yes—
285C22×C13#56011yescharacteristic
286C22×C13#56212yes—
287C22×C13#56212yes—
288C22×C13#56212yes—
289C22×C13#56312yes—
290C22×C13#56312yes—
291C22×C13#56311yescharacteristic
292C4×C13—44no—
293C4×C13—44no—
294C4×C13—42no—
295C4×C13—42no—
296C4×C13—44no—
297C4×C13—82no—
298C4×C13—82no—
299C4×C13—82no—
300C25C23×C1311yescharacteristic
301C23×C4C23×C1312yes—
302C23×C4C23×C1312yes—
303C23×C4C23×C1312yes—
304C23×C4C23×C1312yes—
305C23×C4C23×C1311yescharacteristic
306C23×C4C23×C1312yes—
307C23×C4C23×C1311yescharacteristic
308C23×C4C23×C1312yes—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4C2×C4×C1318yes—
317C2×C4⋊C4C2×C4×C1314yes—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—41no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—41no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—41no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—41no—
329C2×C22⋊C4C2×C4×C1314yes—
330C2×C22⋊C4C2×C4×C1318yes—
331C2×C42—41no—
332C2×C42—42no—
333#95—24no—
334#95—24no—
335#95—42no—
336#95—42no—
337#95—42no—
338#95—42no—
339#95—42no—
340#95—42no—
341#95—41no—
342#95—42no—
343#95—42no—
344#95C2×C4×C1314yes—
345C2×C13—82no—
346C2×C13#233211yescharacteristic
347C2×C13#233512yes—
348C2×C13#237611yescharacteristic
349C2×C13#237812yes—
350C2×C13#238011yescharacteristic
351C2×C13#282712yes—
352C2×C13#282912yes—
353C2×C13#283712yes—
354C2×C13#283812yes—
355C24—22no—
356C24—22no—
357C24—21no—
358C24—22no—
359C24—21no—
360C24—22no—
361C24—22no—
362C24—22no—
363C24C22×C4×C1312yes—
364C24C24×C1311yescharacteristic
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
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—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4C22×C4×C1314yes—
413C22×C4C22×C4×C1312yes—
414C22×C4C22×C4×C1314yes—
415C22×C4C22×C4×C1312yes—
416C22×C4C13×#4114yes—
417C4⋊C4—48no—
418C4⋊C4—44no—
419C4⋊C4—48no—
420C22⋊C4—48no—
421C22⋊C4—44no—
422C22⋊C4—48no—
423C22⋊C4—44no—
424C22⋊C4—44no—
425C42—44no—
426C13#1464611yescharacteristic, direct product factor, Sylow
427C23—22no—
428C23—22no—
429C23—24no—
430C23—22no—
431C23—24no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—41no—
446C23—42no—
447C23—42no—
448C23C23×C4×C1311yescharacteristic
449C23C2×C13×#4112yes—
450C23C13×H(5,𝔽2)12yes—
451C23C13×H(5,𝔽2)11yescharacteristic
452C23C13×H(5,𝔽2)12yes—
453C23C13×H(5,𝔽2)11yescharacteristic
454C23C13×H(5,𝔽2)12yes—
455C23C13×2−1+412yes—
456C23C13×2−1+412yes—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C22—42no—
510C22—44no—
511C22—42no—
512C22—44no—
513C22—42no—
514C22—82no—
515C22—82no—
516C22—82no—
517C22—82no—
518C22C4×C13×#4111yescharacteristic
519C22C13×#51811yescharacteristic
520C22C13×#51812yes—
521C22C13×#51911yescharacteristic
522C22C13×#52012yes—
523C22C13×#53812yes—
524C22C13×#53912yes—
525C22C13×#53912yes—
526C22C13×#54012yes—
527C22C13×#54212yes—
528C22C13×#54212yes—
529C22C13×#56011yescharacteristic
530C22C13×#56011yescharacteristic
531C22C13×#56012yes—
532C22C13×#56011yescharacteristic
533C22C13×#56212yes—
534C22C13×#56212yes—
535C22C13×#56212yes—
536C22C13×#56312yes—
537C22C13×#56312yes—
538C22C13×#56311yescharacteristic
539C4—44no—
540C4—44no—
541C4—42no—
542C4—42no—
543C4—44no—
544C4—82no—
545C4—82no—
546C4—82no—
547C2—82no—
548C2C13×#233211yescharacteristic
549C2C13×#233512yes—
550C2C13×#237611yescharacteristic
551C2C13×#237812yes—
552C2C13×#238011yescharacteristic
553C2C13×#282712yes—
554C2C13×#282912yes—
555C2C13×#283712yes—
556C2C13×#283812yes—
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
2. C13×#1443C2semidirect
3. C13×#1441C2semidirect
4. C13×#1441C2semidirect
9. C13×#1436C2semidirect
19. C13×#399C4semidirect
77. #14646C13direct (N × H)
150. #1443C2×C13semidirect
151. #1441C2×C13semidirect
152. #1441C2×C13semidirect
157. #1436C2×C13semidirect
249. #399C4×C13semidirect
426. C13#14646direct (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
C13×#14432
C13×#14412
C13×#14402
C13×#14392
C13×#14372
C13×#14362
#1464613