Finite Group Databasebeta

← C13×#15080 #15701419

Subgroups — C13×#15080 #15701419

Order 3328.

1238 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#387C212yesmaximal
2C2×C13×#387C211yesmaximal, characteristic
3C2×C4×C13×C4⋊C4C211yesmaximal, characteristic
4C13×#1444C211yesmaximal, characteristic
5C13×#1443C212yesmaximal
6C13×#1442C211yesmaximal, characteristic
7C13×#1442C212yesmaximal
8C13×#1441C211yesmaximal, characteristic
9C13×#1441C211yesmaximal, characteristic
10C13×#1434C212yesmaximal
11C13×#1434C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2212yes—
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C42×C13C2212yes—
18C22×C42×C13C2211yescharacteristic
19C13×#387—28no—
20C13×#387—24no—
21C4×C13×C4⋊C4—24no—
22C2×C13×#95C2212yes—
23C2×C13×#95C2211yescharacteristic
24C2×C13×#95C2212yes—
25C2×C13×#95C2212yes—
26C2×C13×#95C2212yes—
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2212yes—
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2212yes—
32C2×C13×#95C2212yes—
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C23×C4×C13C2311yescharacteristic
39C23×C4×C13C2312yes—
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C23×C4×C13C2312yes—
46C23×C4×C13C2312yes—
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C2×C13×C4⋊C4—22no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—24no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4—24no—
55C2×C13×C4⋊C4—24no—
56C2×C13×C4⋊C4—24no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4D414yes—
62C2×C42×C13—22no—
63C2×C42×C13—22no—
64C2×C42×C13—24no—
65C2×C42×C13—24no—
66C2×C42×C13—24no—
67C2×C42×C13D414yes—
68C13×#95—24no—
69C13×#95—24no—
70C13×#95—24no—
71C13×#95—24no—
72C13×#95—22no—
73C13×#95—22no—
74C13×#95—24no—
75C13×#95—22no—
76C13×#95—22no—
77C13×#95—22no—
78C13×#95—24no—
79C13×#95—24no—
80C13×#95—24no—
81C13×#95—24no—
82C13×#95—24no—
83C13×#95—22no—
84#15080C1311yesmaximal, characteristic, direct product factor, Sylow
85C24×C13C2411yescharacteristic
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—22no—
89C22×C4×C13—22no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—22no—
93C22×C4×C13—21no—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
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—21no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—21no—
125C22×C4×C13—22no—
126C22×C4×C13—21no—
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—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13C2×D412yes—
142C22×C4×C13C2×D412yes—
143C22×C4×C13C2×D412yes—
144C22×C4×C13C2×D412yes—
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2×D412yes—
147C22×C4×C13#4114yes—
148C22×C4×C13#4114yes—
149C22×C4×C13#4114yes—
150C22×C4×C13#4112yes—
151C22×C4×C13#4112yes—
152C22×C4×C13#4112yes—
153C13×C4⋊C4—28no—
154C13×C4⋊C4—28no—
155C13×C4⋊C4—216no—
156C13×C4⋊C4—28no—
157C13×C4⋊C4—44no—
158C42×C13—28no—
159C42×C13—48no—
160C2×#387C2×C1311yescharacteristic
161C2×#387C2×C1312yes—
162C2×C4×C4⋊C4C2×C1311yescharacteristic
163#1444C2×C1311yescharacteristic
164#1443C2×C1312yes—
165#1442C2×C1311yescharacteristic
166#1442C2×C1312yes—
167#1441C2×C1311yescharacteristic
168#1441C2×C1311yescharacteristic
169#1434C2×C1312yes—
170#1434C2×C1311yescharacteristic
171C23×C13C22×D411yescharacteristic
172C23×C13C22×D411yescharacteristic
173C23×C13C2×#4111yescharacteristic
174C23×C13C2×#4111yescharacteristic
175C23×C13C2×#4111yescharacteristic
176C23×C13C2×#4112yes—
177C23×C13C2×#4112yes—
178C23×C13C2×#4112yes—
179C23×C132−1+411yescharacteristic
180C23×C132−1+411yescharacteristic
181C23×C132−1+412yes—
182C2×C4×C13—22no—
183C2×C4×C13—22no—
184C2×C4×C13—22no—
185C2×C4×C13—24no—
186C2×C4×C13—24no—
187C2×C4×C13—22no—
188C2×C4×C13—22no—
189C2×C4×C13—22no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—22no—
193C2×C4×C13—22no—
194C2×C4×C13—22no—
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—22no—
202C2×C4×C13—22no—
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—24no—
206C2×C4×C13—24no—
207C2×C4×C13—24no—
208C2×C4×C13—24no—
209C2×C4×C13—42no—
210C2×C4×C13—42no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—41no—
218C2×C4×C13—42no—
219C2×C4×C13—41no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—41no—
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×C13#12114yes—
248C2×C4×C13#12314yes—
249C22×C4⋊C4C22×C1311yescharacteristic
250C22×C4⋊C4C22×C1311yescharacteristic
251C22×C4⋊C4C22×C1311yescharacteristic
252C22×C4⋊C4C22×C1312yes—
253C22×C4⋊C4C22×C1311yescharacteristic
254C22×C42C22×C1312yes—
255C22×C42C22×C1311yescharacteristic
256#387—28no—
257#387—24no—
258C4×C4⋊C4—24no—
259C2×#95C22×C1311yescharacteristic
260C2×#95C22×C1312yes—
261C2×#95C22×C1312yes—
262C2×#95C22×C1312yes—
263C2×#95C22×C1311yescharacteristic
264C2×#95C22×C1311yescharacteristic
265C2×#95C22×C1312yes—
266C2×#95C22×C1312yes—
267C2×#95C22×C1312yes—
268C2×#95C22×C1312yes—
269C2×#95C22×C1312yes—
270C2×#95C22×C1311yescharacteristic
271C2×#95C22×C1312yes—
272C2×#95C22×C1312yes—
273C2×#95C22×C1311yescharacteristic
274C2×#95C22×C1311yescharacteristic
275C22×C13C2×#12111yescharacteristic
276C22×C13C2×#12311yescharacteristic
277C22×C13#52511yescharacteristic
278C22×C13#52511yescharacteristic
279C22×C13#52512yes—
280C22×C13#52912yes—
281C22×C13#52912yes—
282C22×C13#52912yes—
283C22×C13#53211yescharacteristic
284C22×C13#53611yescharacteristic
285C22×C13#53611yescharacteristic
286C22×C13#54112yes—
287C22×C13#54112yes—
288C22×C13#54711yescharacteristic
289C22×C13#54711yescharacteristic
290C22×C13#54812yes—
291C22×C13#55212yes—
292C22×C13#55212yes—
293C22×C13#55211yescharacteristic
294C22×C13#55211yescharacteristic
295C22×C13#55212yes—
296C22×C13#55612yes—
297C22×C13#55612yes—
298C4×C13—24no—
299C4×C13—24no—
300C4×C13—42no—
301C4×C13—44no—
302C4×C13—44no—
303C4×C13—42no—
304C4×C13—42no—
305C4×C13—44no—
306C4×C13—81no—
307C4×C13—81no—
308C4×C13—82no—
309C23×C4C23×C1311yescharacteristic
310C23×C4C23×C1312yes—
311C23×C4C23×C1311yescharacteristic
312C23×C4C23×C1311yescharacteristic
313C23×C4C23×C1311yescharacteristic
314C23×C4C23×C1311yescharacteristic
315C23×C4C23×C1312yes—
316C23×C4C23×C1312yes—
317C23×C4C23×C1312yes—
318C23×C4C23×C1311yescharacteristic
319C23×C4C23×C1311yescharacteristic
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4D4×C1314yes—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—24no—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42D4×C1314yes—
339#95—24no—
340#95—24no—
341#95—24no—
342#95—24no—
343#95—22no—
344#95—22no—
345#95—24no—
346#95—22no—
347#95—22no—
348#95—22no—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—22no—
355C2×C13#239211yescharacteristic
356C2×C13#246912yes—
357C2×C13#247512yes—
358C2×C13#248611yescharacteristic
359C2×C13#249911yescharacteristic
360C2×C13#252412yes—
361C2×C13#252812yes—
362C2×C13#253611yescharacteristic
363C2×C13#260411yescharacteristic
364C2×C13#263411yescharacteristic
365C2×C13#285311yescharacteristic
366C24C24×C1311yescharacteristic
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
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—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4C2×D4×C1312yes—
423C22×C4C2×D4×C1312yes—
424C22×C4C2×D4×C1312yes—
425C22×C4C2×D4×C1312yes—
426C22×C4C2×D4×C1312yes—
427C22×C4C2×D4×C1312yes—
428C22×C4C13×#4114yes—
429C22×C4C13×#4114yes—
430C22×C4C13×#4114yes—
431C22×C4C13×#4112yes—
432C22×C4C13×#4112yes—
433C22×C4C13×#4112yes—
434C4⋊C4—28no—
435C4⋊C4—28no—
436C4⋊C4—216no—
437C4⋊C4—28no—
438C4⋊C4—44no—
439C42—28no—
440C42—48no—
441C13#1508011yescharacteristic, direct product factor, Sylow
442C23C22×D4×C1311yescharacteristic
443C23C22×D4×C1311yescharacteristic
444C23C2×C13×#4111yescharacteristic
445C23C2×C13×#4111yescharacteristic
446C23C2×C13×#4111yescharacteristic
447C23C2×C13×#4112yes—
448C23C2×C13×#4112yes—
449C23C2×C13×#4112yes—
450C23C13×2−1+411yescharacteristic
451C23C13×2−1+411yescharacteristic
452C23C13×2−1+412yes—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4C13×#12114yes—
519C2×C4C13×#12314yes—
520C22C2×C13×#12111yescharacteristic
521C22C2×C13×#12311yescharacteristic
522C22C13×#52511yescharacteristic
523C22C13×#52511yescharacteristic
524C22C13×#52512yes—
525C22C13×#52912yes—
526C22C13×#52912yes—
527C22C13×#52912yes—
528C22C13×#53211yescharacteristic
529C22C13×#53611yescharacteristic
530C22C13×#53611yescharacteristic
531C22C13×#54112yes—
532C22C13×#54112yes—
533C22C13×#54711yescharacteristic
534C22C13×#54711yescharacteristic
535C22C13×#54812yes—
536C22C13×#55212yes—
537C22C13×#55211yescharacteristic
538C22C13×#55212yes—
539C22C13×#55212yes—
540C22C13×#55211yescharacteristic
541C22C13×#55612yes—
542C22C13×#55612yes—
543C4—24no—
544C4—24no—
545C4—42no—
546C4—44no—
547C4—42no—
548C4—44no—
549C4—44no—
550C4—42no—
551C4—81no—
552C4—81no—
553C4—82no—
554C2C13×#239211yescharacteristic
555C2C13×#246912yes—
556C2C13×#247512yes—
557C2C13×#248611yescharacteristic
558C2C13×#249911yescharacteristic
559C2C13×#252412yes—
560C2C13×#252812yes—
561C2C13×#253611yescharacteristic
562C2C13×#260411yescharacteristic
563C2C13×#263411yescharacteristic
564C2C13×#285311yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C13C24
commutator, Frattini, cosocleC24C24×C13
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
84. #15080C13direct (N × H)
441. C13#15080direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3872
C2×C4×C13×C4⋊C42
C13×#14442
C13×#14432
C13×#14422
C13×#14412
C13×#14342
#1508013