Finite Group Databasebeta

← C13×#15539 #15701878

Subgroups — C13×#15539 #15701878

Order 3328.

1570 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#397C212yesmaximal
2C2×C13×#397C211yesmaximal, characteristic
3C2×C13×#385C212yesmaximal
4C2×C13×#381C211yesmaximal, characteristic
5C13×#1445C212yesmaximal, complemented
6C13×#1445C212yesmaximal, complemented
7C13×#1444C212yesmaximal, complemented
8C13×#1437C211yesmaximal, characteristic
9C13×C4⋊#95C212yesmaximal, complemented
10C24×C4×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2212yes—
12C22×C13×C4⋊C4C2212yes—
13C22×C13×C4⋊C4C2212yes—
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2211yescharacteristic
16C22×C13×C22⋊C4C2212yes—
17C22×C13×C22⋊C4C2212yes—
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C13×#397—28no—
21C13×#397—24no—
22C13×#385—28no—
23C13×#381—24no—
24C2×C13×#95C2212yes—
25C2×C13×#95C2212yes—
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2212yes—
33C2×C13×#95C2212yes—
34C2×C13×#95C2211yescharacteristic
35C25×C13C2311yescharacteristic
36C23×C4×C13—22no—
37C23×C4×C13—24no—
38C23×C4×C13—24no—
39C23×C4×C13—41no—
40C23×C4×C13—41no—
41C23×C4×C13C2312yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2312yes—
47C23×C4×C13C2312yes—
48C23×C4×C13C2312yes—
49C2×C13×C4⋊C4—24no—
50C2×C13×C4⋊C4—24no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—24no—
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4—24no—
55C2×C13×C4⋊C4—24no—
56C2×C13×C4⋊C4—24no—
57C2×C13×C4⋊C4—42no—
58C2×C13×C4⋊C4—42no—
59C2×C13×C4⋊C4—41no—
60C2×C13×C4⋊C4—41no—
61C2×C13×C22⋊C4—24no—
62C2×C13×C22⋊C4—24no—
63C2×C13×C22⋊C4—22no—
64C2×C13×C22⋊C4—24no—
65C2×C13×C22⋊C4—24no—
66C2×C13×C22⋊C4—24no—
67C2×C13×C22⋊C4—24no—
68C2×C13×C22⋊C4—41no—
69C2×C13×C22⋊C4—41no—
70C2×C13×C22⋊C4D418yes—
71C2×C13×C22⋊C4D414yes—
72C2×C42×C13—24no—
73C2×C42×C13—41no—
74C13×#95—24no—
75C13×#95—24no—
76C13×#95—24no—
77C13×#95—24no—
78C13×#95—22no—
79C13×#95—24no—
80C13×#95—24no—
81C13×#95—24no—
82C13×#95—24no—
83C13×#95—24no—
84C13×#95—41no—
85#15539C1311yesmaximal, characteristic, direct product factor, Sylow
86C24×C13—22no—
87C24×C13—22no—
88C24×C13—22no—
89C24×C13—21no—
90C24×C13—21no—
91C24×C13—22no—
92C24×C13—22no—
93C24×C13C2×D414yes—
94C24×C13C2×D412yes—
95C24×C13C2411yescharacteristic
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—28no—
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—21no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
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×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—48no—
143C22×C4×C13—48no—
144C22×C4×C13—44no—
145C22×C4×C13—44no—
146C22×C4×C13C2×D412yes—
147C22×C4×C13C2×D414yes—
148C22×C4×C13C2×D412yes—
149C22×C4×C13C2×D414yes—
150C22×C4×C13#4114yes—
151C22×C4×C13#4114yes—
152C22×C4×C13#4114yes—
153C13×C4⋊C4—48no—
154C13×C4⋊C4—48no—
155C13×C4⋊C4—44no—
156C13×C4⋊C4—48no—
157C13×C22⋊C4—216no—
158C13×C22⋊C4—44no—
159C13×C22⋊C4—44no—
160C13×C22⋊C4—48no—
161C42×C13—44no—
162C2×#397C2×C1312yes—
163C2×#397C2×C1311yescharacteristic
164C2×#385C2×C1312yes—
165C2×#381C2×C1311yescharacteristic
166#1445C2×C1312yescomplemented
167#1445C2×C1312yescomplemented
168#1444C2×C1312yescomplemented
169#1437C2×C1311yescharacteristic
170C4⋊#95C2×C1312yescomplemented
171C23×C13—24no—
172C23×C13—22no—
173C23×C13—22no—
174C23×C13—24no—
175C23×C13—24no—
176C23×C13—24no—
177C23×C13—24no—
178C23×C13—24no—
179C23×C13—24no—
180C23×C13—24no—
181C23×C13—42no—
182C23×C13—42no—
183C23×C13—42no—
184C23×C13—42no—
185C23×C13—41no—
186C23×C13—42no—
187C23×C13—42no—
188C23×C13—41no—
189C23×C13—41no—
190C23×C13—41no—
191C23×C13#12714yes—
192C23×C13C22×D412yes—
193C23×C13C22×D411yescharacteristic
194C23×C13C2×#4112yes—
195C23×C13C2×#4112yes—
196C23×C13C2×#4112yes—
197C23×C13H(5,𝔽2)11yescharacteristic
198C23×C13H(5,𝔽2)11yescharacteristic
199C23×C132−1+412yes—
200C23×C132−1+412yes—
201C2×C4×C13—24no—
202C2×C4×C13—24no—
203C2×C4×C13—24no—
204C2×C4×C13—24no—
205C2×C4×C13—24no—
206C2×C4×C13—24no—
207C2×C4×C13—24no—
208C2×C4×C13—24no—
209C2×C4×C13—22no—
210C2×C4×C13—22no—
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—416no—
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—42no—
225C2×C4×C13—42no—
226C2×C4×C13—41no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
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—
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—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13#12318yes—
254C24×C4C22×C1311yescharacteristic
255C22×C4⋊C4C22×C1312yes—
256C22×C4⋊C4C22×C1312yes—
257C22×C4⋊C4C22×C1312yes—
258C22×C4⋊C4C22×C1311yescharacteristic
259C22×C22⋊C4C22×C1311yescharacteristic
260C22×C22⋊C4C22×C1312yes—
261C22×C22⋊C4C22×C1312yes—
262C22×C22⋊C4C22×C1311yescharacteristic
263C22×C42C22×C1311yescharacteristic
264#397—28no—
265#397—24no—
266#385—28no—
267#381—24no—
268C2×#95C22×C1312yes—
269C2×#95C22×C1312yes—
270C2×#95C22×C1312yes—
271C2×#95C22×C1311yescharacteristic
272C2×#95C22×C1312yes—
273C2×#95C22×C1312yes—
274C2×#95C22×C1312yes—
275C2×#95C22×C1312yes—
276C2×#95C22×C1312yes—
277C2×#95C22×C1312yes—
278C2×#95C22×C1311yescharacteristic
279C22×C13—28no—
280C22×C13—24no—
281C22×C13—44no—
282C22×C13—44no—
283C22×C13—44no—
284C22×C13—44no—
285C22×C13—42no—
286C22×C13—42no—
287C22×C13—44no—
288C22×C13C2×#12312yes—
289C22×C13#52511yescharacteristic
290C22×C13#52912yes—
291C22×C13C2×#12711yescharacteristic
292C22×C13#53411yescharacteristic
293C22×C13#53612yes—
294C22×C13#53912yes—
295C22×C13#54112yes—
296C22×C13#54212yes—
297C22×C13#54612yes—
298C22×C13#54612yes—
299C22×C13#54712yes—
300C22×C13#54712yes—
301C22×C13#54712yes—
302C22×C13#54712yes—
303C22×C13#55111yescharacteristic
304C22×C13#55212yes—
305C22×C13#55612yes—
306C22×C13#55911yescharacteristic
307C22×C13#56311yescharacteristic
308C22×C13#56311yescharacteristic
309C4×C13—28no—
310C4×C13—44no—
311C4×C13—42no—
312C4×C13—42no—
313C4×C13—44no—
314C4×C13—82no—
315C4×C13—82no—
316C4×C13—82no—
317C25C23×C1311yescharacteristic
318C23×C4—22no—
319C23×C4—24no—
320C23×C4—24no—
321C23×C4—41no—
322C23×C4—41no—
323C23×C4C23×C1312yes—
324C23×C4C23×C1312yes—
325C23×C4C23×C1312yes—
326C23×C4C23×C1311yescharacteristic
327C23×C4C23×C1312yes—
328C23×C4C23×C1311yescharacteristic
329C23×C4C23×C1312yes—
330C23×C4C23×C1312yes—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—41no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4D4×C1318yes—
353C2×C22⋊C4D4×C1314yes—
354C2×C42—24no—
355C2×C42—41no—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—24no—
360#95—22no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—41no—
367C2×C13—44no—
368C2×C13#241912yes—
369C2×C13#244712yes—
370C2×C13#247812yes—
371C2×C13#250112yes—
372C2×C13#253911yescharacteristic
373C2×C13#268912yes—
374C2×C13#269812yes—
375C2×C13#271711yescharacteristic
376C2×C13#272411yescharacteristic
377C24—22no—
378C24—22no—
379C24—22no—
380C24—21no—
381C24—21no—
382C24—22no—
383C24—22no—
384C24C2×D4×C1314yes—
385C24C2×D4×C1312yes—
386C24C24×C1311yescharacteristic
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—28no—
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—21no—
403C22×C4—22no—
404C22×C4—21no—
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×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—48no—
434C22×C4—48no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4C2×D4×C1312yes—
438C22×C4C2×D4×C1314yes—
439C22×C4C2×D4×C1312yes—
440C22×C4C2×D4×C1314yes—
441C22×C4C13×#4114yes—
442C22×C4C13×#4114yes—
443C22×C4C13×#4114yes—
444C4⋊C4—48no—
445C4⋊C4—48no—
446C4⋊C4—44no—
447C4⋊C4—48no—
448C22⋊C4—216no—
449C22⋊C4—44no—
450C22⋊C4—44no—
451C22⋊C4—48no—
452C42—44no—
453C13#1553911yescharacteristic, direct product factor, Sylow
454C23—24no—
455C23—22no—
456C23—22no—
457C23—24no—
458C23—24no—
459C23—24no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—24no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—41no—
469C23—42no—
470C23—42no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23C13×#12714yes—
475C23C22×D4×C1312yes—
476C23C22×D4×C1311yescharacteristic
477C23C2×C13×#4112yes—
478C23C2×C13×#4112yes—
479C23C2×C13×#4112yes—
480C23C13×H(5,𝔽2)11yescharacteristic
481C23C13×H(5,𝔽2)11yescharacteristic
482C23C13×2−1+412yes—
483C23C13×2−1+412yes—
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—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—416no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4C13×#12318yes—
537C22—28no—
538C22—24no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22—44no—
543C22—42no—
544C22—42no—
545C22—44no—
546C22C2×C13×#12312yes—
547C22C13×#52511yescharacteristic
548C22C13×#52912yes—
549C22C2×C13×#12711yescharacteristic
550C22C13×#53411yescharacteristic
551C22C13×#53612yes—
552C22C13×#53912yes—
553C22C13×#54112yes—
554C22C13×#54212yes—
555C22C13×#54612yes—
556C22C13×#54612yes—
557C22C13×#54712yes—
558C22C13×#54712yes—
559C22C13×#54712yes—
560C22C13×#54712yes—
561C22C13×#55111yescharacteristic
562C22C13×#55212yes—
563C22C13×#55612yes—
564C22C13×#55911yescharacteristic
565C22C13×#56311yescharacteristic
566C22C13×#56311yescharacteristic
567C4—28no—
568C4—44no—
569C4—44no—
570C4—42no—
571C4—42no—
572C4—82no—
573C4—82no—
574C4—82no—
575C2—44no—
576C2C13×#241912yes—
577C2C13×#244712yes—
578C2C13×#247812yes—
579C2C13×#250112yes—
580C2C13×#253911yescharacteristic
581C2C13×#268912yes—
582C2C13×#269812yes—
583C2C13×#271711yescharacteristic
584C2C13×#272411yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
5. C13×#1445C2semidirect
6. C13×#1445C2semidirect
7. C13×#1444C2semidirect
9. C13×C4⋊#95C2semidirect
85. #15539C13direct (N × H)
166. #1445C2×C13semidirect
167. #1445C2×C13semidirect
168. #1444C2×C13semidirect
170. C4⋊#95C2×C13semidirect
453. C13#15539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3972
C2×C13×#3852
C2×C13×#3812
C13×#14452
C13×#14442
C13×#14372
C13×C4⋊#952
#1553913