Finite Group Databasebeta

← C13×#9963 #15696302

Subgroups — C13×#9963 #15696302

Order 3328.

1046 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×#450C211yesmaximal, characteristic, complemented
2C2×C13×#447C211yesmaximal, characteristic
3C13×#2639C211yesmaximal, characteristic, complemented
4C2×C13×#328C211yesmaximal, characteristic, complemented
5C2×C13×#327C211yesmaximal, characteristic, complemented
6C13×#1438C211yesmaximal, characteristic, complemented
7C13×#1280C211yesmaximal, characteristic, complemented
8C23×D4×C13C2211yescharacteristic
9C22×C13×SD16—21no—
10C22×C13×D8—21no—
11C2×C13×C22⋊Q8C2211yescharacteristic
12C2×C13×#121C2211yescharacteristic
13C22×C13×C22⋊C4—22no—
14C13×#450—22no—
15C13×#450—22no—
16C13×#447—22no—
17C13×#447—22no—
18C2×C13×#102—21no—
19C2×C13×#102—21no—
20C2×C13×C22⋊C8C2211yescharacteristic
21C2×C13×C22⋊C8C2211yescharacteristic
22C13×#400—21no—
23C13×#397—21no—
24C13×#394—21no—
25C13×#393—21no—
26C13×#386—22no—
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29C13×#328—22no—
30C13×#327—22no—
31C25×C13—21no—
32C22×Q8×C13D411yescharacteristic
33C22×D4×C13—21no—
34C22×D4×C13—21no—
35C22×D4×C13—21no—
36C22×D4×C13—21no—
37C22×D4×C13—21no—
38C22×D4×C13—21no—
39C22×D4×C13—44no—
40C22×D4×C13D411yescharacteristic
41C22×D4×C13D412yes—
42C23×C4×C13—21no—
43C23×C4×C13D412yes—
44C23×C4×C13C2311yescharacteristic
45C2×C13×SD16—24no—
46C2×C13×SD16—44no—
47C2×C13×D8—24no—
48C2×C13×D8—44no—
49C22×C8×C13—21no—
50C22×C8×C13—21no—
51C13×C22⋊Q8—21no—
52C13×C22⋊Q8—21no—
53C13×C22⋊Q8—21no—
54C13×C22⋊Q8—21no—
55C13×#121—21no—
56C13×#121—21no—
57C13×#121—21no—
58C13×#121—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4D411yescharacteristic
61C2×C13×C4⋊C4D411yescharacteristic
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4—22no—
65C2×C13×C22⋊C4—22no—
66C2×C13×C22⋊C4—44no—
67C2×C13×C22⋊C4—44no—
68C2×C13×C22⋊C4—44no—
69C13×#102—24no—
70C13×#102—24no—
71C13×C22⋊C8—21no—
72C13×C22⋊C8—21no—
73C13×C22⋊C8D412yes—
74C13×C22⋊C8D412yes—
75C13×#95—22no—
76C13×#95—22no—
77C13×#95—21no—
78C13×#95—21no—
79C13×#95—21no—
80C13×#95—21no—
81#9963C1311yesmaximal, characteristic, direct product factor, Sylow
82C24×C13—24no—
83C24×C13—22no—
84C24×C13—21no—
85C24×C13—42no—
86C24×C13—42no—
87C24×C13—42no—
88C24×C13—41no—
89C24×C13—41no—
90C24×C13—42no—
91C24×C13—42no—
92C24×C13C2×D411yescharacteristic
93C2×Q8×C13—21no—
94C2×Q8×C13—21no—
95C2×Q8×C13—42no—
96C2×D4×C13—24no—
97C2×D4×C13—24no—
98C2×D4×C13—22no—
99C2×D4×C13—22no—
100C2×D4×C13—21no—
101C2×D4×C13—21no—
102C2×D4×C13—42no—
103C2×D4×C13—42no—
104C2×D4×C13—42no—
105C2×D4×C13—44no—
106C2×D4×C13—44no—
107C2×D4×C13—44no—
108C2×D4×C13—44no—
109C2×D4×C13—41no—
110C2×D4×C13—41no—
111C2×D4×C13—42no—
112C2×D4×C13—42no—
113C2×D4×C13—41no—
114C2×D4×C13—41no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—42no—
123C22×C4×C13—42no—
124C22×C4×C13—42no—
125C22×C4×C13—42no—
126C22×C4×C13—41no—
127C22×C4×C13—41no—
128C22×C4×C13—42no—
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13#4111yescharacteristic
135C13×SD16—48no—
136C13×D8—48no—
137C2×C8×C13—22no—
138C2×C8×C13—22no—
139C2×C8×C13—42no—
140C2×C8×C13—42no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—41no—
146C13×C4⋊C4—41no—
147C13×C22⋊C4—416no—
148C13×C22⋊C4—41no—
149C13×C22⋊C4—41no—
150C13×C22⋊C4—41no—
151C13×C22⋊C4—41no—
152C13×C22⋊C4—82no—
153C13×C22⋊C4—82no—
154C2×#450C2×C1311yescharacteristic, complemented
155C2×#447C2×C1311yescharacteristic
156#2639C2×C1311yescharacteristic, complemented
157C2×#328C2×C1311yescharacteristic, complemented
158C2×#327C2×C1311yescharacteristic, complemented
159#1438C2×C1311yescharacteristic, complemented
160#1280C2×C1311yescharacteristic, complemented
161C23×C13—21no—
162C23×C13—21no—
163C23×C13—22no—
164C23×C13—24no—
165C23×C13—44no—
166C23×C13—44no—
167C23×C13—42no—
168C23×C13—44no—
169C23×C13—44no—
170C23×C13—44no—
171C23×C13—44no—
172C23×C13—42no—
173C23×C13—44no—
174C23×C13—44no—
175C23×C13—41no—
176C23×C13—42no—
177C23×C13—41no—
178C23×C13—41no—
179C23×C13—42no—
180C23×C13—82no—
181C23×C13—82no—
182C23×C13—82no—
183C23×C13—82no—
184C23×C13—82no—
185C23×C13—82no—
186C23×C13—81no—
187C23×C13—81no—
188C23×C13—81no—
189C23×C13—81no—
190C23×C13#12011yescharacteristic
191C23×C13#12111yescharacteristic
192C23×C13#12711yescharacteristic
193C23×C13#13512yes—
194C23×C13AGL(1,ℤ/8)12yes—
195Q8×C13—42no—
196Q8×C13—81no—
197D4×C13—24no—
198D4×C13—24no—
199D4×C13—42no—
200D4×C13—42no—
201D4×C13—44no—
202D4×C13—44no—
203D4×C13—42no—
204D4×C13—81no—
205D4×C13—82no—
206D4×C13—81no—
207D4×C13—81no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—44no—
215C2×C4×C13—44no—
216C2×C4×C13—42no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—41no—
223C2×C4×C13—42no—
224C2×C4×C13—41no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—82no—
228C2×C4×C13—81no—
229C2×C4×C13—81no—
230C2×C4×C13—82no—
231C2×C4×C13#12011yescharacteristic
232C2×C4×C13#12011yescharacteristic
233C2×C4×C13#12111yescharacteristic
234C2×C4×C13#12111yescharacteristic
235C8×C13—42no—
236C8×C13—42no—
237C23×D4C22×C1311yescharacteristic
238C22×SD16—21no—
239C22×D8—21no—
240C2×C22⋊Q8C22×C1311yescharacteristic
241C2×#121C22×C1311yescharacteristic
242C22×C22⋊C4—22no—
243#450—22no—
244#450—22no—
245#447—22no—
246#447—22no—
247C2×#102—21no—
248C2×#102—21no—
249C2×C22⋊C8C22×C1311yescharacteristic
250C2×C22⋊C8C22×C1311yescharacteristic
251#400—21no—
252#397—21no—
253#394—21no—
254#393—21no—
255#386—22no—
256C2×#95C22×C1311yescharacteristic
257C2×#95C22×C1311yescharacteristic
258#328—22no—
259#327—22no—
260C22×C13—22no—
261C22×C13—22no—
262C22×C13—22no—
263C22×C13—22no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—21no—
268C22×C13—48no—
269C22×C13—44no—
270C22×C13—84no—
271C22×C13—84no—
272C22×C13—84no—
273C22×C13—84no—
274C22×C13—84no—
275C22×C13—82no—
276C22×C13—82no—
277C22×C13—82no—
278C22×C13—82no—
279C22×C13—81no—
280C22×C13—81no—
281C22×C13—81no—
282C22×C13#39211yescharacteristic
283C22×C13#44912yes—
284C22×C13#45311yescharacteristic
285C22×C13#45411yescharacteristic
286C22×C13B(4,𝔽2)12yes—
287C22×C13#46312yes—
288C22×C13#49511yescharacteristic
289C22×C13#49611yescharacteristic
290C4×C13—21no—
291C4×C13—21no—
292C4×C13—21no—
293C4×C13—21no—
294C4×C13—82no—
295C4×C13—82no—
296C4×C13—81no—
297C4×C13—81no—
298C4×C13—81no—
299C25—21no—
300C22×Q8D4×C1311yescharacteristic
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4—44no—
308C22×D4D4×C1311yescharacteristic
309C22×D4D4×C1312yes—
310C23×C4—21no—
311C23×C4D4×C1312yes—
312C23×C4C23×C1311yescharacteristic
313C2×SD16—24no—
314C2×SD16—44no—
315C2×D8—24no—
316C2×D8—44no—
317C22×C8—21no—
318C22×C8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4D4×C1311yescharacteristic
329C2×C4⋊C4D4×C1311yescharacteristic
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337#102—24no—
338#102—24no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8D4×C1312yes—
342C22⋊C8D4×C1312yes—
343#95—22no—
344#95—22no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349C2×C13—21no—
350C2×C13—22no—
351C2×C13—21no—
352C2×C13—84no—
353C2×C13—161no—
354C2×C13#159712yes—
355C2×C13#160012yes—
356C2×C13#200611yescharacteristic
357C2×C13#201211yescharacteristic
358C2×C13#202111yescharacteristic
359C24—24no—
360C24—22no—
361C24—21no—
362C24—42no—
363C24—42no—
364C24—42no—
365C24—41no—
366C24—41no—
367C24—42no—
368C24—42no—
369C24C2×D4×C1311yescharacteristic
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—42no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—42no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—44no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—41no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—42no—
406C22×C4C2×D4×C1311yescharacteristic
407C22×C4C2×D4×C1311yescharacteristic
408C22×C4C2×D4×C1311yescharacteristic
409C22×C4C2×D4×C1311yescharacteristic
410C22×C4C2×D4×C1311yescharacteristic
411C22×C4C13×#4111yescharacteristic
412SD16—48no—
413D8—48no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—42no—
417C2×C8—42no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C22⋊C4—416no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—82no—
430C22⋊C4—82no—
431C13#996311yescharacteristic, direct product factor, Sylow
432C23—21no—
433C23—21no—
434C23—22no—
435C23—24no—
436C23—44no—
437C23—44no—
438C23—42no—
439C23—44no—
440C23—44no—
441C23—44no—
442C23—44no—
443C23—42no—
444C23—44no—
445C23—44no—
446C23—41no—
447C23—42no—
448C23—41no—
449C23—41no—
450C23—42no—
451C23—82no—
452C23—82no—
453C23—82no—
454C23—82no—
455C23—82no—
456C23—82no—
457C23—81no—
458C23—81no—
459C23—81no—
460C23—81no—
461C23C13×#12011yescharacteristic
462C23C13×#12111yescharacteristic
463C23C13×#12711yescharacteristic
464C23C13×#13512yes—
465C23C13×AGL(1,ℤ/8)12yes—
466Q8—42no—
467Q8—81no—
468D4—24no—
469D4—24no—
470D4—42no—
471D4—42no—
472D4—44no—
473D4—44no—
474D4—42no—
475D4—81no—
476D4—82no—
477D4—81no—
478D4—81no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—81no—
499C2×C4—82no—
500C2×C4—81no—
501C2×C4—82no—
502C2×C4C13×#12011yescharacteristic
503C2×C4C13×#12011yescharacteristic
504C2×C4C13×#12111yescharacteristic
505C2×C4C13×#12111yescharacteristic
506C8—42no—
507C8—42no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—48no—
517C22—44no—
518C22—84no—
519C22—84no—
520C22—84no—
521C22—82no—
522C22—82no—
523C22—84no—
524C22—84no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—82no—
529C22—82no—
530C22C13×#39211yescharacteristic
531C22C13×#44912yes—
532C22C13×#45311yescharacteristic
533C22C13×#45411yescharacteristic
534C22C13×B(4,𝔽2)12yes—
535C22C13×#46312yes—
536C22C13×#49511yescharacteristic
537C22C13×#49611yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—82no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4—82no—
547C2—21no—
548C2—22no—
549C2—21no—
550C2—84no—
551C2—161no—
552C2C13×#159712yes—
553C2C13×#160012yes—
554C2C13×#200611yescharacteristic
555C2C13×#201211yescharacteristic
556C2C13×#202111yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#447C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#450C2semidirect
3. C13×#2639C2semidirect
4. C2×C13×#328C2semidirect
5. C2×C13×#327C2semidirect
6. C13×#1438C2semidirect
7. C13×#1280C2semidirect
81. #9963C13direct (N × H)
154. C2×#450C2×C13semidirect
156. #2639C2×C13semidirect
157. C2×#328C2×C13semidirect
158. C2×#327C2×C13semidirect
159. #1438C2×C13semidirect
160. #1280C2×C13semidirect
431. C13#9963direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4502
C2×C13×#4472
C13×#26392
C2×C13×#3282
C2×C13×#3272
C13×#14382
C13×#12802
#996313