Finite Group Databasebeta

← C13×#9924 #15696263

Subgroups — C13×#9924 #15696263

Order 3328.

890 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#451C211yesmaximal, characteristic, complemented
2C13×#2626C211yesmaximal, characteristic
3C2×C13×#393C211yesmaximal, characteristic
4C13×#1787C211yesmaximal, characteristic, complemented
5C2×C13×#328C211yesmaximal, characteristic, complemented
6C2×C13×#323C211yesmaximal, characteristic
7C13×#1294C211yesmaximal, characteristic, complemented
8C23×Q8×C13C2211yescharacteristic
9C22×C13×Q16—21no—
10C2×C13×C22⋊Q8C2211yescharacteristic
11C22×C13×C22⋊C4—21no—
12C22×C13×C22⋊C4C2211yescharacteristic
13C13×#451—22no—
14C13×#451—22no—
15C2×C13×#103—21no—
16C2×C13×#103—22no—
17C2×C13×C22⋊C8C2211yescharacteristic
18C2×C13×C22⋊C8C2211yescharacteristic
19C13×#399—21no—
20C13×#396—22no—
21C13×#393—21no—
22C13×#393—22no—
23C13×#393—22no—
24C13×#385—21no—
25C13×#380C2211yescharacteristic
26C13×#379—21no—
27C2×C13×#95—21no—
28C2×C13×#95C2211yescharacteristic
29C13×#328—22no—
30C13×#323—22no—
31C25×C13D411yescharacteristic
32C22×Q8×C13—21no—
33C22×Q8×C13—21no—
34C22×Q8×C13—21no—
35C22×Q8×C13—21no—
36C22×Q8×C13—21no—
37C22×Q8×C13—44no—
38C22×Q8×C13D412yes—
39C22×Q8×C13D411yescharacteristic
40C23×C4×C13—21no—
41C23×C4×C13—21no—
42C23×C4×C13D411yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C2×C13×Q16—24no—
45C2×C13×Q16—44no—
46C22×C8×C13—21no—
47C22×C8×C13—21no—
48C13×C22⋊Q8—21no—
49C13×C22⋊Q8—21no—
50C13×C22⋊Q8—21no—
51C13×C22⋊Q8—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4D411yescharacteristic
55C2×C13×C4⋊C4D412yes—
56C2×C13×C22⋊C4—24no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4—21no—
65C2×C13×C22⋊C4—22no—
66C2×C13×C22⋊C4—22no—
67C2×C13×C22⋊C4—44no—
68C13×#103—24no—
69C13×#103—44no—
70C13×C22⋊C8—21no—
71C13×C22⋊C8—21no—
72C13×C22⋊C8—21no—
73C13×C22⋊C8D412yes—
74C13×#95—22no—
75C13×#95—24no—
76C13×#95—21no—
77C13×#95—21no—
78C13×#95D412yes—
79#9924C1311yesmaximal, characteristic, direct product factor, Sylow
80C24×C13—21no—
81C24×C13—21no—
82C24×C13—21no—
83C24×C13—21no—
84C24×C13—21no—
85C24×C13—21no—
86C24×C13—42no—
87C24×C13—42no—
88C24×C13Q1612yescomplemented
89C24×C13C2×D411yescharacteristic
90C2×Q8×C13—24no—
91C2×Q8×C13—24no—
92C2×Q8×C13—22no—
93C2×Q8×C13—21no—
94C2×Q8×C13—22no—
95C2×Q8×C13—21no—
96C2×Q8×C13—44no—
97C2×Q8×C13—42no—
98C2×Q8×C13—42no—
99C2×Q8×C13—44no—
100C2×Q8×C13—42no—
101C2×Q8×C13—44no—
102C2×Q8×C13—44no—
103C2×Q8×C13—41no—
104C2×Q8×C13—41no—
105C22×C4×C13—24no—
106C22×C4×C13—22no—
107C22×C4×C13—21no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—42no—
115C22×C4×C13—42no—
116C22×C4×C13—41no—
117C22×C4×C13—41no—
118C22×C4×C13—42no—
119C22×C4×C13—42no—
120C22×C4×C13—42no—
121C22×C4×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13#4111yescharacteristic
129C13×Q16—48no—
130C2×C8×C13—22no—
131C2×C8×C13—42no—
132C2×C8×C13—42no—
133C2×C8×C13—41no—
134C13×C4⋊C4—21no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—42no—
137C13×C4⋊C4—41no—
138C13×C4⋊C4—41no—
139C13×C4⋊C4—82no—
140C13×C22⋊C4—48no—
141C13×C22⋊C4—41no—
142C13×C22⋊C4—41no—
143C13×C22⋊C4—41no—
144C13×C22⋊C4—41no—
145C13×C22⋊C4—41no—
146C13×C22⋊C4—41no—
147C13×C22⋊C4—41no—
148C13×C22⋊C4—41no—
149C13×C22⋊C4—82no—
150C13×C22⋊C4—82no—
151C2×#451C2×C1311yescharacteristic, complemented
152#2626C2×C1311yescharacteristic
153C2×#393C2×C1311yescharacteristic
154#1787C2×C1311yescharacteristic, complemented
155C2×#328C2×C1311yescharacteristic, complemented
156C2×#323C2×C1311yescharacteristic
157#1294C2×C1311yescharacteristic, complemented
158C23×C13—22no—
159C23×C13—22no—
160C23×C13—22no—
161C23×C13—22no—
162C23×C13—22no—
163C23×C13—44no—
164C23×C13—42no—
165C23×C13—44no—
166C23×C13—42no—
167C23×C13—41no—
168C23×C13—41no—
169C23×C13—41no—
170C23×C13—42no—
171C23×C13—42no—
172C23×C13—41no—
173C23×C13—82no—
174C23×C13—82no—
175C23×C13—81no—
176C23×C13—81no—
177C23×C13#12011yescharacteristic
178C23×C13#12011yescharacteristic
179C23×C13#12111yescharacteristic
180C23×C13C2×Q1611yescharacteristic
181C23×C13#13511yescharacteristic
182C23×C13#13711yescharacteristic
183C23×C13#13711yescharacteristic
184Q8×C13—24no—
185Q8×C13—24no—
186Q8×C13—42no—
187Q8×C13—44no—
188Q8×C13—42no—
189Q8×C13—44no—
190Q8×C13—42no—
191Q8×C13—81no—
192C2×C4×C13—22no—
193C2×C4×C13—22no—
194C2×C4×C13—24no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—41no—
199C2×C4×C13—42no—
200C2×C4×C13—44no—
201C2×C4×C13—42no—
202C2×C4×C13—44no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13—42no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—42no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—82no—
217C2×C4×C13—82no—
218C2×C4×C13—81no—
219C2×C4×C13#12011yescharacteristic
220C2×C4×C13#12111yescharacteristic
221C2×C4×C13#12111yescharacteristic
222C2×C4×C13#12711yescharacteristic
223C8×C13—42no—
224C8×C13—81no—
225C23×Q8C22×C1311yescharacteristic
226C22×Q16—21no—
227C2×C22⋊Q8C22×C1311yescharacteristic
228C22×C22⋊C4—21no—
229C22×C22⋊C4C22×C1311yescharacteristic
230#451—22no—
231#451—22no—
232C2×#103—21no—
233C2×#103—22no—
234C2×C22⋊C8C22×C1311yescharacteristic
235C2×C22⋊C8C22×C1311yescharacteristic
236#399—21no—
237#396—22no—
238#393—21no—
239#393—22no—
240#393—22no—
241#385—21no—
242#380C22×C1311yescharacteristic
243#379—21no—
244C2×#95—21no—
245C2×#95C22×C1311yescharacteristic
246#328—22no—
247#323—22no—
248C22×C13—22no—
249C22×C13—22no—
250C22×C13—22no—
251C22×C13—22no—
252C22×C13—21no—
253C22×C13—21no—
254C22×C13—21no—
255C22×C13—21no—
256C22×C13—44no—
257C22×C13—44no—
258C22×C13—42no—
259C22×C13—82no—
260C22×C13—82no—
261C22×C13—82no—
262C22×C13—82no—
263C22×C13—81no—
264C22×C13—81no—
265C22×C13#39211yescharacteristic
266C22×C13#45111yescharacteristic
267C22×C13#45111yescharacteristic
268C22×C13#45211yescharacteristic
269C22×C13#45211yescharacteristic
270C22×C13#45512yes—
271C22×C13B(4,𝔽2)12yes—
272C22×C13#46711yescharacteristic
273C22×C13#47011yescharacteristic
274C4×C13—21no—
275C4×C13—21no—
276C4×C13—21no—
277C4×C13—21no—
278C4×C13—44no—
279C4×C13—82no—
280C4×C13—82no—
281C4×C13—81no—
282C4×C13—81no—
283C4×C13—81no—
284C25D4×C1311yescharacteristic
285C22×Q8—21no—
286C22×Q8—21no—
287C22×Q8—21no—
288C22×Q8—21no—
289C22×Q8—21no—
290C22×Q8—44no—
291C22×Q8D4×C1311yescharacteristic
292C22×Q8D4×C1312yes—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4D4×C1311yescharacteristic
296C23×C4C23×C1311yescharacteristic
297C2×Q16—24no—
298C2×Q16—44no—
299C22×C8—21no—
300C22×C8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4D4×C1311yescharacteristic
308C2×C4⋊C4D4×C1312yes—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—44no—
321#103—24no—
322#103—44no—
323C22⋊C8—21no—
324C22⋊C8—21no—
325C22⋊C8—21no—
326C22⋊C8D4×C1312yes—
327#95—24no—
328#95—22no—
329#95—21no—
330#95—21no—
331#95D4×C1312yes—
332C2×C13—21no—
333C2×C13—21no—
334C2×C13—21no—
335C2×C13—21no—
336C2×C13—82no—
337C2×C13#160212yes—
338C2×C13#160612yes—
339C2×C13#200111yescharacteristic
340C2×C13#200411yescharacteristic
341C2×C13#202111yescharacteristic
342C24—21no—
343C24—21no—
344C24—21no—
345C24—21no—
346C24—21no—
347C24—21no—
348C24—42no—
349C24—42no—
350C24C13×Q1612yescomplemented
351C24C2×D4×C1311yescharacteristic
352C2×Q8—24no—
353C2×Q8—24no—
354C2×Q8—22no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—21no—
358C2×Q8—44no—
359C2×Q8—42no—
360C2×Q8—42no—
361C2×Q8—44no—
362C2×Q8—42no—
363C2×Q8—44no—
364C2×Q8—44no—
365C2×Q8—41no—
366C2×Q8—41no—
367C22×C4—24no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4C2×D4×C1311yescharacteristic
386C22×C4C2×D4×C1311yescharacteristic
387C22×C4C2×D4×C1311yescharacteristic
388C22×C4C2×D4×C1311yescharacteristic
389C22×C4C2×D4×C1311yescharacteristic
390C22×C4C13×#4111yescharacteristic
391Q16—48no—
392C2×C8—22no—
393C2×C8—42no—
394C2×C8—42no—
395C2×C8—41no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—42no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—82no—
402C22⋊C4—48no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—82no—
412C22⋊C4—82no—
413C13#992411yescharacteristic, direct product factor, Sylow
414C23—22no—
415C23—22no—
416C23—22no—
417C23—22no—
418C23—22no—
419C23—44no—
420C23—42no—
421C23—42no—
422C23—44no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—42no—
427C23—42no—
428C23—41no—
429C23—82no—
430C23—81no—
431C23—81no—
432C23—82no—
433C23C13×#12011yescharacteristic
434C23C13×#12011yescharacteristic
435C23C13×#12111yescharacteristic
436C23C2×C13×Q1611yescharacteristic
437C23C13×#13511yescharacteristic
438C23C13×#13711yescharacteristic
439C23C13×#13711yescharacteristic
440Q8—24no—
441Q8—24no—
442Q8—42no—
443Q8—44no—
444Q8—42no—
445Q8—44no—
446Q8—42no—
447Q8—81no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—44no—
457C2×C4—42no—
458C2×C4—44no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—82no—
473C2×C4—82no—
474C2×C4—81no—
475C2×C4C13×#12011yescharacteristic
476C2×C4C13×#12111yescharacteristic
477C2×C4C13×#12111yescharacteristic
478C2×C4C13×#12711yescharacteristic
479C8—42no—
480C8—81no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—44no—
490C22—42no—
491C22—44no—
492C22—82no—
493C22—82no—
494C22—82no—
495C22—81no—
496C22—81no—
497C22—82no—
498C22C13×#39211yescharacteristic
499C22C13×#45111yescharacteristic
500C22C13×#45111yescharacteristic
501C22C13×#45211yescharacteristic
502C22C13×#45211yescharacteristic
503C22C13×#45512yes—
504C22C13×B(4,𝔽2)12yes—
505C22C13×#46711yescharacteristic
506C22C13×#47011yescharacteristic
507C4—21no—
508C4—21no—
509C4—21no—
510C4—21no—
511C4—44no—
512C4—82no—
513C4—81no—
514C4—81no—
515C4—81no—
516C4—82no—
517C2—21no—
518C2—21no—
519C2—21no—
520C2—21no—
521C2—82no—
522C2C13×#160212yes—
523C2C13×#160612yes—
524C2C13×#200111yescharacteristic
525C2C13×#200411yescharacteristic
526C2C13×#202111yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC25×C13D4
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×#451C2semidirect
4. C13×#1787C2semidirect
5. C2×C13×#328C2semidirect
7. C13×#1294C2semidirect
79. #9924C13direct (N × H)
88. C24×C13Q16semidirect
151. C2×#451C2×C13semidirect
154. #1787C2×C13semidirect
155. C2×#328C2×C13semidirect
157. #1294C2×C13semidirect
350. C24C13×Q16semidirect
413. C13#9924direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4512
C13×#26262
C2×C13×#3932
C13×#17872
C2×C13×#3282
C2×C13×#3232
C13×#12942
#992413