Finite Group Databasebeta

← C13×#9445 #15695784

Subgroups — C13×#9445 #15695784

Order 3328.

770 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2879C211yesmaximal, characteristic, complemented
2C13×#2431C211yesmaximal, characteristic
3C13×#1782C211yesmaximal, characteristic, complemented
4C13×#1510C212yesmaximal, complemented
5C13×#1284C212yesmaximal, complemented
6C22×C13×#41C2211yescharacteristic
7C22×C13×M16—21no—
8C2×C13×#127C411yescharacteristic, complemented
9C2×C13×#124C411yescharacteristic, complemented
10C2×C13×#121C2211yescharacteristic
11C2×C13×#99—21no—
12C2×C13×#99—21no—
13C13×#408—24no—
14C13×#407—21no—
15C13×#407C2212yes—
16C13×#392—21no—
17C13×#392—21no—
18C13×#391C411yescharacteristic, complemented
19C13×#390C411yescharacteristic, complemented
20C13×#386—21no—
21C13×#386—21no—
22C13×#381C2212yes—
23C4×C13×C22⋊C4C2211yescharacteristic
24C13×#327—24no—
25C2×C13×#41—22no—
26C2×C13×#41—22no—
27C2×C13×#41—42no—
28C2×C13×#41—42no—
29C22×Q8×C13C2×C411yescharacteristic
30C22×D4×C13—21no—
31C22×D4×C13—21no—
32C22×D4×C13—21no—
33C22×D4×C13C2×C411yescharacteristic
34C22×D4×C13C2×C411yescharacteristic
35C22×D4×C13D411yescharacteristic
36C22×D4×C13D411yescharacteristic
37C23×C4×C13D411yescharacteristic
38C23×C4×C13D411yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C2×C13×M16—22no—
41C2×C13×M16—22no—
42C2×C13×M16—42no—
43C2×C13×M16—42no—
44C22×C8×C13—22no—
45C13×#127—42no—
46C13×#124—42no—
47C13×#121—22no—
48C13×#121—22no—
49C2×C13×C4⋊C4C2×C411yescharacteristic
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—22no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C42×C13C2×C411yescharacteristic
58C2×C42×C13C2×C411yescharacteristic
59C13×#99—42no—
60C13×#99—42no—
61C13×C22⋊C8—24no—
62C13×C22⋊C8—22no—
63C13×C22⋊C8D414yescomplemented
64C13×#95—21no—
65C13×#95—21no—
66C13×#95—21no—
67C13×#95—22no—
68C13×#95—22no—
69#9445C1311yesmaximal, characteristic, direct product factor, Sylow
70C24×C13—21no—
71C24×C13C22⋊C411yescharacteristic
72C24×C13C22⋊C411yescharacteristic
73C24×C13C2×D411yescharacteristic
74C13×#41—44no—
75C13×#41—44no—
76C13×#41—48no—
77C2×Q8×C13—22no—
78C2×Q8×C13—22no—
79C2×Q8×C13—41no—
80C2×D4×C13—22no—
81C2×D4×C13—22no—
82C2×D4×C13—22no—
83C2×D4×C13—22no—
84C2×D4×C13—22no—
85C2×D4×C13—22no—
86C2×D4×C13—22no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13—42no—
93C2×D4×C13—42no—
94C2×D4×C13—42no—
95C2×D4×C13—42no—
96C2×D4×C13—42no—
97C2×D4×C13—81no—
98C2×D4×C13—81no—
99C2×D4×C13—81no—
100C2×D4×C13—81no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—41no—
111C22×C4×C13—41no—
112C22×C4×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13—42no—
115C22×C4×C13C22⋊C411yescharacteristic
116C22×C4×C13C22⋊C411yescharacteristic
117C22×C4×C13C22×C411yescharacteristic
118C22×C4×C13C2×D411yescharacteristic
119C22×C4×C13C2×D412yes—
120C22×C4×C13#4112yes—
121C13×M16—44no—
122C13×M16—42no—
123C13×M16—42no—
124C2×C8×C13—24no—
125C2×C8×C13—44no—
126C13×C4⋊C4—22no—
127C13×C22⋊C4—42no—
128C13×C22⋊C4—42no—
129C13×C22⋊C4—42no—
130C13×C22⋊C4—41no—
131C13×C22⋊C4—41no—
132C13×C22⋊C4—42no—
133C13×C22⋊C4—42no—
134C13×C22⋊C4—81no—
135C13×C22⋊C4—81no—
136C42×C13—41no—
137C42×C13—41no—
138#2879C2×C1311yescharacteristic, complemented
139#2431C2×C1311yescharacteristic
140#1782C2×C1311yescharacteristic, complemented
141#1510C2×C1312yescomplemented
142#1284C2×C1312yescomplemented
143C23×C13—21no—
144C23×C13—21no—
145C23×C13—21no—
146C23×C13—21no—
147C23×C13—21no—
148C23×C13—21no—
149C23×C13—21no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13—41no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13—41no—
156C23×C13—41no—
157C23×C13—41no—
158C23×C13—41no—
159C23×C13—41no—
160C23×C13—41no—
161C23×C13—41no—
162C23×C13—41no—
163C23×C13#9912yes—
164C23×C13C2×C22⋊C411yescharacteristic
165C23×C13#12112yes—
166Q8×C13—44no—
167D4×C13—44no—
168D4×C13—44no—
169D4×C13—44no—
170D4×C13—82no—
171D4×C13—84no—
172D4×C13—84no—
173D4×C13—84no—
174C2×C4×C13—22no—
175C2×C4×C13—22no—
176C2×C4×C13—24no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—21no—
181C2×C4×C13—21no—
182C2×C4×C13—21no—
183C2×C4×C13—22no—
184C2×C4×C13—21no—
185C2×C4×C13—21no—
186C2×C4×C13—21no—
187C2×C4×C13—42no—
188C2×C4×C13—42no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13—41no—
199C2×C4×C13—82no—
200C2×C4×C13—82no—
201C2×C4×C13—82no—
202C2×C4×C13#9912yes—
203C2×C4×C13C4×D412yes—
204C2×C4×C13#12011yescharacteristic
205C2×C4×C13#12311yescharacteristic
206C8×C13—44no—
207C22×#41C22×C1311yescharacteristic
208C22×M16—21no—
209C2×#127C4×C1311yescharacteristic, complemented
210C2×#124C4×C1311yescharacteristic, complemented
211C2×#121C22×C1311yescharacteristic
212C2×#99—21no—
213C2×#99—21no—
214#408—24no—
215#407—21no—
216#407C22×C1312yes—
217#392—21no—
218#392—21no—
219#391C4×C1311yescharacteristic, complemented
220#390C4×C1311yescharacteristic, complemented
221#386—21no—
222#386—21no—
223#381C22×C1312yes—
224C4×C22⋊C4C22×C1311yescharacteristic
225#327—24no—
226C22×C13—21no—
227C22×C13—21no—
228C22×C13—22no—
229C22×C13—22no—
230C22×C13—22no—
231C22×C13—22no—
232C22×C13—42no—
233C22×C13—42no—
234C22×C13—41no—
235C22×C13—41no—
236C22×C13—41no—
237C22×C13—41no—
238C22×C13—41no—
239C22×C13—81no—
240C22×C13—81no—
241C22×C13—81no—
242C22×C13—81no—
243C22×C13—81no—
244C22×C13—81no—
245C22×C13—81no—
246C22×C13—81no—
247C22×C13—81no—
248C22×C13—81no—
249C22×C13—81no—
250C22×C13#38611yescharacteristic
251C22×C13C2×#9911yescharacteristic
252C22×C13C2×#9911yescharacteristic
253C4×C13—21no—
254C4×C13—21no—
255C4×C13—22no—
256C4×C13—22no—
257C4×C13—42no—
258C4×C13—41no—
259C4×C13—81no—
260C4×C13—81no—
261C4×C13—162no—
262C2×#41—22no—
263C2×#41—22no—
264C2×#41—42no—
265C2×#41—42no—
266C22×Q8C2×C4×C1311yescharacteristic
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4C2×C4×C1311yescharacteristic
271C22×D4C2×C4×C1311yescharacteristic
272C22×D4D4×C1311yescharacteristic
273C22×D4D4×C1311yescharacteristic
274C23×C4D4×C1311yescharacteristic
275C23×C4D4×C1311yescharacteristic
276C23×C4C23×C1311yescharacteristic
277C2×M16—22no—
278C2×M16—22no—
279C2×M16—42no—
280C2×M16—42no—
281C22×C8—22no—
282#127—42no—
283#124—42no—
284#121—22no—
285#121—22no—
286C2×C4⋊C4C2×C4×C1311yescharacteristic
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C42C2×C4×C1311yescharacteristic
295C2×C42C2×C4×C1311yescharacteristic
296#99—42no—
297#99—42no—
298C22⋊C8—24no—
299C22⋊C8—22no—
300C22⋊C8D4×C1314yescomplemented
301#95—21no—
302#95—21no—
303#95—21no—
304#95—22no—
305#95—22no—
306C2×C13—21no—
307C2×C13—21no—
308C2×C13—42no—
309C2×C13—42no—
310C2×C13—81no—
311C2×C13—161no—
312C2×C13#188411yescharacteristic
313C2×C13#189811yescharacteristic
314C2×C13#191011yescharacteristic
315C24—21no—
316C24C13×C22⋊C411yescharacteristic
317C24C13×C22⋊C411yescharacteristic
318C24C2×D4×C1311yescharacteristic
319#41—44no—
320#41—44no—
321#41—48no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—41no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—42no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—42no—
342C2×D4—81no—
343C2×D4—81no—
344C2×D4—81no—
345C2×D4—81no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—42no—
360C22×C4C13×C22⋊C411yescharacteristic
361C22×C4C13×C22⋊C411yescharacteristic
362C22×C4C22×C4×C1311yescharacteristic
363C22×C4C2×D4×C1311yescharacteristic
364C22×C4C2×D4×C1312yes—
365C22×C4C13×#4112yes—
366M16—44no—
367M16—42no—
368M16—42no—
369C2×C8—24no—
370C2×C8—44no—
371C4⋊C4—22no—
372C22⋊C4—42no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—42no—
378C22⋊C4—42no—
379C22⋊C4—81no—
380C22⋊C4—81no—
381C42—41no—
382C42—41no—
383C13#944511yescharacteristic, direct product factor, Sylow
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23C13×#9912yes—
405C23C2×C13×C22⋊C411yescharacteristic
406C23C13×#12112yes—
407Q8—44no—
408D4—44no—
409D4—44no—
410D4—44no—
411D4—82no—
412D4—84no—
413D4—84no—
414D4—84no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4C13×#9912yes—
444C2×C4C4×D4×C1312yes—
445C2×C4C13×#12011yescharacteristic
446C2×C4C13×#12311yescharacteristic
447C8—44no—
448C22—21no—
449C22—21no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—42no—
455C22—42no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22C13×#38611yescharacteristic
473C22C2×C13×#9911yescharacteristic
474C22C2×C13×#9911yescharacteristic
475C4—21no—
476C4—21no—
477C4—22no—
478C4—22no—
479C4—42no—
480C4—41no—
481C4—81no—
482C4—81no—
483C4—162no—
484C2—21no—
485C2—21no—
486C2—42no—
487C2—42no—
488C2—81no—
489C2—161no—
490C2C13×#188411yescharacteristic
491C2C13×#189811yescharacteristic
492C2C13×#191011yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC13×#2431C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2879C2semidirect
3. C13×#1782C2semidirect
4. C13×#1510C2semidirect
5. C13×#1284C2semidirect
8. C2×C13×#127C4semidirect
9. C2×C13×#124C4semidirect
18. C13×#391C4semidirect
19. C13×#390C4semidirect
63. C13×C22⋊C8D4semidirect
69. #9445C13direct (N × H)
138. #2879C2×C13semidirect
140. #1782C2×C13semidirect
141. #1510C2×C13semidirect
142. #1284C2×C13semidirect
209. C2×#127C4×C13semidirect
210. C2×#124C4×C13semidirect
219. #391C4×C13semidirect
220. #390C4×C13semidirect
300. C22⋊C8D4×C13semidirect
383. C13#9445direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28792
C13×#24312
C13×#17822
C13×#15102
C13×#12842
#944513