Finite Group Databasebeta

← C13×#9965 #15696304

Subgroups — C13×#9965 #15696304

Order 3328.

830 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
1C2×C13×#451C211yesmaximal, characteristic, complemented
2C2×C13×#448C211yesmaximal, characteristic
3C13×#2639C211yesmaximal, characteristic
4C2×C13×#328C211yesmaximal, characteristic, complemented
5C2×C13×#327C211yesmaximal, characteristic
6C13×#1446C211yesmaximal, characteristic, complemented
7C13×#1280C211yesmaximal, characteristic, complemented
8C23×Q8×C13C2211yescharacteristic
9C22×C13×Q16—21no—
10C22×C13×SD16—21no—
11C2×C13×C22⋊Q8C2211yescharacteristic
12C2×C13×#121C2211yescharacteristic
13C13×#451—22no—
14C13×#451—22no—
15C13×#448—22no—
16C13×#448—22no—
17C2×C13×#103—21no—
18C2×C13×#103—21no—
19C2×C13×C22⋊C8C2211yescharacteristic
20C2×C13×C22⋊C8C2211yescharacteristic
21C13×#400—21no—
22C13×#397—21no—
23C13×#394—21no—
24C13×#393—21no—
25C13×#386—22no—
26C2×C13×#95—22no—
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29C13×#328—22no—
30C13×#327—22no—
31C22×Q8×C13—21no—
32C22×Q8×C13—21no—
33C22×Q8×C13—21no—
34C22×Q8×C13—21no—
35C22×Q8×C13—21no—
36C22×Q8×C13—44no—
37C22×Q8×C13D411yescharacteristic
38C22×Q8×C13D412yes—
39C22×D4×C13—21no—
40C22×D4×C13D411yescharacteristic
41C23×C4×C13—21no—
42C23×C4×C13—21no—
43C23×C4×C13D412yes—
44C23×C4×C13C2311yescharacteristic
45C2×C13×Q16—24no—
46C2×C13×Q16—44no—
47C2×C13×SD16—24no—
48C2×C13×SD16—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—
66C13×#103—24no—
67C13×#103—24no—
68C13×C22⋊C8—21no—
69C13×C22⋊C8—21no—
70C13×C22⋊C8D412yes—
71C13×C22⋊C8D412yes—
72C13×#95—22no—
73C13×#95—22no—
74C13×#95—21no—
75C13×#95—21no—
76C13×#95—21no—
77C13×#95—21no—
78C13×#95—44no—
79#9965C1311yesmaximal, characteristic, direct product factor, Sylow
80C24×C13—21no—
81C24×C13C2×D411yescharacteristic
82C2×Q8×C13—24no—
83C2×Q8×C13—24no—
84C2×Q8×C13—22no—
85C2×Q8×C13—22no—
86C2×Q8×C13—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13—44no—
89C2×Q8×C13—42no—
90C2×Q8×C13—42no—
91C2×Q8×C13—44no—
92C2×Q8×C13—42no—
93C2×Q8×C13—44no—
94C2×Q8×C13—44no—
95C2×Q8×C13—41no—
96C2×Q8×C13—41no—
97C2×D4×C13—21no—
98C2×D4×C13—21no—
99C2×D4×C13—42no—
100C2×D4×C13—41no—
101C2×D4×C13—41no—
102C2×D4×C13—42no—
103C2×D4×C13—42no—
104C22×C4×C13—24no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—42no—
114C22×C4×C13—42no—
115C22×C4×C13—41no—
116C22×C4×C13—41no—
117C22×C4×C13—42no—
118C22×C4×C13—42no—
119C22×C4×C13—42no—
120C22×C4×C13—41no—
121C22×C4×C13—41no—
122C22×C4×C13—42no—
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—
130C13×SD16—48no—
131C2×C8×C13—22no—
132C2×C8×C13—22no—
133C2×C8×C13—42no—
134C2×C8×C13—42no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—41no—
140C13×C4⋊C4—41no—
141C13×C22⋊C4—41no—
142C13×C22⋊C4—41no—
143C13×C22⋊C4—41no—
144C13×C22⋊C4—41no—
145C13×C22⋊C4—82no—
146C13×C22⋊C4—82no—
147C2×#451C2×C1311yescharacteristic, complemented
148C2×#448C2×C1311yescharacteristic
149#2639C2×C1311yescharacteristic
150C2×#328C2×C1311yescharacteristic, complemented
151C2×#327C2×C1311yescharacteristic
152#1446C2×C1311yescharacteristic, complemented
153#1280C2×C1311yescharacteristic, complemented
154C23×C13—21no—
155C23×C13—21no—
156C23×C13—22no—
157C23×C13—41no—
158C23×C13—42no—
159C23×C13—41no—
160C23×C13—41no—
161C23×C13—42no—
162C23×C13#12011yescharacteristic
163C23×C13#12111yescharacteristic
164C23×C13#12711yescharacteristic
165C23×C13#13512yes—
166C23×C13#13712yes—
167Q8×C13—24no—
168Q8×C13—24no—
169Q8×C13—42no—
170Q8×C13—42no—
171Q8×C13—44no—
172Q8×C13—44no—
173Q8×C13—42no—
174Q8×C13—81no—
175D4×C13—42no—
176D4×C13—81no—
177D4×C13—82no—
178D4×C13—81no—
179D4×C13—81no—
180C2×C4×C13—22no—
181C2×C4×C13—22no—
182C2×C4×C13—24no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—42no—
188C2×C4×C13—44no—
189C2×C4×C13—42no—
190C2×C4×C13—44no—
191C2×C4×C13—44no—
192C2×C4×C13—42no—
193C2×C4×C13—44no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—42no—
198C2×C4×C13—42no—
199C2×C4×C13—41no—
200C2×C4×C13—42no—
201C2×C4×C13—41no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—82no—
205C2×C4×C13—81no—
206C2×C4×C13—81no—
207C2×C4×C13—82no—
208C2×C4×C13#12011yescharacteristic
209C2×C4×C13#12011yescharacteristic
210C2×C4×C13#12111yescharacteristic
211C2×C4×C13#12111yescharacteristic
212C8×C13—42no—
213C8×C13—42no—
214C23×Q8C22×C1311yescharacteristic
215C22×Q16—21no—
216C22×SD16—21no—
217C2×C22⋊Q8C22×C1311yescharacteristic
218C2×#121C22×C1311yescharacteristic
219#451—22no—
220#451—22no—
221#448—22no—
222#448—22no—
223C2×#103—21no—
224C2×#103—21no—
225C2×C22⋊C8C22×C1311yescharacteristic
226C2×C22⋊C8C22×C1311yescharacteristic
227#400—21no—
228#397—21no—
229#394—21no—
230#393—21no—
231#386—22no—
232C2×#95—22no—
233C2×#95C22×C1311yescharacteristic
234C2×#95C22×C1311yescharacteristic
235#328—22no—
236#327—22no—
237C22×C13—22no—
238C22×C13—22no—
239C22×C13—22no—
240C22×C13—22no—
241C22×C13—21no—
242C22×C13—21no—
243C22×C13—21no—
244C22×C13—21no—
245C22×C13—82no—
246C22×C13—82no—
247C22×C13—81no—
248C22×C13—81no—
249C22×C13—81no—
250C22×C13#39211yescharacteristic
251C22×C13#45212yes—
252C22×C13#45511yescharacteristic
253C22×C13#45611yescharacteristic
254C22×C13B(4,𝔽2)12yes—
255C22×C13#46412yes—
256C22×C13#49511yescharacteristic
257C22×C13#49711yescharacteristic
258C4×C13—21no—
259C4×C13—21no—
260C4×C13—21no—
261C4×C13—21no—
262C4×C13—44no—
263C4×C13—82no—
264C4×C13—82no—
265C4×C13—81no—
266C4×C13—81no—
267C4×C13—81no—
268C22×Q8—21no—
269C22×Q8—21no—
270C22×Q8—21no—
271C22×Q8—21no—
272C22×Q8—21no—
273C22×Q8—44no—
274C22×Q8D4×C1311yescharacteristic
275C22×Q8D4×C1312yes—
276C22×D4—21no—
277C22×D4D4×C1311yescharacteristic
278C23×C4—21no—
279C23×C4—21no—
280C23×C4D4×C1312yes—
281C23×C4C23×C1311yescharacteristic
282C2×Q16—24no—
283C2×Q16—44no—
284C2×SD16—24no—
285C2×SD16—44no—
286C22×C8—21no—
287C22×C8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292#121—21no—
293#121—21no—
294#121—21no—
295#121—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4D4×C1311yescharacteristic
298C2×C4⋊C4D4×C1311yescharacteristic
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303#103—24no—
304#103—24no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8D4×C1312yes—
308C22⋊C8D4×C1312yes—
309#95—22no—
310#95—22no—
311#95—21no—
312#95—21no—
313#95—21no—
314#95—21no—
315#95—44no—
316C2×C13—21no—
317C2×C13—22no—
318C2×C13—21no—
319C2×C13—161no—
320C2×C13#160312yes—
321C2×C13#160612yes—
322C2×C13#200711yescharacteristic
323C2×C13#201511yescharacteristic
324C2×C13#202111yescharacteristic
325C24—21no—
326C24C2×D4×C1311yescharacteristic
327C2×Q8—24no—
328C2×Q8—24no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—44no—
334C2×Q8—42no—
335C2×Q8—42no—
336C2×Q8—44no—
337C2×Q8—42no—
338C2×Q8—44no—
339C2×Q8—44no—
340C2×Q8—41no—
341C2×Q8—41no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—42no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—42no—
348C2×D4—42no—
349C22×C4—24no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—42no—
368C22×C4C2×D4×C1311yescharacteristic
369C22×C4C2×D4×C1311yescharacteristic
370C22×C4C2×D4×C1311yescharacteristic
371C22×C4C2×D4×C1311yescharacteristic
372C22×C4C2×D4×C1311yescharacteristic
373C22×C4C13×#4111yescharacteristic
374Q16—48no—
375SD16—48no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—42no—
379C2×C8—42no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—82no—
391C22⋊C4—82no—
392C13#996511yescharacteristic, direct product factor, Sylow
393C23—21no—
394C23—21no—
395C23—22no—
396C23—41no—
397C23—42no—
398C23—41no—
399C23—41no—
400C23—42no—
401C23C13×#12011yescharacteristic
402C23C13×#12111yescharacteristic
403C23C13×#12711yescharacteristic
404C23C13×#13512yes—
405C23C13×#13712yes—
406Q8—24no—
407Q8—24no—
408Q8—42no—
409Q8—42no—
410Q8—44no—
411Q8—44no—
412Q8—42no—
413Q8—81no—
414D4—42no—
415D4—81no—
416D4—82no—
417D4—81no—
418D4—81no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—44no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—81no—
444C2×C4—82no—
445C2×C4—81no—
446C2×C4—82no—
447C2×C4C13×#12011yescharacteristic
448C2×C4C13×#12011yescharacteristic
449C2×C4C13×#12111yescharacteristic
450C2×C4C13×#12111yescharacteristic
451C8—42no—
452C8—42no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—82no—
465C22—82no—
466C22C13×#39211yescharacteristic
467C22C13×#45212yes—
468C22C13×#45511yescharacteristic
469C22C13×#45611yescharacteristic
470C22C13×B(4,𝔽2)12yes—
471C22C13×#46412yes—
472C22C13×#49511yescharacteristic
473C22C13×#49711yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—44no—
479C4—82no—
480C4—81no—
481C4—81no—
482C4—81no—
483C4—82no—
484C2—21no—
485C2—22no—
486C2—21no—
487C2—161no—
488C2C13×#160312yes—
489C2C13×#160612yes—
490C2C13×#200711yescharacteristic
491C2C13×#201511yescharacteristic
492C2C13×#202111yescharacteristic
subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC23×C4C23×C13
prime radicalC2×C13×#121C22
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. C2×C13×#328C2semidirect
6. C13×#1446C2semidirect
7. C13×#1280C2semidirect
79. #9965C13direct (N × H)
147. C2×#451C2×C13semidirect
150. C2×#328C2×C13semidirect
152. #1446C2×C13semidirect
153. #1280C2×C13semidirect
392. C13#9965direct (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
C2×C13×#4482
C13×#26392
C2×C13×#3282
C2×C13×#3272
C13×#14462
C13×#12802
#996513