Finite Group Databasebeta

← C13×#13096 #15699435

Subgroups — C13×#13096 #15699435

Order 3328.

624 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3011C211yesmaximal, characteristic
2C13×#2889C211yesmaximal, characteristic
3C13×#2135C211yesmaximal, characteristic, complemented
4C13×#2123C211yesmaximal, characteristic, complemented
5C13×#1796C211yesmaximal, characteristic
6C13×#1395C211yesmaximal, characteristic, complemented
7C13×#1392C211yesmaximal, characteristic, complemented
8C2×C13×2−1+4C2211yescharacteristic
9C2×C13×#137C411yescharacteristic, complemented
10C22×C13×Q16C411yescharacteristic, complemented
11C13×#568—21no—
12C13×#536C2211yescharacteristic
13C13×#452—21no—
14C13×#452—21no—
15C13×#451—21no—
16C13×#451—21no—
17C13×#421—21no—
18C13×#419—21no—
19C13×#419C411yescharacteristic, complemented
20C13×#416C411yescharacteristic, complemented
21C13×#413—22no—
22C13×#413C2211yescharacteristic
23C13×#413C2211yescharacteristic
24C13×#413C2211yescharacteristic
25C2×C13×#101—21no—
26C2×C13×#101—22no—
27C13×#410C2211yescharacteristic
28C13×#408C2211yescharacteristic
29C13×#356—22no—
30C13×#352—22no—
31C13×2−1+4—42no—
32C13×2−1+4—42no—
33C2×C13×#41—21no—
34C2×C13×#41—21no—
35C2×C13×#41—21no—
36C2×C13×#41C2×C411yescharacteristic
37C2×C13×#41D411yescharacteristic
38C2×C13×#41D411yescharacteristic
39C2×C13×#41C2311yescharacteristic
40C22×Q8×C13—21no—
41C22×Q8×C13C2×C411yescharacteristic
42C22×Q8×C13C2×C411yescharacteristic
43C22×Q8×C13D411yescharacteristic
44C22×Q8×C13D411yescharacteristic
45C13×#137—42no—
46C2×C13×Q16—21no—
47C2×C13×Q16—21no—
48C2×C13×Q16—21no—
49C2×C13×Q16—42no—
50C2×C13×SD16—21no—
51C13×#131—42no—
52C13×#131—42no—
53C2×C13×M16—24no—
54C2×C13×M16—21no—
55C2×C13×M16—21no—
56C2×C13×M16—21no—
57C2×C13×M16C2×C411yescharacteristic
58C22×C8×C13C2×C411yescharacteristic
59C13×C4⋊Q8—21no—
60C13×#124—21no—
61C13×#123—21no—
62C13×#123—21no—
63C13×C22⋊Q8—21no—
64C13×C22⋊Q8—21no—
65C13×#117—21no—
66C13×#117C2×C411yescharacteristic
67C13×#104—42no—
68C13×#103—21no—
69C13×#103—21no—
70C13×#103—21no—
71C13×#103—42no—
72C13×#102—21no—
73C13×#101—24no—
74C13×#101—21no—
75C13×#101—21no—
76C13×#101D412yes—
77C13×#100—21no—
78C13×#100—21no—
79C13×#100D412yes—
80C13×#99—21no—
81C13×#99—21no—
82C13×C22⋊C8—21no—
83C13×C22⋊C8—21no—
84#13096C1311yesmaximal, characteristic, direct product factor, Sylow
85C13×#41—22no—
86C13×#41—22no—
87C13×#41—22no—
88C13×#41—22no—
89C13×#41—41no—
90C13×#41—41no—
91C13×#41—41no—
92C13×#41—41no—
93C13×#41—44no—
94C13×#41—44no—
95C13×#41—44no—
96C2×Q8×C13—21no—
97C2×Q8×C13—21no—
98C2×Q8×C13—21no—
99C2×Q8×C13—22no—
100C2×Q8×C13—22no—
101C2×Q8×C13—21no—
102C2×Q8×C13—21no—
103C2×Q8×C13—41no—
104C2×Q8×C13—41no—
105C2×Q8×C13—41no—
106C2×Q8×C13—41no—
107C2×Q8×C13—44no—
108C2×Q8×C13—41no—
109C2×Q8×C13—41no—
110C2×Q8×C13C22⋊C411yescharacteristic
111C2×Q8×C13C22⋊C411yescharacteristic
112C2×Q8×C13C22⋊C411yescharacteristic
113C2×Q8×C13C2×D411yescharacteristic
114C2×D4×C13—21no—
115C2×D4×C13—21no—
116C2×D4×C13—21no—
117C2×D4×C13C22⋊C411yescharacteristic
118C2×D4×C13C2×D411yescharacteristic
119C2×D4×C13#4111yescharacteristic
120C2×D4×C13#4111yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13C22×C411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C13×Q16—42no—
132C13×Q16—42no—
133C13×Q16—42no—
134C13×SD16—42no—
135C13×M16—22no—
136C13×M16—22no—
137C13×M16—44no—
138C13×M16—41no—
139C13×M16—41no—
140C13×M16—41no—
141C13×M16—41no—
142C13×M16—41no—
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—44no—
146C2×C8×C13—41no—
147C2×C8×C13—41no—
148C2×C8×C13—41no—
149C2×C8×C13—41no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—41no—
152C13×C4⋊C4—41no—
153C13×C4⋊C4—41no—
154C13×C22⋊C4—21no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4—41no—
157C13×C22⋊C4—41no—
158C42×C13—21no—
159C42×C13—41no—
160#3011C2×C1311yescharacteristic
161#2889C2×C1311yescharacteristic
162#2135C2×C1311yescharacteristic, complemented
163#2123C2×C1311yescharacteristic, complemented
164#1796C2×C1311yescharacteristic
165#1395C2×C1311yescharacteristic, complemented
166#1392C2×C1311yescharacteristic, complemented
167C23×C13—21no—
168C23×C13C4×D411yescharacteristic
169C23×C13#12111yescharacteristic
170C23×C13#12311yescharacteristic
171Q8×C13—21no—
172Q8×C13—21no—
173Q8×C13—21no—
174Q8×C13—21no—
175Q8×C13—21no—
176Q8×C13—41no—
177Q8×C13—42no—
178Q8×C13—42no—
179Q8×C13—42no—
180Q8×C13—41no—
181Q8×C13—41no—
182Q8×C13—81no—
183Q8×C13#9912yes—
184D4×C13—24no—
185D4×C13—21no—
186D4×C13—41no—
187D4×C13—41no—
188D4×C13—41no—
189D4×C13—42no—
190D4×C13—42no—
191D4×C13#9912yes—
192C2×C4×C13—24no—
193C2×C4×C13—21no—
194C2×C4×C13—21no—
195C2×C4×C13—21no—
196C2×C4×C13—21no—
197C2×C4×C13—21no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13—42no—
206C2×C4×C13—42no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—81no—
210C2×C4×C13—81no—
211C2×C4×C13C2×C22⋊C411yescharacteristic
212C2×C4×C13C4×D411yescharacteristic
213C2×C4×C13#12011yescharacteristic
214C2×C4×C13#12111yescharacteristic
215C8×C13—42no—
216C8×C13—42no—
217C8×C13—41no—
218C8×C13—41no—
219C8×C13—81no—
220C2×2−1+4C22×C1311yescharacteristic
221C2×#137C4×C1311yescharacteristic, complemented
222C22×Q16C4×C1311yescharacteristic, complemented
223#568—21no—
224#536C22×C1311yescharacteristic
225#452—21no—
226#452—21no—
227#451—21no—
228#451—21no—
229#421—21no—
230#419—21no—
231#419C4×C1311yescharacteristic, complemented
232#416C4×C1311yescharacteristic, complemented
233#413—22no—
234#413C22×C1311yescharacteristic
235#413C22×C1311yescharacteristic
236#413C22×C1311yescharacteristic
237C2×#101—21no—
238C2×#101—22no—
239#410C22×C1311yescharacteristic
240#408C22×C1311yescharacteristic
241#356—22no—
242#352—22no—
243C22×C13—21no—
244C22×C13—21no—
245C22×C13—21no—
246C22×C13—22no—
247C22×C13—41no—
248C22×C13—41no—
249C22×C13—41no—
250C22×C13—81no—
251C22×C13#38611yescharacteristic
252C4×C13—21no—
253C4×C13—21no—
254C4×C13—22no—
255C4×C13—21no—
256C4×C13—41no—
257C4×C13—41no—
258C4×C13—81no—
259C4×C13—81no—
260C4×C13—161no—
261C4×C13C2×#9911yescharacteristic
262C4×C13C2×#9911yescharacteristic
2632−1+4—42no—
2642−1+4—42no—
265C2×#41—21no—
266C2×#41—21no—
267C2×#41—21no—
268C2×#41C2×C4×C1311yescharacteristic
269C2×#41D4×C1311yescharacteristic
270C2×#41D4×C1311yescharacteristic
271C2×#41C23×C1311yescharacteristic
272C22×Q8—21no—
273C22×Q8C2×C4×C1311yescharacteristic
274C22×Q8C2×C4×C1311yescharacteristic
275C22×Q8D4×C1311yescharacteristic
276C22×Q8D4×C1311yescharacteristic
277#137—42no—
278C2×Q16—21no—
279C2×Q16—21no—
280C2×Q16—21no—
281C2×Q16—42no—
282C2×SD16—21no—
283#131—42no—
284#131—42no—
285C2×M16—24no—
286C2×M16—21no—
287C2×M16—21no—
288C2×M16—21no—
289C2×M16C2×C4×C1311yescharacteristic
290C22×C8C2×C4×C1311yescharacteristic
291C4⋊Q8—21no—
292#124—21no—
293#123—21no—
294#123—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297#117—21no—
298#117C2×C4×C1311yescharacteristic
299#104—42no—
300#103—21no—
301#103—21no—
302#103—21no—
303#103—42no—
304#102—21no—
305#101—24no—
306#101—21no—
307#101—21no—
308#101D4×C1312yes—
309#100—21no—
310#100—21no—
311#100D4×C1312yes—
312#99—21no—
313#99—21no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316C2×C13—21no—
317C2×C13—41no—
318C2×C13—41no—
319C2×C13—41no—
320C2×C13—42no—
321C2×C13#189811yescharacteristic
322#41—22no—
323#41—22no—
324#41—22no—
325#41—22no—
326#41—41no—
327#41—41no—
328#41—41no—
329#41—41no—
330#41—44no—
331#41—44no—
332#41—44no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—41no—
341C2×Q8—41no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—44no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8C13×C22⋊C411yescharacteristic
348C2×Q8C13×C22⋊C411yescharacteristic
349C2×Q8C13×C22⋊C411yescharacteristic
350C2×Q8C2×D4×C1311yescharacteristic
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4C13×C22⋊C411yescharacteristic
355C2×D4C2×D4×C1311yescharacteristic
356C2×D4C13×#4111yescharacteristic
357C2×D4C13×#4111yescharacteristic
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4C22×C4×C1311yescharacteristic
366C22×C4C2×D4×C1311yescharacteristic
367C22×C4C2×D4×C1311yescharacteristic
368Q16—42no—
369Q16—42no—
370Q16—42no—
371SD16—42no—
372M16—22no—
373M16—22no—
374M16—44no—
375M16—41no—
376M16—41no—
377M16—41no—
378M16—41no—
379M16—41no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—44no—
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—41no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C22⋊C4—21no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C42—21no—
396C42—41no—
397C13#1309611yescharacteristic, direct product factor, Sylow
398C23—21no—
399C23C4×D4×C1311yescharacteristic
400C23C13×#12111yescharacteristic
401C23C13×#12311yescharacteristic
402Q8—21no—
403Q8—21no—
404Q8—21no—
405Q8—21no—
406Q8—21no—
407Q8—41no—
408Q8—42no—
409Q8—42no—
410Q8—42no—
411Q8—41no—
412Q8—41no—
413Q8—81no—
414Q8C13×#9912yes—
415D4—24no—
416D4—21no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—42no—
421D4—42no—
422D4C13×#9912yes—
423C2×C4—24no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4C2×C13×C22⋊C411yescharacteristic
443C2×C4C4×D4×C1311yescharacteristic
444C2×C4C13×#12011yescharacteristic
445C2×C4C13×#12111yescharacteristic
446C8—42no—
447C8—42no—
448C8—41no—
449C8—41no—
450C8—81no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—22no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—81no—
459C22C13×#38611yescharacteristic
460C4—21no—
461C4—21no—
462C4—22no—
463C4—21no—
464C4—41no—
465C4—41no—
466C4—81no—
467C4—81no—
468C4—161no—
469C4C2×C13×#9911yescharacteristic
470C4C2×C13×#9911yescharacteristic
471C2—21no—
472C2—41no—
473C2—41no—
474C2—41no—
475C2—42no—
476C2C13×#189811yescharacteristic
subgroupG/H
center, socleC2×C13#1898
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×#41C23×C13
prime radicalC2×C13×2−1+4C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×2−1+4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#2135C2semidirect
4. C13×#2123C2semidirect
6. C13×#1395C2semidirect
7. C13×#1392C2semidirect
9. C2×C13×#137C4semidirect
10. C22×C13×Q16C4semidirect
19. C13×#419C4semidirect
20. C13×#416C4semidirect
84. #13096C13direct (N × H)
162. #2135C2×C13semidirect
163. #2123C2×C13semidirect
165. #1395C2×C13semidirect
166. #1392C2×C13semidirect
221. C2×#137C4×C13semidirect
222. C22×Q16C4×C13semidirect
231. #419C4×C13semidirect
232. #416C4×C13semidirect
397. C13#13096direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30112
C13×#28892
C13×#21352
C13×#21232
C13×#17962
C13×#13952
C13×#13922
#1309613