Finite Group Databasebeta

← C13×#13101 #15699440

Subgroups — C13×#13101 #15699440

Order 3328.

630 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3011C211yesmaximal, characteristic
2C13×#2884C211yesmaximal, characteristic
3C13×#2129C211yesmaximal, characteristic, complemented
4C13×#2123C211yesmaximal, characteristic, complemented
5C13×#1796C211yesmaximal, characteristic
6C13×#1395C211yesmaximal, characteristic, complemented
7C13×#1391C211yesmaximal, characteristic, complemented
8C2×C13×2−1+4C2211yescharacteristic
9C2×C13×#137C411yescharacteristic, complemented
10C22×C13×Q16C411yescharacteristic, complemented
11C13×#536C2211yescharacteristic
12C13×#519—21no—
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×#413C2211yescharacteristic
22C13×#410—21no—
23C13×#410—22no—
24C13×#410—22no—
25C13×#410C2211yescharacteristic
26C13×#410C2211yescharacteristic
27C13×#410C2211yescharacteristic
28C13×#408C2211yescharacteristic
29C13×#354—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—
51C2×C13×M16—21no—
52C2×C13×M16C2×C411yescharacteristic
53C22×C8×C13C2×C411yescharacteristic
54C13×C4⋊Q8—21no—
55C13×#124—21no—
56C13×#123—21no—
57C13×#123—21no—
58C13×C22⋊Q8—21no—
59C13×C22⋊Q8—21no—
60C4×Q8×C13—42no—
61C4×Q8×C13—42no—
62C13×#117—24no—
63C13×#117—21no—
64C13×#117—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—21no—
74C13×#100—21no—
75C13×#99—24no—
76C13×#99—21no—
77C13×#99—21no—
78C13×#99—21no—
79C13×#99—21no—
80C13×#99D412yes—
81C13×#99D412yes—
82C13×C22⋊C8—21no—
83C13×C22⋊C8—21no—
84#13101C1311yesmaximal, characteristic, direct product factor, Sylow
85C13×#41—22no—
86C13×#41—22no—
87C13×#41—41no—
88C13×#41—41no—
89C13×#41—41no—
90C13×#41—41no—
91C13×#41—41no—
92C13×#41—41no—
93C13×#41—44no—
94C13×#41—44no—
95C13×#41—44no—
96C2×Q8×C13—22no—
97C2×Q8×C13—22no—
98C2×Q8×C13—21no—
99C2×Q8×C13—21no—
100C2×Q8×C13—21no—
101C2×Q8×C13—22no—
102C2×Q8×C13—22no—
103C2×Q8×C13—21no—
104C2×Q8×C13—21no—
105C2×Q8×C13—41no—
106C2×Q8×C13—41no—
107C2×Q8×C13—41no—
108C2×Q8×C13—41no—
109C2×Q8×C13—44no—
110C2×Q8×C13C22⋊C411yescharacteristic
111C2×Q8×C13C22⋊C411yescharacteristic
112C2×Q8×C13C22⋊C411yescharacteristic
113C2×Q8×C13#4111yescharacteristic
114C2×D4×C13—21no—
115C2×D4×C13—21no—
116C2×D4×C13—21no—
117C2×D4×C13C22⋊C411yescharacteristic
118C2×D4×C13C2×D411yescharacteristic
119C2×D4×C13C2×D411yescharacteristic
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—41no—
136C13×M16—41no—
137C13×M16—41no—
138C2×C8×C13—21no—
139C2×C8×C13—21no—
140C2×C8×C13—41no—
141C2×C8×C13—41no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—44no—
144C13×C4⋊C4—41no—
145C13×C4⋊C4—41no—
146C13×C4⋊C4—41no—
147C13×C4⋊C4—41no—
148C13×C4⋊C4—41no—
149C13×C22⋊C4—21no—
150C13×C22⋊C4—22no—
151C13×C22⋊C4—22no—
152C13×C22⋊C4—41no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4—41no—
155C42×C13—21no—
156C42×C13—44no—
157C42×C13—41no—
158C42×C13—41no—
159C42×C13—41no—
160#3011C2×C1311yescharacteristic
161#2884C2×C1311yescharacteristic
162#2129C2×C1311yescharacteristic, complemented
163#2123C2×C1311yescharacteristic, complemented
164#1796C2×C1311yescharacteristic
165#1395C2×C1311yescharacteristic, complemented
166#1391C2×C1311yescharacteristic, complemented
167C23×C13—21no—
168C23×C13C4×D411yescharacteristic
169C23×C13#12011yescharacteristic
170C23×C13#12111yescharacteristic
171Q8×C13—24no—
172Q8×C13—21no—
173Q8×C13—21no—
174Q8×C13—21no—
175Q8×C13—21no—
176Q8×C13—41no—
177Q8×C13—42no—
178Q8×C13—42no—
179Q8×C13—41no—
180Q8×C13—41no—
181Q8×C13—81no—
182Q8×C13#9912yes—
183Q8×C13#9912yes—
184D4×C13—21no—
185D4×C13—21no—
186D4×C13—41no—
187D4×C13—41no—
188D4×C13—41no—
189D4×C13—42no—
190D4×C13—42no—
191D4×C13—42no—
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—42no—
208C2×C4×C13—42no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—81no—
212C2×C4×C13—81no—
213C2×C4×C13C2×C22⋊C411yescharacteristic
214C2×C4×C13C4×D411yescharacteristic
215C2×C4×C13#12111yescharacteristic
216C2×C4×C13#12311yescharacteristic
217C8×C13—41no—
218C8×C13—41no—
219C8×C13—81no—
220C2×2−1+4C22×C1311yescharacteristic
221C2×#137C4×C1311yescharacteristic, complemented
222C22×Q16C4×C1311yescharacteristic, complemented
223#536C22×C1311yescharacteristic
224#519—21no—
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#413C22×C1311yescharacteristic
234#410—21no—
235#410—22no—
236#410—22no—
237#410C22×C1311yescharacteristic
238#410C22×C1311yescharacteristic
239#410C22×C1311yescharacteristic
240#408C22×C1311yescharacteristic
241#354—22no—
242#352—22no—
243C22×C13—21no—
244C22×C13—21no—
245C22×C13—21no—
246C22×C13—41no—
247C22×C13—41no—
248C22×C13—41no—
249C22×C13—41no—
250C22×C13—81no—
251C22×C13#38611yescharacteristic
252C4×C13—21no—
253C4×C13—22no—
254C4×C13—22no—
255C4×C13—21no—
256C4×C13—21no—
257C4×C13—41no—
258C4×C13—81no—
259C4×C13—82no—
260C4×C13—82no—
261C4×C13—81no—
262C4×C13—161no—
263C4×C13C2×#9911yescharacteristic
264C4×C13C2×#9911yescharacteristic
2652−1+4—42no—
2662−1+4—42no—
267C2×#41—21no—
268C2×#41—21no—
269C2×#41—21no—
270C2×#41C2×C4×C1311yescharacteristic
271C2×#41D4×C1311yescharacteristic
272C2×#41D4×C1311yescharacteristic
273C2×#41C23×C1311yescharacteristic
274C22×Q8—21no—
275C22×Q8C2×C4×C1311yescharacteristic
276C22×Q8C2×C4×C1311yescharacteristic
277C22×Q8D4×C1311yescharacteristic
278C22×Q8D4×C1311yescharacteristic
279#137—42no—
280C2×Q16—21no—
281C2×Q16—21no—
282C2×Q16—21no—
283C2×Q16—42no—
284C2×SD16—21no—
285C2×M16—21no—
286C2×M16C2×C4×C1311yescharacteristic
287C22×C8C2×C4×C1311yescharacteristic
288C4⋊Q8—21no—
289#124—21no—
290#123—21no—
291#123—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C4×Q8—42no—
295C4×Q8—42no—
296#117—24no—
297#117—21no—
298#117—21no—
299#117—21no—
300#117C2×C4×C1311yescharacteristic
301#104—42no—
302#103—21no—
303#103—21no—
304#103—21no—
305#103—42no—
306#102—21no—
307#101—21no—
308#100—21no—
309#99—24no—
310#99—21no—
311#99—21no—
312#99—21no—
313#99—21no—
314#99D4×C1312yes—
315#99D4×C1312yes—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C2×C13—21no—
319C2×C13—41no—
320C2×C13—41no—
321C2×C13—41no—
322C2×C13—81no—
323C2×C13#189811yescharacteristic
324#41—22no—
325#41—22no—
326#41—41no—
327#41—41no—
328#41—41no—
329#41—41no—
330#41—41no—
331#41—41no—
332#41—44no—
333#41—44no—
334#41—44no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—41no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8—44no—
349C2×Q8C13×C22⋊C411yescharacteristic
350C2×Q8C13×C22⋊C411yescharacteristic
351C2×Q8C13×C22⋊C411yescharacteristic
352C2×Q8C13×#4111yescharacteristic
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4C13×C22⋊C411yescharacteristic
357C2×D4C2×D4×C1311yescharacteristic
358C2×D4C2×D4×C1311yescharacteristic
359C2×D4C13×#4111yescharacteristic
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4C22×C4×C1311yescharacteristic
368C22×C4C2×D4×C1311yescharacteristic
369C22×C4C2×D4×C1311yescharacteristic
370Q16—42no—
371Q16—42no—
372Q16—42no—
373SD16—42no—
374M16—41no—
375M16—41no—
376M16—41no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—41no—
380C2×C8—41no—
381C4⋊C4—21no—
382C4⋊C4—44no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C22⋊C4—21no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C42—21no—
395C42—44no—
396C42—41no—
397C42—41no—
398C42—41no—
399C13#1310111yescharacteristic, direct product factor, Sylow
400C23—21no—
401C23C4×D4×C1311yescharacteristic
402C23C13×#12011yescharacteristic
403C23C13×#12111yescharacteristic
404Q8—24no—
405Q8—21no—
406Q8—21no—
407Q8—21no—
408Q8—21no—
409Q8—41no—
410Q8—42no—
411Q8—42no—
412Q8—41no—
413Q8—41no—
414Q8—81no—
415Q8C13×#9912yes—
416Q8C13×#9912yes—
417D4—21no—
418D4—21no—
419D4—41no—
420D4—41no—
421D4—41no—
422D4—42no—
423D4—42no—
424D4—42no—
425C2×C4—24no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4C2×C13×C22⋊C411yescharacteristic
447C2×C4C4×D4×C1311yescharacteristic
448C2×C4C13×#12111yescharacteristic
449C2×C4C13×#12311yescharacteristic
450C8—41no—
451C8—41no—
452C8—81no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—81no—
461C22C13×#38611yescharacteristic
462C4—21no—
463C4—22no—
464C4—22no—
465C4—21no—
466C4—21no—
467C4—41no—
468C4—81no—
469C4—82no—
470C4—82no—
471C4—81no—
472C4—161no—
473C4C2×C13×#9911yescharacteristic
474C4C2×C13×#9911yescharacteristic
475C2—21no—
476C2—41no—
477C2—41no—
478C2—41no—
479C2—81no—
480C2C13×#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×#2129C2semidirect
4. C13×#2123C2semidirect
6. C13×#1395C2semidirect
7. C13×#1391C2semidirect
9. C2×C13×#137C4semidirect
10. C22×C13×Q16C4semidirect
19. C13×#419C4semidirect
20. C13×#416C4semidirect
84. #13101C13direct (N × H)
162. #2129C2×C13semidirect
163. #2123C2×C13semidirect
165. #1395C2×C13semidirect
166. #1391C2×C13semidirect
221. C2×#137C4×C13semidirect
222. C22×Q16C4×C13semidirect
231. #419C4×C13semidirect
232. #416C4×C13semidirect
399. C13#13101direct (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×#28842
C13×#21292
C13×#21232
C13×#17962
C13×#13952
C13×#13912
#1310113