Finite Group Databasebeta

← C13×#12720 #15699059

Subgroups — C13×#12720 #15699059

Order 3328.

694 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×#3455C211yesmaximal, characteristic
2C13×#2132C211yesmaximal, characteristic, complemented
3C13×#2126C211yesmaximal, characteristic, complemented
4C13×#2120C212yesmaximal, complemented
5C13×#1827C212yesmaximal, complemented
6C13×#542—21no—
7C13×#542—21no—
8C13×#541—21no—
9C13×#540—21no—
10C13×#539—22no—
11C13×#538—22no—
12C13×#533C411yescharacteristic, complemented
13C13×#532C2211yescharacteristic
14C13×#529—22no—
15C13×#529—22no—
16C13×#525C411yescharacteristic, complemented
17C13×#525C2211yescharacteristic
18C4×C13×#41C411yescharacteristic, complemented
19C4×C13×#41C2211yescharacteristic
20C2×C13×#117C411yescharacteristic, complemented
21C13×#413C2212yes—
22C13×#410C2212yes—
23C13×#356—21no—
24C13×#355—21no—
25C13×#354—21no—
26C13×#353—21no—
27C13×#352—22no—
28C13×AΣL(1,𝔽16)—22no—
29C13×#339—22no—
30C13×H(3,ℤ/4)—22no—
31C2×C13×#41C2×C411yescharacteristic
32C2×C13×#41C2311yescharacteristic
33C23×C4×C13C2×C411yescharacteristic
34C2×C13×M16—22no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8D411yescharacteristic
37C13×#127D411yescharacteristic
38C13×#126—22no—
39C13×#126—22no—
40C13×#126—22no—
41C13×#126—22no—
42C13×#125—22no—
43C13×#125—22no—
44C13×#125—21no—
45C13×#124—22no—
46C13×#124—22no—
47C13×#124D411yescharacteristic
48C13×#124D411yescharacteristic
49C13×#123—22no—
50C13×#123—22no—
51C13×#123—22no—
52C13×#123—22no—
53C13×#123—21no—
54C13×#123D412yes—
55C13×C22⋊Q8—22no—
56C13×C22⋊Q8—22no—
57C13×C22⋊Q8—21no—
58C13×C22⋊Q8—21no—
59C13×C22⋊Q8—22no—
60C13×#121—22no—
61C13×#121—22no—
62C13×#121—21no—
63C13×#121—21no—
64C13×#121—22no—
65C13×#120—21no—
66C13×#120D412yes—
67C4×Q8×C13—21no—
68C4×Q8×C13—21no—
69C4×Q8×C13—22no—
70C4×D4×C13—21no—
71C4×D4×C13—22no—
72C4×D4×C13—21no—
73C4×D4×C13—22no—
74C4×D4×C13—22no—
75C4×D4×C13—22no—
76C4×D4×C13—22no—
77C13×#117—21no—
78C13×#117—21no—
79C13×#117—21no—
80C13×#117—21no—
81C13×#117—21no—
82C13×#117—22no—
83C13×#117C2×C411yescharacteristic
84C13×#117C2×C411yescharacteristic
85C13×#117D412yes—
86C2×C13×C4⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C42×C13—21no—
89C2×C42×C13C2×C411yescharacteristic
90C2×C42×C13C2×C411yescharacteristic
91C2×C42×C13D412yes—
92C13×#101—22no—
93C13×#100—22no—
94C13×#99—22no—
95C13×#99—22no—
96#12720C1311yesmaximal, characteristic, direct product factor, Sylow
97C24×C13C22⋊C411yescharacteristic
98C13×#41—41no—
99C13×#41—41no—
100C13×#41—41no—
101C13×#41—41no—
102C2×Q8×C13—22no—
103C2×Q8×C13C22⋊C411yescharacteristic
104C2×Q8×C13C2×D411yescharacteristic
105C2×D4×C13—21no—
106C2×D4×C13—22no—
107C2×D4×C13—22no—
108C2×D4×C13—22no—
109C2×D4×C13C22⋊C411yescharacteristic
110C2×D4×C13C2×D411yescharacteristic
111C2×D4×C13C2×D412yes—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—22no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—41no—
120C22×C4×C13—41no—
121C22×C4×C13C22⋊C411yescharacteristic
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C2×D412yes—
124C13×M16—42no—
125C13×M16—42no—
126C2×C8×C13—42no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—22no—
132C13×C4⋊C4—22no—
133C13×C4⋊C4—22no—
134C13×C4⋊C4—22no—
135C13×C4⋊C4—22no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4—22no—
139C13×C4⋊C4—22no—
140C13×C4⋊C4—22no—
141C13×C4⋊C4—42no—
142C13×C22⋊C4—21no—
143C13×C22⋊C4—21no—
144C13×C22⋊C4—21no—
145C13×C22⋊C4—21no—
146C13×C22⋊C4—22no—
147C13×C22⋊C4—22no—
148C13×C22⋊C4—22no—
149C13×C22⋊C4—21no—
150C13×C22⋊C4—22no—
151C13×C22⋊C4—22no—
152C13×C22⋊C4—22no—
153C13×C22⋊C4—22no—
154C13×C22⋊C4—22no—
155C13×C22⋊C4—42no—
156C13×C22⋊C4C22⋊C412yes—
157C42×C13—22no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—22no—
162C42×C13—42no—
163C42×C13C22⋊C411yescharacteristic
164C42×C13C22⋊C411yescharacteristic
165C42×C13C22⋊C411yescharacteristic
166C42×C13C22⋊C412yes—
167C42×C13C22⋊C411yescharacteristic
168#3455C2×C1311yescharacteristic
169#2132C2×C1311yescharacteristic, complemented
170#2126C2×C1311yescharacteristic, complemented
171#2120C2×C1312yescomplemented
172#1827C2×C1312yescomplemented
173C23×C13—21no—
174C23×C13—21no—
175C23×C13—41no—
176C23×C13—81no—
177C23×C13C2×C22⋊C411yescharacteristic
178C23×C13#12012yes—
179Q8×C13—41no—
180Q8×C13—41no—
181Q8×C13—82no—
182D4×C13—42no—
183D4×C13—41no—
184D4×C13—41no—
185D4×C13—42no—
186D4×C13—82no—
187D4×C13—82no—
188D4×C13—82no—
189C2×C4×C13—22no—
190C2×C4×C13—21no—
191C2×C4×C13—22no—
192C2×C4×C13—21no—
193C2×C4×C13—21no—
194C2×C4×C13—21no—
195C2×C4×C13—21no—
196C2×C4×C13—22no—
197C2×C4×C13—21no—
198C2×C4×C13—22no—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—42no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—81no—
208C2×C4×C13—82no—
209C2×C4×C13—82no—
210C2×C4×C13—81no—
211C2×C4×C13—82no—
212C2×C4×C13C2×C22⋊C411yescharacteristic
213C2×C4×C13C2×C22⋊C411yescharacteristic
214C2×C4×C13#12012yes—
215C8×C13—82no—
216#542—21no—
217#542—21no—
218#541—21no—
219#540—21no—
220#539—22no—
221#538—22no—
222#533C4×C1311yescharacteristic, complemented
223#532C22×C1311yescharacteristic
224#529—22no—
225#529—22no—
226#525C4×C1311yescharacteristic, complemented
227#525C22×C1311yescharacteristic
228C4×#41C4×C1311yescharacteristic, complemented
229C4×#41C22×C1311yescharacteristic
230C2×#117C4×C1311yescharacteristic, complemented
231#413C22×C1312yes—
232#410C22×C1312yes—
233#356—21no—
234#355—21no—
235#354—21no—
236#353—21no—
237#352—22no—
238AΣL(1,𝔽16)—22no—
239#339—22no—
240H(3,ℤ/4)—22no—
241C22×C13—21no—
242C22×C13—22no—
243C22×C13—41no—
244C22×C13—42no—
245C22×C13—42no—
246C22×C13—41no—
247C22×C13—41no—
248C22×C13—41no—
249C22×C13—41no—
250C22×C13—82no—
251C22×C13#37911yescharacteristic
252C4×C13—22no—
253C4×C13—21no—
254C4×C13—41no—
255C4×C13—41no—
256C4×C13—41no—
257C4×C13—42no—
258C4×C13—42no—
259C4×C13—41no—
260C4×C13—41no—
261C4×C13—41no—
262C4×C13—162no—
263C4×C13#41011yescharacteristic
264C4×C13#41011yescharacteristic
265C2×#41C2×C4×C1311yescharacteristic
266C2×#41C23×C1311yescharacteristic
267C23×C4C2×C4×C1311yescharacteristic
268C2×M16—22no—
269C4⋊Q8—21no—
270C4⋊Q8D4×C1311yescharacteristic
271#127D4×C1311yescharacteristic
272#126—22no—
273#126—22no—
274#126—22no—
275#126—22no—
276#125—22no—
277#125—22no—
278#125—21no—
279#124—22no—
280#124—22no—
281#124D4×C1311yescharacteristic
282#124D4×C1311yescharacteristic
283#123—22no—
284#123—22no—
285#123—22no—
286#123—22no—
287#123—21no—
288#123D4×C1312yes—
289C22⋊Q8—22no—
290C22⋊Q8—22no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—22no—
294#121—22no—
295#121—22no—
296#121—21no—
297#121—21no—
298#121—22no—
299#120—21no—
300#120D4×C1312yes—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—22no—
304C4×D4—21no—
305C4×D4—22no—
306C4×D4—21no—
307C4×D4—22no—
308C4×D4—22no—
309C4×D4—22no—
310C4×D4—22no—
311#117—21no—
312#117—21no—
313#117—21no—
314#117—21no—
315#117—21no—
316#117—22no—
317#117C2×C4×C1311yescharacteristic
318#117C2×C4×C1311yescharacteristic
319#117D4×C1312yes—
320C2×C4⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C42—21no—
323C2×C42C2×C4×C1311yescharacteristic
324C2×C42C2×C4×C1311yescharacteristic
325C2×C42D4×C1312yes—
326#101—22no—
327#100—22no—
328#99—22no—
329#99—22no—
330C2×C13—21no—
331C2×C13—42no—
332C2×C13—41no—
333C2×C13—81no—
334C2×C13—81no—
335C2×C13#178211yescharacteristic
336C24C13×C22⋊C411yescharacteristic
337#41—41no—
338#41—41no—
339#41—41no—
340#41—41no—
341C2×Q8—22no—
342C2×Q8C13×C22⋊C411yescharacteristic
343C2×Q8C2×D4×C1311yescharacteristic
344C2×D4—21no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4C13×C22⋊C411yescharacteristic
349C2×D4C2×D4×C1311yescharacteristic
350C2×D4C2×D4×C1312yes—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4C13×C22⋊C411yescharacteristic
361C22×C4C22×C4×C1311yescharacteristic
362C22×C4C2×D4×C1312yes—
363M16—42no—
364M16—42no—
365C2×C8—42no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—42no—
381C22⋊C4—21no—
382C22⋊C4—21no—
383C22⋊C4—21no—
384C22⋊C4—21no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—21no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—42no—
395C22⋊C4C13×C22⋊C412yes—
396C42—22no—
397C42—21no—
398C42—21no—
399C42—21no—
400C42—22no—
401C42—42no—
402C42C13×C22⋊C411yescharacteristic
403C42C13×C22⋊C411yescharacteristic
404C42C13×C22⋊C411yescharacteristic
405C42C13×C22⋊C411yescharacteristic
406C42C13×C22⋊C412yes—
407C13#1272011yescharacteristic, direct product factor, Sylow
408C23—21no—
409C23—21no—
410C23—41no—
411C23—81no—
412C23C2×C13×C22⋊C411yescharacteristic
413C23C13×#12012yes—
414Q8—41no—
415Q8—41no—
416Q8—82no—
417D4—42no—
418D4—41no—
419D4—41no—
420D4—42no—
421D4—82no—
422D4—82no—
423D4—82no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—81no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4—81no—
446C2×C4—82no—
447C2×C4C2×C13×C22⋊C411yescharacteristic
448C2×C4C2×C13×C22⋊C411yescharacteristic
449C2×C4C13×#12012yes—
450C8—82no—
451C22—21no—
452C22—22no—
453C22—41no—
454C22—42no—
455C22—42no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—82no—
461C22C13×#37911yescharacteristic
462C4—22no—
463C4—21no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—42no—
468C4—42no—
469C4—41no—
470C4—41no—
471C4—41no—
472C4—162no—
473C4C13×#41011yescharacteristic
474C4C13×#41011yescharacteristic
475C2—21no—
476C2—42no—
477C2—41no—
478C2—81no—
479C2—81no—
480C2C13×#178211yescharacteristic
subgroupG/H
centerC4×C13#410
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×#41C23×C13
socleC2×C13#1782
prime radicalC13×#3455C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C13 ◁ C42×C13 ◁ C4×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2132C2semidirect
3. C13×#2126C2semidirect
4. C13×#2120C2semidirect
5. C13×#1827C2semidirect
12. C13×#533C4semidirect
16. C13×#525C4semidirect
18. C4×C13×#41C4semidirect
20. C2×C13×#117C4semidirect
96. #12720C13direct (N × H)
169. #2132C2×C13semidirect
170. #2126C2×C13semidirect
171. #2120C2×C13semidirect
172. #1827C2×C13semidirect
222. #533C4×C13semidirect
226. #525C4×C13semidirect
228. C4×#41C4×C13semidirect
230. C2×#117C4×C13semidirect
407. C13#12720direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34552
C13×#21322
C13×#21262
C13×#21202
C13×#18272
#1272013