Finite Group Databasebeta

← C13×#36676 #15723015

Subgroups — C13×#36676 #15723015

Order 3328.

2006 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2842C211yesmaximal, characteristic, complemented
2C13×#2834C211yesmaximal, characteristic, complemented
3C13×#2827C216yesmaximal, complemented
4C13×#2826C213yesmaximal, complemented
5C13×#2825C212yesmaximal, complemented
6C13×#2812C213yesmaximal, complemented
7C13×#2401C212yesmaximal, complemented
8C13×#2397C211yesmaximal, characteristic, complemented
9C13×#2395C213yesmaximal, complemented
10C13×#2392C216yesmaximal, complemented
11C4×C13×#120C213yesmaximal, complemented
12C24×C4×C13C2211yescharacteristic
13C2×C13×#120C2213yes—
14C2×C4×D4×C13C2216yes—
15C2×C4×D4×C13C2213yes—
16C2×C4×D4×C13C2213yescomplemented
17C2×C13×#117C2213yescomplemented
18C13×#401C2212yescomplemented
19C13×#400C2216yescomplemented
20C13×#400C2213yescomplemented
21C13×#399C2213yes—
22C13×#399C2211yescharacteristic
23C13×#399C2213yescomplemented
24C13×#398C2213yescomplemented
25C13×#398C2216yescomplemented
26C13×#397C2216yes—
27C13×#397C2213yes—
28C13×#397C2216yescomplemented
29C13×#397C2216yescomplemented
30C13×#396C2212yes—
31C13×#396C2216yes—
32C13×#396C2216yescomplemented
33C13×#394C2216yes—
34C13×#394C2216yes—
35C13×#394C2216yes—
36C13×#394C2216yescomplemented
37C13×#392C2216yes—
38C13×#392C2213yes—
39C13×#392C2211yescharacteristic, complemented
40C13×#386C2216yes—
41C13×#386C2213yes—
42C13×#385C2213yes—
43C13×#385C2216yes—
44C13×#379C2213yes—
45C4×C13×C4⋊C4C2216yescomplemented
46C4×C13×C22⋊C4C2216yes—
47C4×C13×C22⋊C4C2213yes—
48C4×C13×C22⋊C4C2213yescomplemented
49C13×#376C2211yescharacteristic, complemented
50C25×C13C2311yescharacteristic
51C22×D4×C13C2316yes—
52C22×D4×C13C2313yes—
53C22×D4×C13C2313yes—
54C23×C4×C13—46no—
55C23×C4×C13C2312yes—
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2313yes—
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2312yes—
60C13×#120—212no—
61C4×D4×C13—412no—
62C4×D4×C13—46no—
63C4×D4×C13—46no—
64C13×#117—46no—
65C2×C13×C4⋊C4C2316yes—
66C2×C13×C4⋊C4C2316yes—
67C2×C13×C4⋊C4C2316yes—
68C2×C13×C4⋊C4C2313yes—
69C2×C13×C4⋊C4C2313yes—
70C2×C13×C4⋊C4C2313yes—
71C2×C13×C4⋊C4C2313yes—
72C2×C13×C22⋊C4C2316yes—
73C2×C13×C22⋊C4C2313yes—
74C2×C13×C22⋊C4C2316yes—
75C2×C13×C22⋊C4C2313yes—
76C2×C13×C22⋊C4C2316yes—
77C2×C13×C22⋊C4C2313yes—
78C2×C13×C22⋊C4C2316yes—
79C2×C13×C22⋊C4C2313yes—
80C2×C13×C22⋊C4C2316yes—
81C2×C13×C22⋊C4C2316yes—
82C2×C13×C22⋊C4C2316yes—
83C2×C42×C13C2316yes—
84C2×C42×C13C2313yes—
85C13×#95C2316yes—
86C13×#95C2316yes—
87C13×#95C2316yes—
88C13×#95C2313yes—
89C13×#95C2313yes—
90C13×#95C2316yes—
91C13×#95C2316yes—
92C13×#95C2313yes—
93C13×#95C2311yescharacteristic
94#36676C1311yesmaximal, characteristic, direct product factor, Sylow
95C24×C13—43no—
96C24×C13—43no—
97C24×C13#4114yes—
98C24×C13C2413yes—
99C24×C13C2412yes—
100C24×C13C2411yescharacteristic
101C2×D4×C13—212no—
102C2×D4×C13—26no—
103C2×D4×C13—43no—
104C2×D4×C13—43no—
105C2×D4×C13—46no—
106C2×D4×C13—46no—
107C2×D4×C13—46no—
108C2×D4×C13—43no—
109C22×C4×C13—26no—
110C22×C4×C13—212no—
111C22×C4×C13—212no—
112C22×C4×C13—26no—
113C22×C4×C13—43no—
114C22×C4×C13—46no—
115C22×C4×C13—416no—
116C22×C4×C13C2413yes—
117C22×C4×C13C2416yes—
118C22×C4×C13C2413yes—
119C22×C4×C13C2412yes—
120C22×C4×C13C2411yescharacteristic
121C22×C4×C13C2416yes—
122C22×C4×C13C2413yes—
123C22×C4×C13C2411yescharacteristic
124C13×C4⋊C4—46no—
125C13×C4⋊C4—46no—
126C13×C4⋊C4—43no—
127C13×C4⋊C4—43no—
128C13×C4⋊C4—43no—
129C13×C4⋊C4—43no—
130C13×C4⋊C4—46no—
131C13×C22⋊C4—212no—
132C13×C22⋊C4—26no—
133C13×C22⋊C4—43no—
134C13×C22⋊C4—46no—
135C13×C22⋊C4—46no—
136C13×C22⋊C4—46no—
137C13×C22⋊C4—46no—
138C13×C22⋊C4—46no—
139C13×C22⋊C4—46no—
140C13×C22⋊C4—43no—
141C13×C22⋊C4—43no—
142C42×C13—212no—
143C42×C13—26no—
144#2842C2×C1311yescharacteristic, complemented
145#2834C2×C1311yescharacteristic, complemented
146#2827C2×C1316yescomplemented
147#2826C2×C1313yescomplemented
148#2825C2×C1312yescomplemented
149#2812C2×C1313yescomplemented
150#2401C2×C1312yescomplemented
151#2397C2×C1311yescharacteristic, complemented
152#2395C2×C1313yescomplemented
153#2392C2×C1316yescomplemented
154C4×#120C2×C1313yescomplemented
155C23×C13—26no—
156C23×C13—23no—
157C23×C13—23no—
158C23×C13—26no—
159C23×C13—23no—
160C23×C13—23no—
161C23×C13—26no—
162C23×C13—26no—
163C23×C13—23no—
164C23×C13—412no—
165C23×C13—44no—
166C23×C13—412no—
167C23×C13C2×#4114yes—
168C23×C13C2×#4112yes—
169C23×C13C2511yescharacteristic
170D4×C13—412no—
171D4×C13—424no—
172D4×C13—412no—
173C2×C4×C13—23no—
174C2×C4×C13—26no—
175C2×C4×C13—26no—
176C2×C4×C13—23no—
177C2×C4×C13—23no—
178C2×C4×C13—26no—
179C2×C4×C13—26no—
180C2×C4×C13—23no—
181C2×C4×C13—26no—
182C2×C4×C13—23no—
183C2×C4×C13—26no—
184C2×C4×C13—26no—
185C2×C4×C13—26no—
186C2×C4×C13—26no—
187C2×C4×C13—23no—
188C2×C4×C13—44no—
189C2×C4×C13—48no—
190C2×C4×C13—412no—
191C2×C4×C13—48no—
192C2×C4×C13—44no—
193C2×C4×C13H(5,𝔽2)16yes—
194C24×C4C22×C1311yescharacteristic
195C2×#120C22×C1313yes—
196C2×C4×D4C22×C1316yes—
197C2×C4×D4C22×C1313yes—
198C2×C4×D4C22×C1313yescomplemented
199C2×#117C22×C1313yescomplemented
200#401C22×C1312yescomplemented
201#400C22×C1316yescomplemented
202#400C22×C1313yescomplemented
203#399C22×C1313yes—
204#399C22×C1311yescharacteristic
205#399C22×C1313yescomplemented
206#398C22×C1313yescomplemented
207#398C22×C1316yescomplemented
208#397C22×C1316yes—
209#397C22×C1313yes—
210#397C22×C1316yescomplemented
211#397C22×C1316yescomplemented
212#396C22×C1312yes—
213#396C22×C1316yes—
214#396C22×C1316yescomplemented
215#394C22×C1316yes—
216#394C22×C1316yes—
217#394C22×C1316yes—
218#394C22×C1316yescomplemented
219#392C22×C1316yes—
220#392C22×C1313yes—
221#392C22×C1311yescharacteristic, complemented
222#386C22×C1316yes—
223#386C22×C1313yes—
224#385C22×C1313yes—
225#385C22×C1316yes—
226#379C22×C1313yes—
227C4×C4⋊C4C22×C1316yescomplemented
228C4×C22⋊C4C22×C1316yes—
229C4×C22⋊C4C22×C1313yes—
230C4×C22⋊C4C22×C1313yescomplemented
231#376C22×C1311yescharacteristic, complemented
232C22×C13—26no—
233C22×C13—212no—
234C22×C13—416no—
235C22×C13—42no—
236C22×C13—41no—
237C22×C13—46no—
238C22×C13—43no—
239C22×C13—43no—
240C22×C13—46no—
241C22×C13—43no—
242C22×C13—46no—
243C22×C13—43no—
244C22×C13C22×#4111yescharacteristic
245C22×C13C2×H(5,𝔽2)13yes—
246C22×C13#58513yes—
247C4×C13—43no—
248C4×C13—46no—
249C4×C13—43no—
250C4×C13—42no—
251C4×C13—41no—
252C4×C13—46no—
253C4×C13—43no—
254C4×C13#56014yes—
255C25C23×C1311yescharacteristic
256C22×D4C23×C1316yes—
257C22×D4C23×C1313yes—
258C22×D4C23×C1313yes—
259C23×C4—46no—
260C23×C4C23×C1313yes—
261C23×C4C23×C1312yes—
262C23×C4C23×C1311yescharacteristic
263C23×C4C23×C1311yescharacteristic
264C23×C4C23×C1312yes—
265#120—212no—
266C4×D4—412no—
267C4×D4—46no—
268C4×D4—46no—
269#117—46no—
270C2×C4⋊C4C23×C1313yes—
271C2×C4⋊C4C23×C1313yes—
272C2×C4⋊C4C23×C1316yes—
273C2×C4⋊C4C23×C1313yes—
274C2×C4⋊C4C23×C1313yes—
275C2×C4⋊C4C23×C1316yes—
276C2×C4⋊C4C23×C1316yes—
277C2×C22⋊C4C23×C1316yes—
278C2×C22⋊C4C23×C1313yes—
279C2×C22⋊C4C23×C1316yes—
280C2×C22⋊C4C23×C1313yes—
281C2×C22⋊C4C23×C1316yes—
282C2×C22⋊C4C23×C1313yes—
283C2×C22⋊C4C23×C1316yes—
284C2×C22⋊C4C23×C1316yes—
285C2×C22⋊C4C23×C1316yes—
286C2×C22⋊C4C23×C1313yes—
287C2×C22⋊C4C23×C1316yes—
288C2×C42C23×C1316yes—
289C2×C42C23×C1313yes—
290#95C23×C1313yes—
291#95C23×C1311yescharacteristic
292#95C23×C1316yes—
293#95C23×C1316yes—
294#95C23×C1316yes—
295#95C23×C1313yes—
296#95C23×C1313yes—
297#95C23×C1316yes—
298#95C23×C1316yes—
299C2×C13—42no—
300C2×C13—44no—
301C2×C13—83no—
302C2×C13#345913yes—
303C2×C13C2×#56011yescharacteristic
304C2×C13#352913yes—
305C24—43no—
306C24—43no—
307C24C13×#4114yes—
308C24C24×C1313yes—
309C24C24×C1311yescharacteristic
310C24C24×C1312yes—
311C2×D4—212no—
312C2×D4—26no—
313C2×D4—43no—
314C2×D4—43no—
315C2×D4—46no—
316C2×D4—46no—
317C2×D4—46no—
318C2×D4—43no—
319C22×C4—26no—
320C22×C4—212no—
321C22×C4—212no—
322C22×C4—26no—
323C22×C4—43no—
324C22×C4—46no—
325C22×C4—416no—
326C22×C4C24×C1313yes—
327C22×C4C24×C1316yes—
328C22×C4C24×C1313yes—
329C22×C4C24×C1312yes—
330C22×C4C24×C1311yescharacteristic
331C22×C4C24×C1316yes—
332C22×C4C24×C1313yes—
333C22×C4C24×C1311yescharacteristic
334C4⋊C4—43no—
335C4⋊C4—43no—
336C4⋊C4—43no—
337C4⋊C4—43no—
338C4⋊C4—46no—
339C4⋊C4—46no—
340C4⋊C4—46no—
341C22⋊C4—212no—
342C22⋊C4—26no—
343C22⋊C4—46no—
344C22⋊C4—46no—
345C22⋊C4—46no—
346C22⋊C4—46no—
347C22⋊C4—43no—
348C22⋊C4—43no—
349C22⋊C4—43no—
350C22⋊C4—46no—
351C22⋊C4—46no—
352C42—212no—
353C42—26no—
354C13#3667611yescharacteristic, direct product factor, Sylow
355C23—26no—
356C23—23no—
357C23—23no—
358C23—26no—
359C23—23no—
360C23—23no—
361C23—26no—
362C23—26no—
363C23—23no—
364C23—412no—
365C23—44no—
366C23—412no—
367C23C2×C13×#4112yes—
368C23C2×C13×#4114yes—
369C23C25×C1311yescharacteristic
370D4—412no—
371D4—424no—
372D4—412no—
373C2×C4—23no—
374C2×C4—26no—
375C2×C4—26no—
376C2×C4—23no—
377C2×C4—23no—
378C2×C4—26no—
379C2×C4—26no—
380C2×C4—23no—
381C2×C4—26no—
382C2×C4—23no—
383C2×C4—26no—
384C2×C4—26no—
385C2×C4—26no—
386C2×C4—26no—
387C2×C4—23no—
388C2×C4—44no—
389C2×C4—48no—
390C2×C4—48no—
391C2×C4—44no—
392C2×C4—412no—
393C2×C4C13×H(5,𝔽2)16yes—
394C22—26no—
395C22—212no—
396C22—416no—
397C22—42no—
398C22—41no—
399C22—46no—
400C22—43no—
401C22—43no—
402C22—46no—
403C22—43no—
404C22—43no—
405C22—46no—
406C22C22×C13×#4111yescharacteristic
407C22C2×C13×H(5,𝔽2)13yes—
408C22C13×#58513yes—
409C4—43no—
410C4—42no—
411C4—41no—
412C4—46no—
413C4—43no—
414C4—43no—
415C4—46no—
416C4C13×#56014yes—
417C2—42no—
418C2—44no—
419C2—83no—
420C2C13×#345913yes—
421C2C2×C13×#56011yescharacteristic
422C2C13×#352913yes—
subgroupG/H
centerC22×C4×C13C24
commutator, Frattini, cosocleC23C25×C13
socleC23×C13C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2842C2semidirect
2. C13×#2834C2semidirect
3. C13×#2827C2semidirect
4. C13×#2826C2semidirect
5. C13×#2825C2semidirect
6. C13×#2812C2semidirect
7. C13×#2401C2semidirect
8. C13×#2397C2semidirect
9. C13×#2395C2semidirect
10. C13×#2392C2semidirect
11. C4×C13×#120C2semidirect
16. C2×C4×D4×C13C22semidirect
17. C2×C13×#117C22semidirect
18. C13×#401C22semidirect
19. C13×#400C22semidirect
20. C13×#400C22semidirect
23. C13×#399C22semidirect
24. C13×#398C22semidirect
25. C13×#398C22semidirect
28. C13×#397C22semidirect
29. C13×#397C22semidirect
32. C13×#396C22semidirect
36. C13×#394C22semidirect
39. C13×#392C22semidirect
45. C4×C13×C4⋊C4C22semidirect
48. C4×C13×C22⋊C4C22semidirect
49. C13×#376C22semidirect
94. #36676C13direct (N × H)
144. #2842C2×C13semidirect
145. #2834C2×C13semidirect
146. #2827C2×C13semidirect
147. #2826C2×C13semidirect
148. #2825C2×C13semidirect
149. #2812C2×C13semidirect
150. #2401C2×C13semidirect
151. #2397C2×C13semidirect
152. #2395C2×C13semidirect
153. #2392C2×C13semidirect
154. C4×#120C2×C13semidirect
198. C2×C4×D4C22×C13semidirect
199. C2×#117C22×C13semidirect
200. #401C22×C13semidirect
201. #400C22×C13semidirect
202. #400C22×C13semidirect
205. #399C22×C13semidirect
206. #398C22×C13semidirect
207. #398C22×C13semidirect
210. #397C22×C13semidirect
211. #397C22×C13semidirect
214. #396C22×C13semidirect
218. #394C22×C13semidirect
221. #392C22×C13semidirect
227. C4×C4⋊C4C22×C13semidirect
230. C4×C22⋊C4C22×C13semidirect
231. #376C22×C13semidirect
354. C13#36676direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28422
C13×#28342
C13×#28272
C13×#28262
C13×#28252
C13×#28122
C13×#24012
C13×#23972
C13×#23952
C13×#23922
C4×C13×#1202
#3667613