Finite Group Databasebeta

← C13×#34512 #15720851

Subgroups — C13×#34512 #15720851

Order 3328.

2576 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×H(3,𝔽4)C211yesmaximal, characteristic
2C13×#2375C213yesmaximal, complemented
3C13×#2372C213yesmaximal, complemented
4C13×#2367C216yesmaximal, complemented
5C13×#2358C213yesmaximal, complemented
6C13×#2337C216yesmaximal, complemented
7C13×#2326C213yesmaximal, complemented
8C13×#2321C213yesmaximal, complemented
9C4×C13×#120C213yesmaximal, complemented
10C24×C4×C13C2211yescharacteristic, complemented
11C13×H(3,𝔽4)C4116yescomplemented
12C2×C13×#124C2213yes—
13C2×C13×#124C2216yes—
14C2×C13×#120C2213yes—
15C2×C13×#120C2213yes—
16C2×C4×Q8×C13C2213yescomplemented
17C2×C4×D4×C13C2213yes—
18C2×C4×D4×C13C2216yes—
19C22×C13×C22⋊C4C2213yescomplemented
20C13×#391C2213yescomplemented
21C13×#391C2216yescomplemented
22C13×#390C2216yes—
23C13×#390C2213yes—
24C13×#388C2216yescomplemented
25C13×#388C2216yescomplemented
26C13×#388C2216yescomplemented
27C13×#388C2216yescomplemented
28C13×#388C2216yescomplemented
29C13×#388C2216yescomplemented
30C13×#386C2216yes—
31C13×#386C2213yes—
32C13×#386C2213yes—
33C13×#386C2216yes—
34C13×#385C2216yescomplemented
35C13×#385C2213yescomplemented
36C13×#385C2213yescomplemented
37C13×#385C2216yescomplemented
38C13×#384C2211yescharacteristic, complemented
39C13×#383C2212yescomplemented
40C13×#379C2213yescomplemented
41C13×#379C2211yescharacteristic, complemented
42C4×C13×C4⋊C4C2216yescomplemented
43C4×C13×C22⋊C4C2213yescomplemented
44C4×C13×C22⋊C4C2216yescomplemented
45C4×C13×C22⋊C4C2213yescomplemented
46C4×C13×C22⋊C4C2216yescomplemented
47C13×#376C2213yescomplemented
48C25×C13C2311yescharacteristic
49C25×C13C2311yescharacteristic
50C22×Q8×C13C2313yes—
51C22×D4×C13C2316yes—
52C22×D4×C13C2313yes—
53C23×C4×C13—46no—
54C23×C4×C13C2313yes—
55C23×C4×C13C2313yes—
56C23×C4×C13C2313yes—
57C23×C4×C13C2313yes—
58C13×#124C2×C4124yescomplemented
59C13×#124C2×C4148yescomplemented
60C13×#120C2×C4124yescomplemented
61C13×#120C2×C4124yescomplemented
62C4×Q8×C13—46no—
63C4×D4×C13—46no—
64C4×D4×C13—412no—
65C2×C13×C4⋊C4C2316yes—
66C2×C13×C4⋊C4C2316yes—
67C2×C13×C4⋊C4C2313yes—
68C2×C13×C4⋊C4C2313yes—
69C2×C13×C22⋊C4—46no—
70C2×C13×C22⋊C4C2316yes—
71C2×C13×C22⋊C4C2313yes—
72C2×C13×C22⋊C4C2316yes—
73C2×C13×C22⋊C4C2313yes—
74C2×C13×C22⋊C4C2313yes—
75C2×C13×C22⋊C4C2316yes—
76C2×C13×C22⋊C4C2313yes—
77C2×C13×C22⋊C4C2316yes—
78C2×C13×C22⋊C4C2313yes—
79C2×C13×C22⋊C4C2316yes—
80C2×C13×C22⋊C4C2313yes—
81C2×C13×C22⋊C4C2316yes—
82C2×C42×C13C2313yes—
83C2×C42×C13C2316yes—
84C2×C42×C13C2313yes—
85C2×C42×C13C2316yes—
86C2×C42×C13C2312yes—
87C2×C42×C13C2311yescharacteristic
88C13×#95C2316yes—
89C13×#95C2316yes—
90C13×#95C2316yes—
91C13×#95C2316yes—
92C13×#95C2316yes—
93C13×#95C2316yes—
94#34512C1311yesmaximal, characteristic, direct product factor, Sylow
95C24×C13—43no—
96C24×C13—43no—
97C24×C13—43no—
98C24×C13—43no—
99C24×C13C22×C414yes—
100C24×C13C22×C414yescomplemented
101C24×C13C2413yes—
102C24×C13C2413yes—
103C2×Q8×C13—43no—
104C2×Q8×C13—43no—
105C2×Q8×C13C22×C4112yescomplemented
106C2×D4×C13—43no—
107C2×D4×C13—46no—
108C2×D4×C13—43no—
109C2×D4×C13—46no—
110C2×D4×C13C22×C4112yes—
111C2×D4×C13C22×C4124yes—
112C22×C4×C13—212no—
113C22×C4×C13—26no—
114C22×C4×C13—26no—
115C22×C4×C13—43no—
116C22×C4×C13—46no—
117C22×C4×C13—43no—
118C22×C4×C13—46no—
119C22×C4×C13—46no—
120C22×C4×C13—416no—
121C22×C4×C13C2416yes—
122C22×C4×C13C2411yescharacteristic
123C22×C4×C13C2413yes—
124C22×C4×C13C2413yes—
125C22×C4×C13C2413yes—
126C22×C4×C13C2416yes—
127C22×C4×C13C2413yes—
128C13×C4⋊C4—212no—
129C13×C4⋊C4—46no—
130C13×C4⋊C4—43no—
131C13×C4⋊C4—43no—
132C13×C22⋊C4—212no—
133C13×C22⋊C4—46no—
134C13×C22⋊C4—46no—
135C13×C22⋊C4—43no—
136C13×C22⋊C4—43no—
137C13×C22⋊C4—43no—
138C13×C22⋊C4—43no—
139C13×C22⋊C4—46no—
140C13×C22⋊C4C22×C4112yes—
141C13×C22⋊C4C22×C4124yes—
142C13×C22⋊C4C22×C4112yescomplemented
143C13×C22⋊C4C22×C4124yescomplemented
144C42×C13—26no—
145C42×C13—43no—
146C42×C13—46no—
147C42×C13—46no—
148C42×C13C22×C418yescomplemented
149C42×C13C22×C414yescomplemented
150C2×H(3,𝔽4)C2×C1311yescharacteristic
151#2375C2×C1313yescomplemented
152#2372C2×C1313yescomplemented
153#2367C2×C1316yescomplemented
154#2358C2×C1313yescomplemented
155#2337C2×C1316yescomplemented
156#2326C2×C1313yescomplemented
157#2321C2×C1313yescomplemented
158C4×#120C2×C1313yescomplemented
159C23×C13—26no—
160C23×C13—23no—
161C23×C13—26no—
162C23×C13—23no—
163C23×C13—26no—
164C23×C13—23no—
165C23×C13—23no—
166C23×C13—26no—
167C23×C13—412no—
168C23×C13—412no—
169C23×C13—44no—
170C23×C13—412no—
171C23×C13—82no—
172C23×C13—86no—
173C23×C13C23×C416yes—
174C23×C13C23×C416yes—
175C23×C13C2511yescharacteristic
176Q8×C13—412no—
177D4×C13—412no—
178D4×C13—424no—
179C2×C4×C13—23no—
180C2×C4×C13—26no—
181C2×C4×C13—26no—
182C2×C4×C13—23no—
183C2×C4×C13—26no—
184C2×C4×C13—23no—
185C2×C4×C13—26no—
186C2×C4×C13—26no—
187C2×C4×C13—23no—
188C2×C4×C13—23no—
189C2×C4×C13—26no—
190C2×C4×C13—26no—
191C2×C4×C13—26no—
192C2×C4×C13—412no—
193C2×C4×C13—412no—
194C2×C4×C13—86no—
195C2×C4×C13—86no—
196C2×C4×C13C23×C416yes—
197C2×C4×C13C23×C4112yes—
198C2×C4×C13H(5,𝔽2)16yes—
199C24×C4C22×C1311yescharacteristic, complemented
200H(3,𝔽4)C4×C13116yescomplemented
201C2×#124C22×C1313yes—
202C2×#124C22×C1316yes—
203C2×#120C22×C1313yes—
204C2×#120C22×C1313yes—
205C2×C4×Q8C22×C1313yescomplemented
206C2×C4×D4C22×C1313yes—
207C2×C4×D4C22×C1316yes—
208C22×C22⋊C4C22×C1313yescomplemented
209#391C22×C1313yescomplemented
210#391C22×C1316yescomplemented
211#390C22×C1316yes—
212#390C22×C1313yes—
213#388C22×C1316yescomplemented
214#388C22×C1316yescomplemented
215#388C22×C1316yescomplemented
216#388C22×C1316yescomplemented
217#388C22×C1316yescomplemented
218#388C22×C1316yescomplemented
219#386C22×C1316yes—
220#386C22×C1313yes—
221#386C22×C1316yes—
222#386C22×C1313yes—
223#385C22×C1313yescomplemented
224#385C22×C1316yescomplemented
225#385C22×C1316yescomplemented
226#385C22×C1313yescomplemented
227#384C22×C1311yescharacteristic, complemented
228#383C22×C1312yescomplemented
229#379C22×C1311yescharacteristic, complemented
230#379C22×C1313yescomplemented
231C4×C4⋊C4C22×C1316yescomplemented
232C4×C22⋊C4C22×C1313yescomplemented
233C4×C22⋊C4C22×C1313yescomplemented
234C4×C22⋊C4C22×C1316yescomplemented
235C4×C22⋊C4C22×C1316yescomplemented
236#376C22×C1313yescomplemented
237C22×C13—26no—
238C22×C13—212no—
239C22×C13—212no—
240C22×C13—26no—
241C22×C13—416no—
242C22×C13—43no—
243C22×C13—43no—
244C22×C13—43no—
245C22×C13—43no—
246C22×C13—46no—
247C22×C13—46no—
248C22×C13—88no—
249C22×C13C24×C411yescharacteristic
250C22×C13C2×H(5,𝔽2)13yes—
251C22×C13#58513yes—
252C4×C13—26no—
253C4×C13—212no—
254C4×C13—26no—
255C4×C13—41no—
256C4×C13—43no—
257C4×C13—43no—
258C4×C13—46no—
259C25C23×C1311yescharacteristic
260C25C23×C1311yescharacteristic
261C22×Q8C23×C1313yes—
262C22×D4C23×C1313yes—
263C22×D4C23×C1316yes—
264C23×C4—46no—
265C23×C4C23×C1313yes—
266C23×C4C23×C1313yes—
267C23×C4C23×C1313yes—
268C23×C4C23×C1313yes—
269#124C2×C4×C13124yescomplemented
270#124C2×C4×C13148yescomplemented
271#120C2×C4×C13124yescomplemented
272#120C2×C4×C13124yescomplemented
273C4×Q8—46no—
274C4×D4—46no—
275C4×D4—412no—
276C2×C4⋊C4C23×C1316yes—
277C2×C4⋊C4C23×C1313yes—
278C2×C4⋊C4C23×C1313yes—
279C2×C4⋊C4C23×C1316yes—
280C2×C22⋊C4—46no—
281C2×C22⋊C4C23×C1316yes—
282C2×C22⋊C4C23×C1316yes—
283C2×C22⋊C4C23×C1313yes—
284C2×C22⋊C4C23×C1316yes—
285C2×C22⋊C4C23×C1313yes—
286C2×C22⋊C4C23×C1313yes—
287C2×C22⋊C4C23×C1316yes—
288C2×C22⋊C4C23×C1313yes—
289C2×C22⋊C4C23×C1316yes—
290C2×C22⋊C4C23×C1313yes—
291C2×C22⋊C4C23×C1316yes—
292C2×C22⋊C4C23×C1313yes—
293C2×C42C23×C1313yes—
294C2×C42C23×C1316yes—
295C2×C42C23×C1316yes—
296C2×C42C23×C1313yes—
297C2×C42C23×C1311yescharacteristic
298C2×C42C23×C1312yes—
299#95C23×C1316yes—
300#95C23×C1316yes—
301#95C23×C1316yes—
302#95C23×C1316yes—
303#95C23×C1316yes—
304#95C23×C1316yes—
305C2×C13—46no—
306C2×C13—46no—
307C2×C13C4×H(5,𝔽2)13yes—
308C2×C13#353211yescharacteristic
309C2×C13#354013yes—
310C24—43no—
311C24—43no—
312C24—43no—
313C24—43no—
314C24C22×C4×C1314yes—
315C24C22×C4×C1314yescomplemented
316C24C24×C1313yes—
317C24C24×C1313yes—
318C2×Q8—43no—
319C2×Q8—43no—
320C2×Q8C22×C4×C13112yescomplemented
321C2×D4—43no—
322C2×D4—46no—
323C2×D4—43no—
324C2×D4—46no—
325C2×D4C22×C4×C13112yes—
326C2×D4C22×C4×C13124yes—
327C22×C4—212no—
328C22×C4—26no—
329C22×C4—26no—
330C22×C4—43no—
331C22×C4—46no—
332C22×C4—43no—
333C22×C4—46no—
334C22×C4—46no—
335C22×C4—416no—
336C22×C4C24×C1316yes—
337C22×C4C24×C1311yescharacteristic
338C22×C4C24×C1313yes—
339C22×C4C24×C1313yes—
340C22×C4C24×C1313yes—
341C22×C4C24×C1316yes—
342C22×C4C24×C1313yes—
343C4⋊C4—212no—
344C4⋊C4—43no—
345C4⋊C4—43no—
346C4⋊C4—46no—
347C22⋊C4—212no—
348C22⋊C4—46no—
349C22⋊C4—43no—
350C22⋊C4—43no—
351C22⋊C4—46no—
352C22⋊C4—46no—
353C22⋊C4—43no—
354C22⋊C4—43no—
355C22⋊C4C22×C4×C13124yes—
356C22⋊C4C22×C4×C13112yes—
357C22⋊C4C22×C4×C13124yescomplemented
358C22⋊C4C22×C4×C13112yescomplemented
359C42—26no—
360C42—46no—
361C42—46no—
362C42—43no—
363C42C22×C4×C1314yescomplemented
364C42C22×C4×C1318yescomplemented
365C13#3451211yescharacteristic, direct product factor, Sylow
366C23—26no—
367C23—23no—
368C23—26no—
369C23—23no—
370C23—26no—
371C23—23no—
372C23—23no—
373C23—26no—
374C23—412no—
375C23—412no—
376C23—44no—
377C23—412no—
378C23—82no—
379C23—86no—
380C23C23×C4×C1316yes—
381C23C23×C4×C1316yes—
382C23C25×C1311yescharacteristic
383Q8—412no—
384D4—412no—
385D4—424no—
386C2×C4—23no—
387C2×C4—26no—
388C2×C4—26no—
389C2×C4—23no—
390C2×C4—26no—
391C2×C4—23no—
392C2×C4—26no—
393C2×C4—26no—
394C2×C4—23no—
395C2×C4—23no—
396C2×C4—26no—
397C2×C4—26no—
398C2×C4—26no—
399C2×C4—412no—
400C2×C4—412no—
401C2×C4—86no—
402C2×C4—86no—
403C2×C4C23×C4×C1316yes—
404C2×C4C23×C4×C13112yes—
405C2×C4C13×H(5,𝔽2)16yes—
406C22—26no—
407C22—212no—
408C22—212no—
409C22—26no—
410C22—416no—
411C22—43no—
412C22—43no—
413C22—43no—
414C22—43no—
415C22—46no—
416C22—46no—
417C22—88no—
418C22C24×C4×C1311yescharacteristic
419C22C2×C13×H(5,𝔽2)13yes—
420C22C13×#58513yes—
421C4—26no—
422C4—26no—
423C4—212no—
424C4—41no—
425C4—43no—
426C4—43no—
427C4—46no—
428C2—46no—
429C2—46no—
430C2C4×C13×H(5,𝔽2)13yes—
431C2C13×#353211yescharacteristic
432C2C13×#354013yes—
subgroupG/H
center, socleC23×C13C25
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
prime radicalC2×C13×H(3,𝔽4)C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2375C2semidirect
3. C13×#2372C2semidirect
4. C13×#2367C2semidirect
5. C13×#2358C2semidirect
6. C13×#2337C2semidirect
7. C13×#2326C2semidirect
8. C13×#2321C2semidirect
9. C4×C13×#120C2semidirect
10. C24×C4×C13C22semidirect
11. C13×H(3,𝔽4)C4semidirect
16. C2×C4×Q8×C13C22semidirect
19. C22×C13×C22⋊C4C22semidirect
20. C13×#391C22semidirect
21. C13×#391C22semidirect
24. C13×#388C22semidirect
25. C13×#388C22semidirect
26. C13×#388C22semidirect
27. C13×#388C22semidirect
28. C13×#388C22semidirect
29. C13×#388C22semidirect
34. C13×#385C22semidirect
35. C13×#385C22semidirect
36. C13×#385C22semidirect
37. C13×#385C22semidirect
38. C13×#384C22semidirect
39. C13×#383C22semidirect
40. C13×#379C22semidirect
41. C13×#379C22semidirect
42. C4×C13×C4⋊C4C22semidirect
43. C4×C13×C22⋊C4C22semidirect
44. C4×C13×C22⋊C4C22semidirect
45. C4×C13×C22⋊C4C22semidirect
46. C4×C13×C22⋊C4C22semidirect
47. C13×#376C22semidirect
58. C13×#124C2×C4semidirect
59. C13×#124C2×C4semidirect
60. C13×#120C2×C4semidirect
61. C13×#120C2×C4semidirect
94. #34512C13direct (N × H)
100. C24×C13C22×C4semidirect
105. C2×Q8×C13C22×C4semidirect
142. C13×C22⋊C4C22×C4semidirect
143. C13×C22⋊C4C22×C4semidirect
148. C42×C13C22×C4semidirect
149. C42×C13C22×C4semidirect
151. #2375C2×C13semidirect
152. #2372C2×C13semidirect
153. #2367C2×C13semidirect
154. #2358C2×C13semidirect
155. #2337C2×C13semidirect
156. #2326C2×C13semidirect
157. #2321C2×C13semidirect
158. C4×#120C2×C13semidirect
199. C24×C4C22×C13semidirect
200. H(3,𝔽4)C4×C13semidirect
205. C2×C4×Q8C22×C13semidirect
208. C22×C22⋊C4C22×C13semidirect
209. #391C22×C13semidirect
210. #391C22×C13semidirect
213. #388C22×C13semidirect
214. #388C22×C13semidirect
215. #388C22×C13semidirect
216. #388C22×C13semidirect
217. #388C22×C13semidirect
218. #388C22×C13semidirect
223. #385C22×C13semidirect
224. #385C22×C13semidirect
225. #385C22×C13semidirect
226. #385C22×C13semidirect
227. #384C22×C13semidirect
228. #383C22×C13semidirect
229. #379C22×C13semidirect
230. #379C22×C13semidirect
231. C4×C4⋊C4C22×C13semidirect
232. C4×C22⋊C4C22×C13semidirect
233. C4×C22⋊C4C22×C13semidirect
234. C4×C22⋊C4C22×C13semidirect
235. C4×C22⋊C4C22×C13semidirect
236. #376C22×C13semidirect
269. #124C2×C4×C13semidirect
270. #124C2×C4×C13semidirect
271. #120C2×C4×C13semidirect
272. #120C2×C4×C13semidirect
315. C24C22×C4×C13semidirect
320. C2×Q8C22×C4×C13semidirect
357. C22⋊C4C22×C4×C13semidirect
358. C22⋊C4C22×C4×C13semidirect
363. C42C22×C4×C13semidirect
364. C42C22×C4×C13semidirect
365. C13#34512direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×H(3,𝔽4)2
C13×#23752
C13×#23722
C13×#23672
C13×#23582
C13×#23372
C13×#23262
C13×#23212
C4×C13×#1202
#3451213