Finite Group Databasebeta

← C13×#36696 #15723035

Subgroups — C13×#36696 #15723035

Order 3328.

1908 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2843C211yesmaximal, characteristic, complemented
2C13×#2830C213yesmaximal, complemented
3C13×#2829C216yesmaximal, complemented
4C13×#2828C213yesmaximal, complemented
5C13×#2823C211yesmaximal, characteristic, complemented
6C13×#2818C212yesmaximal, complemented
7C13×#2395C213yesmaximal, complemented
8C13×#2392C216yesmaximal, complemented
9C13×#2388C213yesmaximal, complemented
10C4×C13×#127C211yesmaximal, characteristic, complemented
11C4×C13×#126C212yesmaximal, complemented
12C22×C13×#41C2211yescharacteristic
13C2×C13×#127C2211yescharacteristic
14C2×C13×#126C2212yes—
15C2×C4×D4×C13C2213yes—
16C2×C4×D4×C13C2213yes—
17C2×C4×D4×C13C2216yes—
18C2×C13×#117C2213yes—
19C13×#400C2213yes—
20C13×#399C2213yes—
21C13×#398C2213yes—
22C13×#398C2216yes—
23C13×#397C2216yes—
24C13×#397C2213yes—
25C13×#397C2216yes—
26C13×#396C2216yes—
27C13×#396C2216yes—
28C13×#395C2213yes—
29C13×#394C2216yes—
30C13×#394C2216yes—
31C13×#394C2213yes—
32C13×#394C2216yes—
33C13×#394C2216yes—
34C13×#394C2216yes—
35C13×#393C2213yes—
36C13×#392C2216yes—
37C13×#392C2216yes—
38C13×#392C2213yes—
39C13×#390C2213yes—
40C13×#390C2213yes—
41C13×#388C2216yes—
42C13×#387C2216yes—
43C13×#384C2211yescharacteristic
44C13×#383C2212yes—
45C4×C13×C4⋊C4C2216yes—
46C4×C13×C22⋊C4C2216yes—
47C4×C13×C22⋊C4C2213yes—
48C4×C13×C22⋊C4C2213yes—
49C43×C13C2211yescharacteristic
50C2×C13×#41—46no—
51C22×Q8×C13C2311yescharacteristic
52C22×D4×C13C2313yes—
53C22×D4×C13C2313yes—
54C22×D4×C13C2316yes—
55C22×D4×C13C2312yes—
56C22×D4×C13C2311yescharacteristic
57C23×C4×C13C2312yes—
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2313yes—
60C13×#127—24no—
61C13×#126—28no—
62C4×D4×C13—412no—
63C4×D4×C13—46no—
64C4×D4×C13—46no—
65C13×#117—46no—
66C2×C13×C4⋊C4C2316yes—
67C2×C13×C4⋊C4C2316yes—
68C2×C13×C4⋊C4C2313yes—
69C2×C13×C4⋊C4C2313yes—
70C2×C13×C4⋊C4C2313yes—
71C2×C13×C4⋊C4C2316yes—
72C2×C13×C4⋊C4C2313yes—
73C2×C13×C22⋊C4C2316yes—
74C2×C13×C22⋊C4C2316yes—
75C2×C13×C22⋊C4C2316yes—
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—
85C2×C42×C13C2313yes—
86C2×C42×C13C2311yescharacteristic
87C13×#95C2316yes—
88C13×#95C2316yes—
89C13×#95C2313yes—
90C13×#95C2313yes—
91C13×#95C2313yes—
92C13×#95C2313yes—
93C13×#95C2316yes—
94C13×#95C2316yes—
95#36696C1311yesmaximal, characteristic, direct product factor, Sylow
96C24×C13C2412yes—
97C24×C13C2413yes—
98C24×C13C2411yescharacteristic
99C13×#41—416no—
100C2×Q8×C13—43no—
101C2×D4×C13—26no—
102C2×D4×C13—26no—
103C2×D4×C13—43no—
104C2×D4×C13—43no—
105C2×D4×C13—46no—
106C2×D4×C13—43no—
107C2×D4×C13—43no—
108C2×D4×C13—46no—
109C2×D4×C13—46no—
110C2×D4×C13—46no—
111C2×D4×C13—43no—
112C22×C4×C13—26no—
113C22×C4×C13—212no—
114C22×C4×C13—26no—
115C22×C4×C13—212no—
116C22×C4×C13C2416yes—
117C22×C4×C13C2412yes—
118C22×C4×C13C2411yescharacteristic
119C22×C4×C13C2413yes—
120C22×C4×C13C2416yes—
121C22×C4×C13C2413yes—
122C22×C4×C13C2413yes—
123C22×C4×C13C2411yescharacteristic
124C13×C4⋊C4—212no—
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—46no—
133C13×C22⋊C4—46no—
134C13×C22⋊C4—46no—
135C13×C22⋊C4—46no—
136C13×C22⋊C4—46no—
137C13×C22⋊C4—43no—
138C13×C22⋊C4—43no—
139C13×C22⋊C4—46no—
140C13×C22⋊C4—46no—
141C42×C13—212no—
142C42×C13—26no—
143C42×C13—43no—
144C42×C13#4114yescomplemented
145#2843C2×C1311yescharacteristic, complemented
146#2830C2×C1313yescomplemented
147#2829C2×C1316yescomplemented
148#2828C2×C1313yescomplemented
149#2823C2×C1311yescharacteristic, complemented
150#2818C2×C1312yescomplemented
151#2395C2×C1313yescomplemented
152#2392C2×C1316yescomplemented
153#2388C2×C1313yescomplemented
154C4×#127C2×C1311yescharacteristic, complemented
155C4×#126C2×C1312yescomplemented
156C23×C13—22no—
157C23×C13—23no—
158C23×C13—21no—
159C23×C13—23no—
160C23×C13—26no—
161C23×C13—23no—
162C23×C13—26no—
163C23×C13—23no—
164C23×C13—26no—
165C23×C13—26no—
166C23×C13—23no—
167C23×C13C2511yescharacteristic
168Q8×C13—44no—
169D4×C13—412no—
170D4×C13—412no—
171D4×C13—424no—
172D4×C13—48no—
173D4×C13—44no—
174C2×C4×C13—23no—
175C2×C4×C13—23no—
176C2×C4×C13—26no—
177C2×C4×C13—23no—
178C2×C4×C13—26no—
179C2×C4×C13—26no—
180C2×C4×C13—26no—
181C2×C4×C13—23no—
182C2×C4×C13—23no—
183C2×C4×C13—26no—
184C2×C4×C13—26no—
185C2×C4×C13—26no—
186C2×C4×C13—26no—
187C2×C4×C13—26no—
188C2×C4×C13—412no—
189C2×C4×C13—44no—
190C2×C4×C13—48no—
191C2×C4×C13C2×#4116yes—
192C2×C4×C13H(5,𝔽2)16yes—
193C22×#41C22×C1311yescharacteristic
194C2×#127C22×C1311yescharacteristic
195C2×#126C22×C1312yes—
196C2×C4×D4C22×C1313yes—
197C2×C4×D4C22×C1313yes—
198C2×C4×D4C22×C1316yes—
199C2×#117C22×C1313yes—
200#400C22×C1313yes—
201#399C22×C1313yes—
202#398C22×C1313yes—
203#398C22×C1316yes—
204#397C22×C1316yes—
205#397C22×C1313yes—
206#397C22×C1316yes—
207#396C22×C1316yes—
208#396C22×C1316yes—
209#395C22×C1313yes—
210#394C22×C1316yes—
211#394C22×C1316yes—
212#394C22×C1313yes—
213#394C22×C1316yes—
214#394C22×C1316yes—
215#394C22×C1316yes—
216#393C22×C1313yes—
217#392C22×C1316yes—
218#392C22×C1316yes—
219#392C22×C1313yes—
220#390C22×C1313yes—
221#390C22×C1313yes—
222#388C22×C1316yes—
223#387C22×C1316yes—
224#384C22×C1311yescharacteristic
225#383C22×C1312yes—
226C4×C4⋊C4C22×C1316yes—
227C4×C22⋊C4C22×C1316yes—
228C4×C22⋊C4C22×C1313yes—
229C4×C22⋊C4C22×C1313yes—
230C43C22×C1311yescharacteristic
231C22×C13—43no—
232C22×C13—46no—
233C22×C13—43no—
234C22×C13—46no—
235C22×C13—41no—
236C22×C13—42no—
237C22×C13—43no—
238C22×C13—46no—
239C22×C13—46no—
240C22×C13—43no—
241C22×C13—43no—
242C22×C13C22×#4111yescharacteristic
243C22×C13C2×H(5,𝔽2)13yes—
244C22×C13#58513yes—
245C4×C13—26no—
246C4×C13—46no—
247C4×C13—43no—
248C4×C13—41no—
249C4×C13—42no—
250C4×C13—43no—
251C4×C13—46no—
252C4×C13#56014yes—
253C2×#41—46no—
254C22×Q8C23×C1311yescharacteristic
255C22×D4C23×C1313yes—
256C22×D4C23×C1313yes—
257C22×D4C23×C1316yes—
258C22×D4C23×C1312yes—
259C22×D4C23×C1311yescharacteristic
260C23×C4C23×C1313yes—
261C23×C4C23×C1311yescharacteristic
262C23×C4C23×C1312yes—
263#127—24no—
264#126—28no—
265C4×D4—412no—
266C4×D4—46no—
267C4×D4—46no—
268#117—46no—
269C2×C4⋊C4C23×C1316yes—
270C2×C4⋊C4C23×C1313yes—
271C2×C4⋊C4C23×C1313yes—
272C2×C4⋊C4C23×C1313yes—
273C2×C4⋊C4C23×C1313yes—
274C2×C4⋊C4C23×C1316yes—
275C2×C4⋊C4C23×C1316yes—
276C2×C22⋊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×C1316yes—
283C2×C22⋊C4C23×C1316yes—
284C2×C22⋊C4C23×C1316yes—
285C2×C22⋊C4C23×C1316yes—
286C2×C42C23×C1316yes—
287C2×C42C23×C1313yes—
288C2×C42C23×C1313yes—
289C2×C42C23×C1311yescharacteristic
290#95C23×C1316yes—
291#95C23×C1316yes—
292#95C23×C1313yes—
293#95C23×C1313yes—
294#95C23×C1313yes—
295#95C23×C1313yes—
296#95C23×C1316yes—
297#95C23×C1316yes—
298C2×C13—81no—
299C2×C13—83no—
300C2×C13—82no—
301C2×C13#346013yes—
302C2×C13C2×#56011yescharacteristic
303C2×C13#352913yes—
304C24C24×C1312yes—
305C24C24×C1313yes—
306C24C24×C1311yescharacteristic
307#41—416no—
308C2×Q8—43no—
309C2×D4—26no—
310C2×D4—26no—
311C2×D4—43no—
312C2×D4—43no—
313C2×D4—46no—
314C2×D4—43no—
315C2×D4—46no—
316C2×D4—43no—
317C2×D4—43no—
318C2×D4—46no—
319C2×D4—46no—
320C22×C4—26no—
321C22×C4—212no—
322C22×C4—212no—
323C22×C4—26no—
324C22×C4C24×C1316yes—
325C22×C4C24×C1312yes—
326C22×C4C24×C1311yescharacteristic
327C22×C4C24×C1313yes—
328C22×C4C24×C1316yes—
329C22×C4C24×C1313yes—
330C22×C4C24×C1313yes—
331C22×C4C24×C1311yescharacteristic
332C4⋊C4—212no—
333C4⋊C4—43no—
334C4⋊C4—43no—
335C4⋊C4—43no—
336C4⋊C4—43no—
337C4⋊C4—46no—
338C4⋊C4—46no—
339C22⋊C4—212no—
340C22⋊C4—46no—
341C22⋊C4—46no—
342C22⋊C4—43no—
343C22⋊C4—43no—
344C22⋊C4—46no—
345C22⋊C4—46no—
346C22⋊C4—46no—
347C22⋊C4—46no—
348C22⋊C4—46no—
349C42—212no—
350C42—26no—
351C42—43no—
352C42C13×#4114yescomplemented
353C13#3669611yescharacteristic, direct product factor, Sylow
354C23—22no—
355C23—23no—
356C23—21no—
357C23—23no—
358C23—26no—
359C23—26no—
360C23—23no—
361C23—23no—
362C23—26no—
363C23—26no—
364C23—23no—
365C23C25×C1311yescharacteristic
366Q8—44no—
367D4—412no—
368D4—412no—
369D4—424no—
370D4—44no—
371D4—48no—
372C2×C4—23no—
373C2×C4—23no—
374C2×C4—26no—
375C2×C4—23no—
376C2×C4—26no—
377C2×C4—26no—
378C2×C4—26no—
379C2×C4—23no—
380C2×C4—23no—
381C2×C4—26no—
382C2×C4—26no—
383C2×C4—26no—
384C2×C4—26no—
385C2×C4—26no—
386C2×C4—412no—
387C2×C4—48no—
388C2×C4—44no—
389C2×C4C2×C13×#4116yes—
390C2×C4C13×H(5,𝔽2)16yes—
391C22—42no—
392C22—41no—
393C22—43no—
394C22—46no—
395C22—46no—
396C22—43no—
397C22—43no—
398C22—43no—
399C22—46no—
400C22—43no—
401C22—46no—
402C22C22×C13×#4111yescharacteristic
403C22C2×C13×H(5,𝔽2)13yes—
404C22C13×#58513yes—
405C4—26no—
406C4—43no—
407C4—41no—
408C4—42no—
409C4—43no—
410C4—46no—
411C4—46no—
412C4C13×#56014yes—
413C2—82no—
414C2—81no—
415C2—83no—
416C2C13×#346013yes—
417C2C2×C13×#56011yescharacteristic
418C2C13×#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×#2843C2semidirect
2. C13×#2830C2semidirect
3. C13×#2829C2semidirect
4. C13×#2828C2semidirect
5. C13×#2823C2semidirect
6. C13×#2818C2semidirect
7. C13×#2395C2semidirect
8. C13×#2392C2semidirect
9. C13×#2388C2semidirect
10. C4×C13×#127C2semidirect
11. C4×C13×#126C2semidirect
95. #36696C13direct (N × H)
144. C42×C13#41semidirect
145. #2843C2×C13semidirect
146. #2830C2×C13semidirect
147. #2829C2×C13semidirect
148. #2828C2×C13semidirect
149. #2823C2×C13semidirect
150. #2818C2×C13semidirect
151. #2395C2×C13semidirect
152. #2392C2×C13semidirect
153. #2388C2×C13semidirect
154. C4×#127C2×C13semidirect
155. C4×#126C2×C13semidirect
352. C42C13×#41semidirect
353. C13#36696direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28432
C13×#28302
C13×#28292
C13×#28282
C13×#28232
C13×#28182
C13×#23952
C13×#23922
C13×#23882
C4×C13×#1272
C4×C13×#1262
#3669613