Finite Group Databasebeta

← C13×#36692 #15723031

Subgroups — C13×#36692 #15723031

Order 3328.

1716 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2837C214yesmaximal, complemented
2C13×#2836C214yesmaximal, complemented
3C13×#2829C214yesmaximal, complemented
4C13×#2828C214yesmaximal, complemented
5C13×#2402C211yesmaximal, characteristic, complemented
6C13×#2397C211yesmaximal, characteristic, complemented
7C13×#2395C214yesmaximal, complemented
8C13×#2392C214yesmaximal, complemented
9C13×#2392C212yesmaximal, complemented
10C13×#2298C211yesmaximal, characteristic, complemented
11C13×#2293C212yesmaximal, complemented
12C2×C4×D4×C13C2212yes—
13C2×C4×D4×C13C2214yes—
14C2×C4×D4×C13C2214yes—
15C2×C13×#117C2211yescharacteristic
16C2×C13×#117C2214yes—
17C13×#400C2214yes—
18C13×#400C2214yes—
19C13×#399C2214yes—
20C13×#399C2214yes—
21C13×#398C2214yes—
22C13×#398C2214yes—
23C13×#398C2212yes—
24C13×#398C2214yes—
25C13×#397C2214yes—
26C13×#397C2214yes—
27C13×#397C2214yes—
28C13×#397C2214yes—
29C13×#397C2212yes—
30C13×#396C2214yes—
31C13×#396C2214yes—
32C13×#396C2214yes—
33C13×#394C2214yes—
34C13×#394C2214yes—
35C13×#394C2214yes—
36C13×#394C2214yes—
37C13×#394C2214yes—
38C13×#394C2214yes—
39C13×#394C2212yes—
40C13×#392C2212yes—
41C13×#392C2214yes—
42C13×#392C2214yes—
43C13×#390C2214yes—
44C13×#389C2214yes—
45C13×#388C2214yes—
46C13×#388C2214yes—
47C13×#388C2214yes—
48C13×#387C2214yes—
49C4×C13×C4⋊C4C2212yes—
50C4×C13×C4⋊C4C2212yes—
51C4×C13×C4⋊C4C2214yes—
52C4×C13×C22⋊C4C2214yes—
53C4×C13×C22⋊C4C2212yes—
54C4×C13×C22⋊C4C2214yes—
55C13×#376C2211yescharacteristic
56C43×C13C2211yescharacteristic
57C22×D4×C13C2312yes—
58C22×D4×C13C2314yes—
59C22×D4×C13C2314yes—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2314yes—
62C4×D4×C13—28no—
63C4×D4×C13—48no—
64C4×D4×C13—48no—
65C13×#117—24no—
66C13×#117—48no—
67C2×C13×C4⋊C4C2312yes—
68C2×C13×C4⋊C4C2312yes—
69C2×C13×C4⋊C4C2314yes—
70C2×C13×C4⋊C4C2314yes—
71C2×C13×C4⋊C4C2314yes—
72C2×C13×C4⋊C4C2314yes—
73C2×C13×C4⋊C4C2314yes—
74C2×C13×C4⋊C4C2314yes—
75C2×C13×C4⋊C4C2314yes—
76C2×C13×C4⋊C4C2314yes—
77C2×C13×C22⋊C4C2312yes—
78C2×C13×C22⋊C4C2314yes—
79C2×C13×C22⋊C4C2314yes—
80C2×C13×C22⋊C4C2314yes—
81C2×C13×C22⋊C4C2314yes—
82C2×C13×C22⋊C4C2314yes—
83C2×C13×C22⋊C4C2314yes—
84C2×C13×C22⋊C4C2314yes—
85C2×C13×C22⋊C4C2314yes—
86C2×C13×C22⋊C4C2314yes—
87C2×C13×C22⋊C4C2314yes—
88C2×C13×C22⋊C4C2314yes—
89C2×C13×C22⋊C4C2314yes—
90C2×C42×C13C2311yescharacteristic
91C2×C42×C13C2312yes—
92C2×C42×C13C2314yes—
93C2×C42×C13C2312yes—
94C2×C42×C13C2314yes—
95C2×C42×C13C2311yescharacteristic
96C13×#95C2314yes—
97C13×#95C2314yes—
98C13×#95C2314yes—
99C13×#95C2314yes—
100C13×#95C2314yes—
101C13×#95C2314yes—
102C13×#95C2312yes—
103C13×#95C2312yes—
104C13×#95C2314yes—
105C13×#95C2314yes—
106C13×#95C2314yes—
107#36692C1311yesmaximal, characteristic, direct product factor, Sylow
108C24×C13C2411yescharacteristic
109C24×C13C2414yes—
110C2×D4×C13—24no—
111C2×D4×C13—44no—
112C2×D4×C13—44no—
113C2×D4×C13—44no—
114C2×D4×C13—44no—
115C2×D4×C13—44no—
116C2×D4×C13—44no—
117C2×D4×C13—44no—
118C22×C4×C13—22no—
119C22×C4×C13—28no—
120C22×C4×C13—28no—
121C22×C4×C13—24no—
122C22×C4×C13—28no—
123C22×C4×C13C2412yes—
124C22×C4×C13C2414yes—
125C22×C4×C13C2414yes—
126C22×C4×C13C2414yes—
127C22×C4×C13C2414yes—
128C22×C4×C13C2414yes—
129C22×C4×C13C2411yescharacteristic
130C22×C4×C13C2412yes—
131C22×C4×C13C2411yescharacteristic
132C13×C4⋊C4—24no—
133C13×C4⋊C4—24no—
134C13×C4⋊C4—44no—
135C13×C4⋊C4—44no—
136C13×C4⋊C4—44no—
137C13×C4⋊C4—44no—
138C13×C4⋊C4—44no—
139C13×C4⋊C4—44no—
140C13×C4⋊C4—44no—
141C13×C4⋊C4—44no—
142C13×C22⋊C4—24no—
143C13×C22⋊C4—28no—
144C13×C22⋊C4—44no—
145C13×C22⋊C4—44no—
146C13×C22⋊C4—44no—
147C13×C22⋊C4—44no—
148C13×C22⋊C4—44no—
149C13×C22⋊C4—44no—
150C13×C22⋊C4—44no—
151C13×C22⋊C4—44no—
152C13×C22⋊C4—44no—
153C13×C22⋊C4—44no—
154C13×C22⋊C4—44no—
155C42×C13—22no—
156C42×C13—24no—
157C42×C13—28no—
158C42×C13—24no—
159C42×C13—44no—
160C42×C13#4114yes—
161#2837C2×C1314yescomplemented
162#2836C2×C1314yescomplemented
163#2829C2×C1314yescomplemented
164#2828C2×C1314yescomplemented
165#2402C2×C1311yescharacteristic, complemented
166#2397C2×C1311yescharacteristic, complemented
167#2395C2×C1314yescomplemented
168#2392C2×C1312yescomplemented
169#2392C2×C1314yescomplemented
170#2298C2×C1311yescharacteristic, complemented
171#2293C2×C1312yescomplemented
172C23×C13—21no—
173C23×C13—24no—
174C23×C13—24no—
175C23×C13—22no—
176C23×C13—24no—
177C23×C13—24no—
178C23×C13—24no—
179C23×C13—24no—
180C23×C13—24no—
181C23×C13—24no—
182C23×C13C2511yescharacteristic
183D4×C13—48no—
184D4×C13—416no—
185D4×C13—416no—
186C2×C4×C13—24no—
187C2×C4×C13—22no—
188C2×C4×C13—24no—
189C2×C4×C13—21no—
190C2×C4×C13—24no—
191C2×C4×C13—24no—
192C2×C4×C13—24no—
193C2×C4×C13—24no—
194C2×C4×C13—24no—
195C2×C4×C13—22no—
196C2×C4×C13—24no—
197C2×C4×C13—24no—
198C2×C4×C13—24no—
199C2×C4×C13—24no—
200C2×C4×C13—24no—
201C2×C4×C13—24no—
202C2×C4×C13—24no—
203C2×C4×C13—24no—
204C2×C4×C13—24no—
205C2×C4×C13—24no—
206C2×C4×C13—44no—
207C2×C4×C13—416no—
208C2×C4×C13C2×#4114yes—
209C2×C4×C13C2×#4112yes—
210C2×C4×C13H(5,𝔽2)14yes—
211C2×C4×D4C22×C1312yes—
212C2×C4×D4C22×C1314yes—
213C2×C4×D4C22×C1314yes—
214C2×#117C22×C1311yescharacteristic
215C2×#117C22×C1314yes—
216#400C22×C1314yes—
217#400C22×C1314yes—
218#399C22×C1314yes—
219#399C22×C1314yes—
220#398C22×C1314yes—
221#398C22×C1314yes—
222#398C22×C1312yes—
223#398C22×C1314yes—
224#397C22×C1314yes—
225#397C22×C1314yes—
226#397C22×C1314yes—
227#397C22×C1314yes—
228#397C22×C1312yes—
229#396C22×C1314yes—
230#396C22×C1314yes—
231#396C22×C1314yes—
232#394C22×C1314yes—
233#394C22×C1314yes—
234#394C22×C1314yes—
235#394C22×C1314yes—
236#394C22×C1314yes—
237#394C22×C1314yes—
238#394C22×C1312yes—
239#392C22×C1312yes—
240#392C22×C1314yes—
241#392C22×C1314yes—
242#390C22×C1314yes—
243#389C22×C1314yes—
244#388C22×C1314yes—
245#388C22×C1314yes—
246#388C22×C1314yes—
247#387C22×C1314yes—
248C4×C4⋊C4C22×C1314yes—
249C4×C4⋊C4C22×C1312yes—
250C4×C4⋊C4C22×C1312yes—
251C4×C22⋊C4C22×C1312yes—
252C4×C22⋊C4C22×C1314yes—
253C4×C22⋊C4C22×C1314yes—
254#376C22×C1311yescharacteristic
255C43C22×C1311yescharacteristic
256C22×C13—41no—
257C22×C13—44no—
258C22×C13—44no—
259C22×C13—42no—
260C22×C13—44no—
261C22×C13—44no—
262C22×C13—44no—
263C22×C13—44no—
264C22×C13—44no—
265C22×C13—44no—
266C22×C13C22×#4111yescharacteristic
267C22×C13C2×H(5,𝔽2)12yes—
268C22×C13#58514yes—
269C4×C13—24no—
270C4×C13—44no—
271C4×C13—41no—
272C4×C13—42no—
273C4×C13—44no—
274C4×C13—44no—
275C4×C13—44no—
276C4×C13—44no—
277C4×C13#54014yes—
278C22×D4C23×C1312yes—
279C22×D4C23×C1314yes—
280C22×D4C23×C1314yes—
281C23×C4C23×C1311yescharacteristic
282C23×C4C23×C1314yes—
283C4×D4—28no—
284C4×D4—48no—
285C4×D4—48no—
286#117—24no—
287#117—48no—
288C2×C4⋊C4C23×C1312yes—
289C2×C4⋊C4C23×C1312yes—
290C2×C4⋊C4C23×C1314yes—
291C2×C4⋊C4C23×C1314yes—
292C2×C4⋊C4C23×C1314yes—
293C2×C4⋊C4C23×C1314yes—
294C2×C4⋊C4C23×C1314yes—
295C2×C4⋊C4C23×C1314yes—
296C2×C4⋊C4C23×C1314yes—
297C2×C4⋊C4C23×C1314yes—
298C2×C22⋊C4C23×C1312yes—
299C2×C22⋊C4C23×C1314yes—
300C2×C22⋊C4C23×C1314yes—
301C2×C22⋊C4C23×C1314yes—
302C2×C22⋊C4C23×C1314yes—
303C2×C22⋊C4C23×C1314yes—
304C2×C22⋊C4C23×C1314yes—
305C2×C22⋊C4C23×C1314yes—
306C2×C22⋊C4C23×C1314yes—
307C2×C22⋊C4C23×C1314yes—
308C2×C22⋊C4C23×C1314yes—
309C2×C22⋊C4C23×C1314yes—
310C2×C22⋊C4C23×C1314yes—
311C2×C42C23×C1312yes—
312C2×C42C23×C1314yes—
313C2×C42C23×C1311yescharacteristic
314C2×C42C23×C1312yes—
315C2×C42C23×C1314yes—
316C2×C42C23×C1311yescharacteristic
317#95C23×C1314yes—
318#95C23×C1314yes—
319#95C23×C1314yes—
320#95C23×C1314yes—
321#95C23×C1314yes—
322#95C23×C1314yes—
323#95C23×C1314yes—
324#95C23×C1312yes—
325#95C23×C1312yes—
326#95C23×C1314yes—
327#95C23×C1314yes—
328C2×C13—84no—
329C2×C13—81no—
330C2×C13C2×#54011yescharacteristic
331C2×C13#345512yes—
332C2×C13#352914yes—
333C24C24×C1311yescharacteristic
334C24C24×C1314yes—
335C2×D4—24no—
336C2×D4—44no—
337C2×D4—44no—
338C2×D4—44no—
339C2×D4—44no—
340C2×D4—44no—
341C2×D4—44no—
342C2×D4—44no—
343C22×C4—22no—
344C22×C4—28no—
345C22×C4—28no—
346C22×C4—24no—
347C22×C4—28no—
348C22×C4C24×C1312yes—
349C22×C4C24×C1314yes—
350C22×C4C24×C1314yes—
351C22×C4C24×C1314yes—
352C22×C4C24×C1314yes—
353C22×C4C24×C1314yes—
354C22×C4C24×C1311yescharacteristic
355C22×C4C24×C1312yes—
356C22×C4C24×C1311yescharacteristic
357C4⋊C4—24no—
358C4⋊C4—24no—
359C4⋊C4—44no—
360C4⋊C4—44no—
361C4⋊C4—44no—
362C4⋊C4—44no—
363C4⋊C4—44no—
364C4⋊C4—44no—
365C4⋊C4—44no—
366C4⋊C4—44no—
367C22⋊C4—24no—
368C22⋊C4—28no—
369C22⋊C4—44no—
370C22⋊C4—44no—
371C22⋊C4—44no—
372C22⋊C4—44no—
373C22⋊C4—44no—
374C22⋊C4—44no—
375C22⋊C4—44no—
376C22⋊C4—44no—
377C22⋊C4—44no—
378C22⋊C4—44no—
379C22⋊C4—44no—
380C42—22no—
381C42—24no—
382C42—28no—
383C42—24no—
384C42—44no—
385C42C13×#4114yes—
386C13#3669211yescharacteristic, direct product factor, Sylow
387C23—21no—
388C23—24no—
389C23—24no—
390C23—24no—
391C23—22no—
392C23—24no—
393C23—24no—
394C23—24no—
395C23—24no—
396C23—24no—
397C23C25×C1311yescharacteristic
398D4—48no—
399D4—416no—
400D4—416no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—24no—
404C2×C4—21no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—44no—
422C2×C4—416no—
423C2×C4C2×C13×#4114yes—
424C2×C4C2×C13×#4112yes—
425C2×C4C13×H(5,𝔽2)14yes—
426C22—44no—
427C22—44no—
428C22—44no—
429C22—44no—
430C22—44no—
431C22—41no—
432C22—44no—
433C22—44no—
434C22—42no—
435C22—44no—
436C22C22×C13×#4111yescharacteristic
437C22C2×C13×H(5,𝔽2)12yes—
438C22C13×#58514yes—
439C4—24no—
440C4—44no—
441C4—44no—
442C4—44no—
443C4—44no—
444C4—44no—
445C4—41no—
446C4—42no—
447C4C13×#54014yes—
448C2—81no—
449C2—84no—
450C2C2×C13×#54011yescharacteristic
451C2C13×#345512yes—
452C2C13×#352914yes—
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×#2837C2semidirect
2. C13×#2836C2semidirect
3. C13×#2829C2semidirect
4. C13×#2828C2semidirect
5. C13×#2402C2semidirect
6. C13×#2397C2semidirect
7. C13×#2395C2semidirect
8. C13×#2392C2semidirect
9. C13×#2392C2semidirect
10. C13×#2298C2semidirect
11. C13×#2293C2semidirect
107. #36692C13direct (N × H)
161. #2837C2×C13semidirect
162. #2836C2×C13semidirect
163. #2829C2×C13semidirect
164. #2828C2×C13semidirect
165. #2402C2×C13semidirect
166. #2397C2×C13semidirect
167. #2395C2×C13semidirect
168. #2392C2×C13semidirect
169. #2392C2×C13semidirect
170. #2298C2×C13semidirect
171. #2293C2×C13semidirect
386. C13#36692direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28372
C13×#28362
C13×#28292
C13×#28282
C13×#24022
C13×#23972
C13×#23952
C13×#23922
C13×#22982
C13×#22932
#3669213