Finite Group Databasebeta

← C13×#34311 #15720650

Subgroups — C13×#34311 #15720650

Order 3328.

2860 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C13C211yesmaximal, characteristic
2C2×C13×#519C212yesmaximal, complemented
3C13×#2365C213yesmaximal, complemented
4C13×#2362C216yesmaximal, complemented
5C13×#2354C213yesmaximal
6Q8×C13×C4⋊C4C211yesmaximal, characteristic, complemented
7Q8×C13×C22⋊C4C212yesmaximal, complemented
8C13×#2323C216yesmaximal, complemented
9C4×C13×C4⋊Q8C213yesmaximal, complemented
10C13×#2293C213yesmaximal
11C42×Q8×C13C211yesmaximal, characteristic, complemented
12C23×Q8×C13C2212yes—
13D4×Q8×C13C4116yescomplemented
14C2×C13×C4⋊Q8C2213yes—
15C2×C13×C22⋊Q8C2216yes—
16C13×#519—216no—
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2216yes—
19C2×C4×Q8×C13C2212yes—
20C2×C4×Q8×C13C2216yes—
21C2×C4×Q8×C13C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×D4×C13C2213yes—
24C2×C13×#117C2216yes—
25C2×C13×#117C2216yes—
26C13×#391C2216yes—
27C13×#391C2216yes—
28C13×#390C2211yescharacteristic
29C13×#390C2213yes—
30C13×#389C2213yes—
31C13×#389C2213yes—
32C13×#389C2216yes—
33C13×#389C2216yes—
34C13×#388C2216yes—
35C13×#388C2216yes—
36C13×#388C22112yes—
37C13×#387C22112yes—
38C13×#384C2213yes—
39C13×#380C2216yes—
40C4×C13×C4⋊C4C2213yes—
41C4×C13×C4⋊C4C2213yes—
42C4×C13×C4⋊C4C2213yes—
43C4×C13×C4⋊C4C2213yes—
44C4×C13×C4⋊C4C2216yes—
45C4×C13×C4⋊C4C2216yes—
46C4×C13×C22⋊C4C2216yes—
47C43×C13C2213yes—
48C22×Q8×C13—28no—
49C22×Q8×C13—28no—
50C22×Q8×C13C2×C4116yes—
51C22×Q8×C13C2316yes—
52C22×Q8×C13C2311yescharacteristic
53C22×D4×C13C2311yescharacteristic
54C23×C4×C13C2316yes—
55C13×C4⋊Q8C2×C4124yes—
56C13×C22⋊Q8C2×C4148yes—
57C4×Q8×C13—28no—
58C4×Q8×C13—24no—
59C4×Q8×C13—224no—
60C4×Q8×C13—224no—
61C4×Q8×C13C2×C418yes—
62C4×Q8×C13D418yescomplemented
63C4×D4×C13C2×C4124yes—
64C13×#117—224no—
65C13×#117—224no—
66C2×C13×C4⋊C4C2313yes—
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2313yes—
69C2×C13×C4⋊C4C2316yes—
70C2×C13×C4⋊C4C2316yes—
71C2×C13×C4⋊C4C2316yes—
72C2×C13×C4⋊C4C2316yes—
73C2×C13×C4⋊C4C2313yes—
74C2×C13×C4⋊C4C2313yes—
75C2×C13×C4⋊C4C2316yes—
76C2×C13×C4⋊C4C2313yes—
77C2×C13×C22⋊C4C2312yes—
78C2×C13×C22⋊C4C2312yes—
79C2×C13×C22⋊C4C2316yes—
80C2×C13×C22⋊C4C2316yes—
81C2×C13×C22⋊C4C2316yes—
82C2×C42×C13C2313yes—
83C2×C42×C13C2316yes—
84C2×C42×C13C2313yes—
85C2×C42×C13C2313yes—
86C2×C42×C13C23112yes—
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2313yes—
89C2×C42×C13C2313yes—
90C2×C42×C13C2313yes—
91C13×#95C2316yes—
92C13×#95C2316yes—
93C13×#95C2316yes—
94C13×#95C23112yes—
95C13×#95C2316yes—
96#34311C1311yesmaximal, characteristic, direct product factor, Sylow
97C24×C13C2412yes—
98C2×Q8×C13—264no—
99C2×Q8×C13—212no—
100C2×Q8×C13—212no—
101C2×Q8×C13C22×C4124yes—
102C2×Q8×C13C22×C414yes—
103C2×Q8×C13C2×D414yes—
104C2×Q8×C13#4114yes—
105C2×D4×C13—22no—
106C2×D4×C13—22no—
107C2×D4×C13C22×C414yes—
108C22×C4×C13—212no—
109C22×C4×C13—212no—
110C22×C4×C13C22×C4124yes—
111C22×C4×C13C2413yes—
112C22×C4×C13C2412yes—
113C22×C4×C13C2416yes—
114C22×C4×C13C2413yes—
115C22×C4×C13C2416yes—
116C22×C4×C13C2413yes—
117C22×C4×C13C2411yescharacteristic
118C22×C4×C13C2411yescharacteristic
119C22×C4×C13C2413yes—
120C22×C4×C13C2411yescharacteristic
121C13×C4⋊C4—212no—
122C13×C4⋊C4—212no—
123C13×C4⋊C4—212no—
124C13×C4⋊C4—26no—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—26no—
127C13×C4⋊C4—46no—
128C13×C4⋊C4C22×C4112yes—
129C13×C4⋊C4C22×C4112yes—
130C13×C4⋊C4C22×C4124yes—
131C13×C4⋊C4C2×D4112yes—
132C13×C22⋊C4—212no—
133C13×C22⋊C4—24no—
134C13×C22⋊C4—24no—
135C13×C22⋊C4—46no—
136C13×C22⋊C4C22×C4124yes—
137C42×C13—224no—
138C42×C13—212no—
139C42×C13—26no—
140C42×C13—26no—
141C42×C13—22no—
142C42×C13—26no—
143C42×C13—43no—
144C42×C13C22×C4112yes—
145C42×C13C2×D4112yes—
146C2×D4×Q8C2×C1311yescharacteristic
147C2×#519C2×C1312yescomplemented
148#2365C2×C1313yescomplemented
149#2362C2×C1316yescomplemented
150#2354C2×C1313yes—
151Q8×C4⋊C4C2×C1311yescharacteristic, complemented
152Q8×C22⋊C4C2×C1312yescomplemented
153#2323C2×C1316yescomplemented
154C4×C4⋊Q8C2×C1313yescomplemented
155#2293C2×C1313yes—
156C42×Q8C2×C1311yescharacteristic, complemented
157C23×C13—22no—
158C23×C13—22no—
159C23×C13—22no—
160C23×C13—22no—
161C23×C13—22no—
162C23×C13—22no—
163C23×C13C23×C414yes—
164C23×C13C2511yescharacteristic
165Q8×C13—248no—
166Q8×C13C4×D4116yes—
167D4×C13—28no—
168C2×C4×C13—26no—
169C2×C4×C13—21no—
170C2×C4×C13—26no—
171C2×C4×C13—23no—
172C2×C4×C13—21no—
173C2×C4×C13—23no—
174C2×C4×C13—23no—
175C2×C4×C13—21no—
176C2×C4×C13—21no—
177C2×C4×C13—23no—
178C2×C4×C13—248no—
179C2×C4×C13—26no—
180C2×C4×C13—22no—
181C2×C4×C13—23no—
182C2×C4×C13—23no—
183C2×C4×C13—22no—
184C2×C4×C13—26no—
185C2×C4×C13—22no—
186C2×C4×C13—23no—
187C2×C4×C13—26no—
188C2×C4×C13C23×C416yes—
189C2×C4×C13C23×C4112yes—
190C2×C4×C13C23×C416yes—
191C2×C4×C13C23×C412yes—
192C2×C4×C13C22×D416yes—
193C2×C4×C13C22×D412yes—
194C2×C4×C13C22×D416yes—
195C2×C4×C13C2×#4116yes—
196C2×C4×C132−1+412yes—
197C2×C4×C132−1+412yes—
198C2×C4×C132−1+412yes—
199C23×Q8C22×C1312yes—
200D4×Q8C4×C13116yescomplemented
201C2×C4⋊Q8C22×C1313yes—
202C2×C22⋊Q8C22×C1316yes—
203#519—216no—
204C2×C4×Q8C22×C1316yes—
205C2×C4×Q8C22×C1311yescharacteristic
206C2×C4×Q8C22×C1312yes—
207C2×C4×Q8C22×C1316yes—
208C2×C4×Q8C22×C1311yescharacteristic
209C2×C4×Q8C22×C1311yescharacteristic
210C2×C4×D4C22×C1313yes—
211C2×#117C22×C1316yes—
212C2×#117C22×C1316yes—
213#391C22×C1316yes—
214#391C22×C1316yes—
215#390C22×C1313yes—
216#390C22×C1311yescharacteristic
217#389C22×C1313yes—
218#389C22×C1316yes—
219#389C22×C1316yes—
220#389C22×C1313yes—
221#388C22×C1316yes—
222#388C22×C13112yes—
223#388C22×C1316yes—
224#387C22×C13112yes—
225#384C22×C1313yes—
226#380C22×C1316yes—
227C4×C4⋊C4C22×C1316yes—
228C4×C4⋊C4C22×C1316yes—
229C4×C4⋊C4C22×C1313yes—
230C4×C4⋊C4C22×C1313yes—
231C4×C4⋊C4C22×C1313yes—
232C4×C4⋊C4C22×C1313yes—
233C4×C22⋊C4C22×C1316yes—
234C43C22×C1313yes—
235C22×C13—24no—
236C22×C13—24no—
237C22×C13—24no—
238C22×C13—42no—
239C22×C13—42no—
240C22×C13—42no—
241C22×C13—42no—
242C22×C13C24×C411yescharacteristic
243C22×C13C23×D411yescharacteristic
244C22×C13C22×#4111yescharacteristic
245C22×C13C2×2−1+411yescharacteristic
246C22×C13C2×2−1+411yescharacteristic
247C22×C13C2×2−1+411yescharacteristic
248C22×C13#58511yescharacteristic
249C4×C13—212no—
250C4×C13—26no—
251C4×C13—22no—
252C4×C13—26no—
253C4×C13—22no—
254C4×C13—46no—
255C4×C13—42no—
256C4×C13—43no—
257C4×C13C2×C4×D4112yes—
258C4×C13#51914yescomplemented
259C22×Q8—28no—
260C22×Q8—28no—
261C22×Q8C2×C4×C13116yes—
262C22×Q8C23×C1316yes—
263C22×Q8C23×C1311yescharacteristic
264C22×D4C23×C1311yescharacteristic
265C23×C4C23×C1316yes—
266C4⋊Q8C2×C4×C13124yes—
267C22⋊Q8C2×C4×C13148yes—
268C4×Q8—28no—
269C4×Q8—24no—
270C4×Q8—224no—
271C4×Q8—224no—
272C4×Q8C2×C4×C1318yes—
273C4×Q8D4×C1318yescomplemented
274C4×D4C2×C4×C13124yes—
275#117—224no—
276#117—224no—
277C2×C4⋊C4C23×C1316yes—
278C2×C4⋊C4C23×C1316yes—
279C2×C4⋊C4C23×C1316yes—
280C2×C4⋊C4C23×C1313yes—
281C2×C4⋊C4C23×C1313yes—
282C2×C4⋊C4C23×C1311yescharacteristic
283C2×C4⋊C4C23×C1316yes—
284C2×C4⋊C4C23×C1313yes—
285C2×C4⋊C4C23×C1313yes—
286C2×C4⋊C4C23×C1316yes—
287C2×C4⋊C4C23×C1313yes—
288C2×C22⋊C4C23×C1312yes—
289C2×C22⋊C4C23×C1316yes—
290C2×C22⋊C4C23×C1312yes—
291C2×C22⋊C4C23×C1316yes—
292C2×C22⋊C4C23×C1316yes—
293C2×C42C23×C1316yes—
294C2×C42C23×C13112yes—
295C2×C42C23×C1313yes—
296C2×C42C23×C1311yescharacteristic
297C2×C42C23×C1313yes—
298C2×C42C23×C1313yes—
299C2×C42C23×C1313yes—
300C2×C42C23×C1313yes—
301C2×C42C23×C1313yes—
302#95C23×C1316yes—
303#95C23×C1316yes—
304#95C23×C1316yes—
305#95C23×C13112yes—
306#95C23×C1316yes—
307C2×C13—44no—
308C2×C13C22×C4×D411yescharacteristic
309C2×C13C2×#51911yescharacteristic
310C2×C13C4×2−1+411yescharacteristic
311C2×C13#349711yescharacteristic
312C2×C13#349911yescharacteristic
313C2×C13#351811yescharacteristic
314C2×C13#352311yescharacteristic
315C24C24×C1312yes—
316C2×Q8—264no—
317C2×Q8—212no—
318C2×Q8—212no—
319C2×Q8C22×C4×C13124yes—
320C2×Q8C22×C4×C1314yes—
321C2×Q8C2×D4×C1314yes—
322C2×Q8C13×#4114yes—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4C22×C4×C1314yes—
326C22×C4—212no—
327C22×C4—212no—
328C22×C4C22×C4×C13124yes—
329C22×C4C24×C1313yes—
330C22×C4C24×C1312yes—
331C22×C4C24×C1316yes—
332C22×C4C24×C1313yes—
333C22×C4C24×C1316yes—
334C22×C4C24×C1313yes—
335C22×C4C24×C1311yescharacteristic
336C22×C4C24×C1311yescharacteristic
337C22×C4C24×C1313yes—
338C22×C4C24×C1311yescharacteristic
339C4⋊C4—212no—
340C4⋊C4—212no—
341C4⋊C4—212no—
342C4⋊C4—26no—
343C4⋊C4—22no—
344C4⋊C4—26no—
345C4⋊C4—46no—
346C4⋊C4C22×C4×C13112yes—
347C4⋊C4C22×C4×C13112yes—
348C4⋊C4C22×C4×C13124yes—
349C4⋊C4C2×D4×C13112yes—
350C22⋊C4—212no—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C22⋊C4—46no—
354C22⋊C4C22×C4×C13124yes—
355C42—224no—
356C42—212no—
357C42—26no—
358C42—26no—
359C42—22no—
360C42—26no—
361C42—43no—
362C42C22×C4×C13112yes—
363C42C2×D4×C13112yes—
364C13#3431111yescharacteristic, direct product factor, Sylow
365C23—22no—
366C23—22no—
367C23—22no—
368C23—22no—
369C23—22no—
370C23—22no—
371C23C23×C4×C1314yes—
372C23C25×C1311yescharacteristic
373Q8—248no—
374Q8C4×D4×C13116yes—
375D4—28no—
376C2×C4—26no—
377C2×C4—21no—
378C2×C4—26no—
379C2×C4—21no—
380C2×C4—23no—
381C2×C4—21no—
382C2×C4—23no—
383C2×C4—23no—
384C2×C4—21no—
385C2×C4—23no—
386C2×C4—248no—
387C2×C4—26no—
388C2×C4—22no—
389C2×C4—23no—
390C2×C4—23no—
391C2×C4—22no—
392C2×C4—26no—
393C2×C4—22no—
394C2×C4—23no—
395C2×C4—26no—
396C2×C4C23×C4×C1316yes—
397C2×C4C23×C4×C13112yes—
398C2×C4C23×C4×C1316yes—
399C2×C4C23×C4×C1312yes—
400C2×C4C22×D4×C1316yes—
401C2×C4C22×D4×C1312yes—
402C2×C4C22×D4×C1316yes—
403C2×C4C2×C13×#4116yes—
404C2×C4C13×2−1+412yes—
405C2×C4C13×2−1+412yes—
406C2×C4C13×2−1+412yes—
407C22—24no—
408C22—24no—
409C22—24no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22C24×C4×C1311yescharacteristic
415C22C23×D4×C1311yescharacteristic
416C22C22×C13×#4111yescharacteristic
417C22C2×C13×2−1+411yescharacteristic
418C22C2×C13×2−1+411yescharacteristic
419C22C2×C13×2−1+411yescharacteristic
420C22C13×#58511yescharacteristic
421C4—22no—
422C4—212no—
423C4—26no—
424C4—22no—
425C4—26no—
426C4—43no—
427C4—46no—
428C4—42no—
429C4C2×C4×D4×C13112yes—
430C4C13×#51914yescomplemented
431C2—44no—
432C2C22×C4×D4×C1311yescharacteristic
433C2C2×C13×#51911yescharacteristic
434C2C4×C13×2−1+411yescharacteristic
435C2C13×#349711yescharacteristic
436C2C13×#349911yescharacteristic
437C2C13×#351811yescharacteristic
438C2C13×#352311yescharacteristic
subgroupG/H
center, socleC23×C13C25
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
prime radicalC22×D4×C13C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#519C2semidirect
3. C13×#2365C2semidirect
4. C13×#2362C2semidirect
6. Q8×C13×C4⋊C4C2semidirect
7. Q8×C13×C22⋊C4C2semidirect
8. C13×#2323C2semidirect
9. C4×C13×C4⋊Q8C2semidirect
11. C42×Q8×C13C2semidirect
13. D4×Q8×C13C4semidirect
62. C4×Q8×C13D4semidirect
96. #34311C13direct (N × H)
147. C2×#519C2×C13semidirect
148. #2365C2×C13semidirect
149. #2362C2×C13semidirect
151. Q8×C4⋊C4C2×C13semidirect
152. Q8×C22⋊C4C2×C13semidirect
153. #2323C2×C13semidirect
154. C4×C4⋊Q8C2×C13semidirect
156. C42×Q8C2×C13semidirect
200. D4×Q8C4×C13semidirect
258. C4×C13#519semidirect
273. C4×Q8D4×C13semidirect
364. C13#34311direct (N × H)
430. C4C13×#519semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C132
C2×C13×#5192
C13×#23652
C13×#23622
C13×#23542
Q8×C13×C4⋊C42
Q8×C13×C22⋊C42
C13×#23232
C4×C13×C4⋊Q82
C13×#22932
C42×Q8×C132
#3431113