Finite Group Databasebeta

← C2×C13×#3523 #15749126

Subgroups — C2×C13×#3523 #15749126

Order 3328.

7022 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3523C2132yesmaximal, direct product factor
2C2×C13×#557C211yesmaximal, characteristic, complemented
3C2×C13×#557C213yesmaximal, complemented
4C2×C13×#556C213yesmaximal, complemented
5C2×C13×#552C216yesmaximal, complemented
6C2×D4×Q8×C13C212yesmaximal, complemented
7C2×D4×Q8×C13C211yesmaximal, characteristic, complemented
8C2×C13×#541C216yesmaximal, complemented
9C2×C13×#533C213yesmaximal, complemented
10C2×C13×#529C213yesmaximal
11C2×C13×#519C212yesmaximal, complemented
12C22×C4×Q8×C13C211yesmaximal, characteristic, complemented
13C23×Q8×C13C2211yescharacteristic
14C23×Q8×C13C2212yes—
15C13×#557C22116yescomplemented
16C13×#557C22148yescomplemented
17C13×#556C22148yescomplemented
18C13×#552C22196yescomplemented
19D4×Q8×C13C22132yescomplemented
20D4×Q8×C13C22116yescomplemented
21C13×#541C22196yescomplemented
22C13×#533C22148yescomplemented
23C2×C13×C4⋊Q8C2213yes—
24C2×C13×C4⋊Q8C2213yes—
25C2×C13×C4⋊Q8C2216yes—
26C13×#529C22148yes—
27C2×C13×#126C2216yes—
28C2×C13×#126C22112yes—
29C2×C13×#125C2213yes—
30C2×C13×#125C2216yes—
31C2×C13×#125C22112yes—
32C2×C13×#125C2216yes—
33C2×C13×#124C2213yes—
34C2×C13×#123C2216yes—
35C2×C13×C22⋊Q8C2213yes—
36C2×C13×C22⋊Q8C2216yes—
37C2×C13×C22⋊Q8C2216yes—
38C2×C13×C22⋊Q8C2216yes—
39C2×C13×#121C2211yescharacteristic
40C13×#519C22132yescomplemented
41C2×C4×Q8×C13C2211yescharacteristic
42C2×C4×Q8×C13C2213yes—
43C2×C4×Q8×C13C2211yescharacteristic
44C2×C4×Q8×C13C2213yes—
45C2×C4×Q8×C13C2216yes—
46C2×C4×Q8×C13C2212yes—
47C2×C4×Q8×C13C2216yes—
48C2×C4×Q8×C13C2213yes—
49C2×C4×Q8×C13C2216yes—
50C2×C4×Q8×C13C22116yescomplemented
51C2×C4×D4×C13C2216yes—
52C2×C4×D4×C13C2213yes—
53C2×C13×#117C2216yes—
54C2×C13×#117C2216yes—
55C2×C13×#117C2216yes—
56C22×C13×C4⋊C4C2213yes—
57C22×C42×C13C2213yes—
58C22×Q8×C13—28no—
59C22×Q8×C13—216no—
60C22×Q8×C13C2313yes—
61C22×Q8×C13C2313yes—
62C22×Q8×C13C2316yes—
63C22×Q8×C13C2318yes—
64C22×Q8×C13C23116yes—
65C22×Q8×C13C2311yescharacteristic
66C22×D4×C13C2312yes—
67C22×D4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2313yes—
70C23×C4×C13C2313yes—
71C23×C4×C13C2316yes—
72C13×C4⋊Q8C23124yes—
73C13×C4⋊Q8C23124yes—
74C13×C4⋊Q8C23148yes—
75C13×#126C23148yes—
76C13×#126C23196yes—
77C13×#125C23124yes—
78C13×#125C23148yes—
79C13×#125C23196yes—
80C13×#125C23148yes—
81C13×#124C23124yes—
82C13×#123C23148yes—
83C13×C22⋊Q8C23124yes—
84C13×C22⋊Q8C23148yes—
85C13×C22⋊Q8C23148yes—
86C13×C22⋊Q8C23148yes—
87C13×#121C2318yes—
88C4×Q8×C13C2318yes—
89C4×Q8×C13C23124yes—
90C4×Q8×C13C2318yes—
91C4×Q8×C13C23124yes—
92C4×Q8×C13C23148yes—
93C4×Q8×C13C23116yes—
94C4×Q8×C13C23148yes—
95C4×Q8×C13C23124yes—
96C4×Q8×C13C23148yes—
97C4×D4×C13C23148yes—
98C4×D4×C13C23124yes—
99C13×#117C23148yes—
100C13×#117C23148yes—
101C13×#117C23148yes—
102C2×C13×C4⋊C4C2313yes—
103C2×C13×C4⋊C4C2313yes—
104C2×C13×C4⋊C4C2316yes—
105C2×C13×C4⋊C4C23124yes—
106C2×C13×C4⋊C4C2316yes—
107C2×C13×C4⋊C4C2316yes—
108C2×C13×C4⋊C4C2316yes—
109C2×C13×C4⋊C4C2316yes—
110C2×C13×C4⋊C4C2316yes—
111C2×C13×C4⋊C4C2313yes—
112C2×C13×C4⋊C4C2316yes—
113C2×C13×C4⋊C4C2311yescharacteristic
114C2×C13×C4⋊C4C23112yes—
115C2×C13×C4⋊C4C2316yes—
116C2×C13×C22⋊C4C2312yes—
117C2×C13×C22⋊C4C2316yes—
118C2×C13×C22⋊C4C2316yes—
119C2×C13×C22⋊C4C2316yes—
120C2×C13×C22⋊C4C2316yes—
121C2×C42×C13C2313yes—
122C2×C42×C13C2313yes—
123C2×C42×C13C2313yes—
124C2×C42×C13C2313yes—
125C2×C42×C13C23124yes—
126C2×C42×C13C23112yes—
127C2×C42×C13C2316yes—
128C2×#3523C1311yesmaximal, characteristic, direct product factor, Sylow
129C24×C13C2412yes—
130C24×C13C2411yescharacteristic
131C2×Q8×C13—232no—
132C2×Q8×C13—264no—
133C2×Q8×C13—212no—
134C2×Q8×C13—224no—
135C2×Q8×C13—212no—
136C2×Q8×C13#4118yes—
137C2×Q8×C13C24112yes—
138C2×Q8×C13C24112yes—
139C2×Q8×C13C24124yes—
140C2×Q8×C13C2414yes—
141C2×D4×C13—28no—
142C2×D4×C13—24no—
143C2×D4×C13C2418yes—
144C2×D4×C13C2414yes—
145C22×C4×C13—212no—
146C22×C4×C13—212no—
147C22×C4×C13—224no—
148C22×C4×C13—24no—
149C22×C4×C13C2414yes—
150C22×C4×C13C24112yes—
151C22×C4×C13C24112yes—
152C22×C4×C13C24124yes—
153C22×C4×C13C2411yescharacteristic
154C22×C4×C13C2413yes—
155C22×C4×C13C2416yes—
156C22×C4×C13C2412yes—
157C22×C4×C13C2413yes—
158C22×C4×C13C2413yes—
159C22×C4×C13C2416yes—
160C22×C4×C13C2413yes—
161C22×C4×C13C2411yescharacteristic
162C13×C4⋊C4C24112yes—
163C13×C4⋊C4C24112yes—
164C13×C4⋊C4C24124yes—
165C13×C4⋊C4C24124yes—
166C13×C4⋊C4C24124yes—
167C13×C4⋊C4C24124yes—
168C13×C4⋊C4C24124yes—
169C13×C4⋊C4C24124yes—
170C13×C4⋊C4C24112yes—
171C13×C4⋊C4C24124yes—
172C13×C4⋊C4C2414yes—
173C13×C4⋊C4C24148yes—
174C13×C4⋊C4C24124yes—
175C13×C22⋊C4C2418yes—
176C13×C22⋊C4C24124yes—
177C13×C22⋊C4C24124yes—
178C13×C22⋊C4C24124yes—
179C13×C22⋊C4C24124yes—
180C42×C13C24112yes—
181C42×C13C24112yes—
182C42×C13C24112yes—
183C42×C13C24112yes—
184C42×C13C24148yes—
185C42×C13C24124yes—
186#3523C2×C13132yesdirect product factor
187C2×#557C2×C1311yescharacteristic, complemented
188C2×#557C2×C1313yescomplemented
189C2×#556C2×C1313yescomplemented
190C2×#552C2×C1316yescomplemented
191C2×D4×Q8C2×C1312yescomplemented
192C2×D4×Q8C2×C1311yescharacteristic, complemented
193C2×#541C2×C1316yescomplemented
194C2×#533C2×C1313yescomplemented
195C2×#529C2×C1313yes—
196C2×#519C2×C1312yescomplemented
197C22×C4×Q8C2×C1311yescharacteristic, complemented
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—24no—
201C23×C13—24no—
202C23×C13—24no—
203C23×C132−1+414yes—
204C23×C13C2514yes—
205C23×C13C2512yes—
206C23×C13C2511yescharacteristic
207Q8×C13—224no—
208Q8×C13—248no—
209Q8×C13—224no—
210Q8×C13C2×#41116yes—
211D4×C13—216no—
212D4×C13—28no—
213C2×C4×C13—26no—
214C2×C4×C13—212no—
215C2×C4×C13—224no—
216C2×C4×C13—26no—
217C2×C4×C13—26no—
218C2×C4×C13—22no—
219C2×C4×C13—24no—
220C2×C4×C13—212no—
221C2×C4×C13—224no—
222C2×C4×C13—248no—
223C2×C4×C13—28no—
224C2×C4×C13C2×#41112yes—
225C2×C4×C132−1+414yes—
226C2×C4×C13C2512yes—
227C2×C4×C13C2516yes—
228C2×C4×C13C25112yes—
229C2×C4×C13C2514yes—
230C2×C4×C13C2516yes—
231C2×C4×C13C2516yes—
232C2×C4×C13C25112yes—
233C2×C4×C13C2516yes—
234C2×C4×C13C2512yes—
235C23×Q8C22×C1311yescharacteristic
236C23×Q8C22×C1312yes—
237#557C22×C13116yescomplemented
238#557C22×C13148yescomplemented
239#556C22×C13148yescomplemented
240#552C22×C13196yescomplemented
241D4×Q8C22×C13132yescomplemented
242D4×Q8C22×C13116yescomplemented
243#541C22×C13196yescomplemented
244#533C22×C13148yescomplemented
245C2×C4⋊Q8C22×C1313yes—
246C2×C4⋊Q8C22×C1313yes—
247C2×C4⋊Q8C22×C1316yes—
248#529C22×C13148yes—
249C2×#126C22×C1316yes—
250C2×#126C22×C13112yes—
251C2×#125C22×C1313yes—
252C2×#125C22×C1316yes—
253C2×#125C22×C13112yes—
254C2×#125C22×C1316yes—
255C2×#124C22×C1313yes—
256C2×#123C22×C1316yes—
257C2×C22⋊Q8C22×C1313yes—
258C2×C22⋊Q8C22×C1316yes—
259C2×C22⋊Q8C22×C1316yes—
260C2×C22⋊Q8C22×C1316yes—
261C2×#121C22×C1311yescharacteristic
262#519C22×C13132yescomplemented
263C2×C4×Q8C22×C1311yescharacteristic
264C2×C4×Q8C22×C1313yes—
265C2×C4×Q8C22×C1311yescharacteristic
266C2×C4×Q8C22×C1313yes—
267C2×C4×Q8C22×C1316yes—
268C2×C4×Q8C22×C1312yes—
269C2×C4×Q8C22×C1316yes—
270C2×C4×Q8C22×C1313yes—
271C2×C4×Q8C22×C1316yes—
272C2×C4×Q8C22×C13116yescomplemented
273C2×C4×D4C22×C1316yes—
274C2×C4×D4C22×C1313yes—
275C2×#117C22×C1316yes—
276C2×#117C22×C1316yes—
277C2×#117C22×C1316yes—
278C22×C4⋊C4C22×C1313yes—
279C22×C42C22×C1313yes—
280C22×C13—22no—
281C22×C13—22no—
282C22×C13—28no—
283C22×C13—24no—
284C22×C13—24no—
285C22×C13—24no—
286C22×C13—48no—
287C22×C13C22×#4112yes—
288C22×C13C2×2−1+414yes—
289C22×C13C2×2−1+412yes—
290C22×C13C2×2−1+412yes—
291C22×C13C2611yescharacteristic
292C4×C13—26no—
293C4×C13—212no—
294C4×C13—26no—
295C4×C13—26no—
296C4×C13—22no—
297C4×C13—24no—
298C4×C13—212no—
299C4×C13C22×#41112yes—
300C4×C13C2×2−1+414yes—
301C22×Q8—28no—
302C22×Q8—216no—
303C22×Q8C23×C1313yes—
304C22×Q8C23×C1313yes—
305C22×Q8C23×C1316yes—
306C22×Q8C23×C1318yes—
307C22×Q8C23×C13116yes—
308C22×Q8C23×C1311yescharacteristic
309C22×D4C23×C1312yes—
310C22×D4C23×C1311yescharacteristic
311C23×C4C23×C1313yes—
312C23×C4C23×C1313yes—
313C23×C4C23×C1316yes—
314C23×C4C23×C1311yescharacteristic
315C4⋊Q8C23×C13124yes—
316C4⋊Q8C23×C13124yes—
317C4⋊Q8C23×C13148yes—
318#126C23×C13148yes—
319#126C23×C13196yes—
320#125C23×C13124yes—
321#125C23×C13148yes—
322#125C23×C13196yes—
323#125C23×C13148yes—
324#124C23×C13124yes—
325#123C23×C13148yes—
326C22⋊Q8C23×C13124yes—
327C22⋊Q8C23×C13148yes—
328C22⋊Q8C23×C13148yes—
329C22⋊Q8C23×C13148yes—
330#121C23×C1318yes—
331C4×Q8C23×C1318yes—
332C4×Q8C23×C13124yes—
333C4×Q8C23×C1318yes—
334C4×Q8C23×C13124yes—
335C4×Q8C23×C13148yes—
336C4×Q8C23×C13116yes—
337C4×Q8C23×C13148yes—
338C4×Q8C23×C13124yes—
339C4×Q8C23×C13148yes—
340C4×D4C23×C13148yes—
341C4×D4C23×C13124yes—
342#117C23×C13148yes—
343#117C23×C13148yes—
344#117C23×C13148yes—
345C2×C4⋊C4C23×C1313yes—
346C2×C4⋊C4C23×C1313yes—
347C2×C4⋊C4C23×C1316yes—
348C2×C4⋊C4C23×C13124yes—
349C2×C4⋊C4C23×C1316yes—
350C2×C4⋊C4C23×C1316yes—
351C2×C4⋊C4C23×C1316yes—
352C2×C4⋊C4C23×C1316yes—
353C2×C4⋊C4C23×C1316yes—
354C2×C4⋊C4C23×C1313yes—
355C2×C4⋊C4C23×C1316yes—
356C2×C4⋊C4C23×C1311yescharacteristic
357C2×C4⋊C4C23×C13112yes—
358C2×C4⋊C4C23×C1316yes—
359C2×C22⋊C4C23×C1312yes—
360C2×C22⋊C4C23×C1316yes—
361C2×C22⋊C4C23×C1316yes—
362C2×C22⋊C4C23×C1316yes—
363C2×C22⋊C4C23×C1316yes—
364C2×C42C23×C1313yes—
365C2×C42C23×C13112yes—
366C2×C42C23×C1316yes—
367C2×C42C23×C1313yes—
368C2×C42C23×C1313yes—
369C2×C42C23×C1313yes—
370C2×C42C23×C13124yes—
371C2×C13—24no—
372C2×C13—44no—
373C2×C13#352314yesdirect product factor
374C2×C13C23×#4111yescharacteristic
375C2×C13C22×2−1+411yescharacteristic
376C2×C13C22×2−1+411yescharacteristic
377C24C24×C1312yes—
378C24C24×C1311yescharacteristic
379C2×Q8—232no—
380C2×Q8—264no—
381C2×Q8—212no—
382C2×Q8—224no—
383C2×Q8—212no—
384C2×Q8C13×#4118yes—
385C2×Q8C24×C13112yes—
386C2×Q8C24×C13112yes—
387C2×Q8C24×C13124yes—
388C2×Q8C24×C1314yes—
389C2×D4—28no—
390C2×D4—24no—
391C2×D4C24×C1318yes—
392C2×D4C24×C1314yes—
393C22×C4—212no—
394C22×C4—212no—
395C22×C4—224no—
396C22×C4—24no—
397C22×C4C24×C1311yescharacteristic
398C22×C4C24×C1313yes—
399C22×C4C24×C1314yes—
400C22×C4C24×C1316yes—
401C22×C4C24×C1312yes—
402C22×C4C24×C1313yes—
403C22×C4C24×C1316yes—
404C22×C4C24×C1313yes—
405C22×C4C24×C13112yes—
406C22×C4C24×C13112yes—
407C22×C4C24×C13124yes—
408C22×C4C24×C1313yes—
409C22×C4C24×C1311yescharacteristic
410C4⋊C4C24×C13112yes—
411C4⋊C4C24×C13112yes—
412C4⋊C4C24×C13124yes—
413C4⋊C4C24×C13124yes—
414C4⋊C4C24×C13124yes—
415C4⋊C4C24×C13124yes—
416C4⋊C4C24×C13124yes—
417C4⋊C4C24×C13124yes—
418C4⋊C4C24×C13112yes—
419C4⋊C4C24×C13124yes—
420C4⋊C4C24×C1314yes—
421C4⋊C4C24×C13148yes—
422C4⋊C4C24×C13124yes—
423C22⋊C4C24×C1318yes—
424C22⋊C4C24×C13124yes—
425C22⋊C4C24×C13124yes—
426C22⋊C4C24×C13124yes—
427C22⋊C4C24×C13124yes—
428C42C24×C13112yes—
429C42C24×C13112yes—
430C42C24×C13112yes—
431C42C24×C13112yes—
432C42C24×C13148yes—
433C42C24×C13124yes—
434C13C2×#352311yescharacteristic, direct product factor, Sylow
435C23—22no—
436C23—22no—
437C23—24no—
438C23—24no—
439C23—24no—
440C23C13×2−1+414yes—
441C23C25×C1314yes—
442C23C25×C1312yes—
443C23C25×C1311yescharacteristic
444Q8—224no—
445Q8—248no—
446Q8—224no—
447Q8C2×C13×#41116yes—
448D4—216no—
449D4—28no—
450C2×C4—26no—
451C2×C4—212no—
452C2×C4—224no—
453C2×C4—26no—
454C2×C4—26no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—212no—
458C2×C4—224no—
459C2×C4—248no—
460C2×C4—28no—
461C2×C4C2×C13×#41112yes—
462C2×C4C13×2−1+414yes—
463C2×C4C25×C1312yes—
464C2×C4C25×C1316yes—
465C2×C4C25×C13112yes—
466C2×C4C25×C1314yes—
467C2×C4C25×C1316yes—
468C2×C4C25×C1316yes—
469C2×C4C25×C13112yes—
470C2×C4C25×C1316yes—
471C2×C4C25×C1312yes—
472C22—28no—
473C22—22no—
474C22—22no—
475C22—24no—
476C22—24no—
477C22—24no—
478C22—48no—
479C22C22×C13×#4112yes—
480C22C2×C13×2−1+414yes—
481C22C2×C13×2−1+412yes—
482C22C2×C13×2−1+412yes—
483C22C26×C1311yescharacteristic
484C4—26no—
485C4—212no—
486C4—26no—
487C4—26no—
488C4—22no—
489C4—24no—
490C4—212no—
491C4C22×C13×#41112yes—
492C4C2×C13×2−1+414yes—
493C2—24no—
494C2—44no—
495C2C13×#352314yesdirect product factor
496C2C23×C13×#4111yescharacteristic
497C2C22×C13×2−1+411yescharacteristic
498C2C22×C13×2−1+411yescharacteristic
subgroupG/H
center, socleC23×C13C25
commutator, Frattini, cosocleC22C26×C13
prime radicalC2×C13×#121C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3523C2direct (N × H)
2. C2×C13×#557C2semidirect
3. C2×C13×#557C2semidirect
4. C2×C13×#556C2semidirect
5. C2×C13×#552C2semidirect
6. C2×D4×Q8×C13C2semidirect
7. C2×D4×Q8×C13C2semidirect
8. C2×C13×#541C2semidirect
9. C2×C13×#533C2semidirect
11. C2×C13×#519C2semidirect
12. C22×C4×Q8×C13C2semidirect
15. C13×#557C22semidirect
16. C13×#557C22semidirect
17. C13×#556C22semidirect
18. C13×#552C22semidirect
19. D4×Q8×C13C22semidirect
20. D4×Q8×C13C22semidirect
21. C13×#541C22semidirect
22. C13×#533C22semidirect
40. C13×#519C22semidirect
50. C2×C4×Q8×C13C22semidirect
128. C2×#3523C13direct (N × H)
186. #3523C2×C13direct (N × H)
187. C2×#557C2×C13semidirect
188. C2×#557C2×C13semidirect
189. C2×#556C2×C13semidirect
190. C2×#552C2×C13semidirect
191. C2×D4×Q8C2×C13semidirect
192. C2×D4×Q8C2×C13semidirect
193. C2×#541C2×C13semidirect
194. C2×#533C2×C13semidirect
196. C2×#519C2×C13semidirect
197. C22×C4×Q8C2×C13semidirect
237. #557C22×C13semidirect
238. #557C22×C13semidirect
239. #556C22×C13semidirect
240. #552C22×C13semidirect
241. D4×Q8C22×C13semidirect
242. D4×Q8C22×C13semidirect
243. #541C22×C13semidirect
244. #533C22×C13semidirect
262. #519C22×C13semidirect
272. C2×C4×Q8C22×C13semidirect
373. C2×C13#3523direct (N × H)
434. C13C2×#3523direct (N × H)
495. C2C13×#3523direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35232
C2×C13×#5572
C2×C13×#5562
C2×C13×#5522
C2×D4×Q8×C132
C2×C13×#5412
C2×C13×#5332
C2×C13×#5292
C2×C13×#5192
C22×C4×Q8×C132
C2×#352313