Finite Group Databasebeta

← C13×#34263 #15720602

Subgroups — C13×#34263 #15720602

Order 3328.

2390 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#520C211yesmaximal, characteristic
2C13×#2357C213yesmaximal, complemented
3C13×#2354C213yesmaximal, complemented
4C13×#2351C211yesmaximal, characteristic, complemented
5Q8×C13×C4⋊C4C211yesmaximal, characteristic, complemented
6C13×#2345C213yesmaximal, complemented
7C13×#2344C213yesmaximal, complemented
8C13×#2341C211yesmaximal, characteristic
9C13×#2341C211yesmaximal, characteristic
10C13×#2319C213yesmaximal, complemented
11C13×#2314C213yesmaximal, complemented
12C13×#2298C213yesmaximal, complemented
13C13×#2293C213yesmaximal, complemented
14C13×#2276C211yesmaximal, characteristic, complemented
15C42×Q8×C13C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C13×#520C4116yescomplemented
18C2×C4×Q8×C13C2211yescharacteristic
19C2×C4×Q8×C13C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×Q8×C13C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×Q8×C13C2211yescharacteristic
24C2×C4×D4×C13C2213yes—
25C2×C4×D4×C13C2213yes—
26C2×C13×#117C2216yes—
27C2×C13×#117C2213yes—
28C22×C13×C4⋊C4C2213yes—
29C13×#390C2213yes—
30C13×#390C2213yes—
31C13×#390C2213yes—
32C13×#390C2213yes—
33C13×#389C2213yes—
34C13×#389C2213yes—
35C13×#389C2213yes—
36C13×#389C2213yes—
37C13×#388C2213yes—
38C13×#388C2216yes—
39C13×#388C2213yes—
40C13×#388C2213yes—
41C13×#388C2213yes—
42C13×#388C2216yes—
43C13×#387C2211yescharacteristic
44C13×#387C2213yes—
45C13×#387C2213yes—
46C13×#387C2213yes—
47C13×#387C2216yes—
48C13×#384C2213yes—
49C13×#382C2213yes—
50C13×#381C2216yes—
51C13×#380C2213yes—
52C13×#380C2213yes—
53C13×#380C2216yes—
54C4×C13×C4⋊C4C2213yes—
55C4×C13×C4⋊C4C2213yes—
56C4×C13×C4⋊C4C2213yes—
57C4×C13×C4⋊C4C2213yes—
58C4×C13×C4⋊C4C2213yes—
59C4×C13×C4⋊C4C2213yes—
60C4×C13×C4⋊C4C2213yes—
61C4×C13×C4⋊C4C2213yes—
62C4×C13×C22⋊C4C2216yes—
63C4×C13×C22⋊C4C2213yes—
64C4×C13×C22⋊C4C2213yes—
65C13×#376C2213yes—
66C43×C13C2213yes—
67C2×C13×#41—24no—
68C2×C13×#41—24no—
69C2×C13×#41C2×C418yes—
70C22×Q8×C13C2311yescharacteristic
71C22×D4×C13C2313yes—
72C23×C4×C13C2313yes—
73C23×C4×C13C2316yes—
74C4×Q8×C13—24no—
75C4×Q8×C13—24no—
76C4×Q8×C13—24no—
77C4×Q8×C13—24no—
78C4×Q8×C13C2×C418yes—
79C4×Q8×C13C2×C418yes—
80C4×D4×C13C2×C4124yes—
81C4×D4×C13C2×C4124yes—
82C13×#117—412no—
83C13×#117C2×C4124yes—
84C2×C13×C4⋊C4C2×C4124yes—
85C2×C13×C4⋊C4C2311yescharacteristic
86C2×C13×C4⋊C4C2313yes—
87C2×C13×C4⋊C4C2313yes—
88C2×C13×C4⋊C4C2313yes—
89C2×C13×C4⋊C4C2313yes—
90C2×C13×C4⋊C4C2313yes—
91C2×C13×C4⋊C4C2313yes—
92C2×C13×C4⋊C4C2313yes—
93C2×C13×C4⋊C4C2316yes—
94C2×C13×C4⋊C4C2313yes—
95C2×C13×C4⋊C4C2313yes—
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C13×C4⋊C4C2313yes—
98C2×C13×C22⋊C4C2313yes—
99C2×C13×C22⋊C4C2313yes—
100C2×C13×C22⋊C4C2316yes—
101C2×C13×C22⋊C4C2313yes—
102C2×C13×C22⋊C4C2313yes—
103C2×C13×C22⋊C4C2316yes—
104C2×C13×C22⋊C4C2313yes—
105C2×C13×C22⋊C4C2313yes—
106C2×C42×C13C2313yes—
107C2×C42×C13C2313yes—
108C2×C42×C13C2313yes—
109C2×C42×C13C2313yes—
110C2×C42×C13C2313yes—
111C2×C42×C13C2311yescharacteristic
112C2×C42×C13C2313yes—
113C2×C42×C13C2316yes—
114C2×C42×C13C2313yes—
115C2×C42×C13C2313yes—
116C2×C42×C13C2313yes—
117C13×#95C2311yescharacteristic
118C13×#95C2311yescharacteristic
119C13×#95C2313yes—
120C13×#95C2313yes—
121C13×#95C2313yes—
122C13×#95C2316yes—
123C13×#95C2316yes—
124C13×#95C2311yescharacteristic
125C13×#95C2313yes—
126C13×#95C2313yes—
127C13×#95C2313yes—
128C13×#95C2313yes—
129C13×#95C2313yes—
130C13×#95C2311yescharacteristic
131#34263C1311yesmaximal, characteristic, direct product factor, Sylow
132C24×C13C2413yes—
133C13×#41—232no—
134C2×Q8×C13C22×C414yes—
135C2×Q8×C13#4114yes—
136C2×Q8×C13#4114yes—
137C2×D4×C13—26no—
138C2×D4×C13—26no—
139C2×D4×C13C22×C4112yes—
140C22×C4×C13—26no—
141C22×C4×C13—26no—
142C22×C4×C13—46no—
143C22×C4×C13—46no—
144C22×C4×C13C22×C4112yes—
145C22×C4×C13C22×C4124yes—
146C22×C4×C13C2411yescharacteristic
147C22×C4×C13C2411yescharacteristic
148C22×C4×C13C2413yes—
149C22×C4×C13C2413yes—
150C22×C4×C13C2413yes—
151C22×C4×C13C2413yes—
152C22×C4×C13C2411yescharacteristic
153C22×C4×C13C2411yescharacteristic
154C22×C4×C13C2413yes—
155C22×C4×C13C2411yescharacteristic
156C22×C4×C13C2413yes—
157C22×C4×C13C2411yescharacteristic
158C22×C4×C13C2411yescharacteristic
159C22×C4×C13C2413yes—
160C13×C4⋊C4—26no—
161C13×C4⋊C4—26no—
162C13×C4⋊C4—26no—
163C13×C4⋊C4—26no—
164C13×C4⋊C4—26no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—43no—
167C13×C4⋊C4—43no—
168C13×C4⋊C4—46no—
169C13×C4⋊C4C22×C4112yes—
170C13×C4⋊C4C22×C4112yes—
171C13×C4⋊C4C22×C4112yes—
172C13×C4⋊C4C22×C414yes—
173C13×C22⋊C4—26no—
174C13×C22⋊C4—26no—
175C13×C22⋊C4—46no—
176C13×C22⋊C4—43no—
177C13×C22⋊C4—43no—
178C13×C22⋊C4—46no—
179C13×C22⋊C4C22×C4112yes—
180C13×C22⋊C4C22×C4112yes—
181C42×C13—26no—
182C42×C13—26no—
183C42×C13—26no—
184C42×C13—26no—
185C42×C13—26no—
186C42×C13—22no—
187C42×C13—43no—
188C42×C13—43no—
189C42×C13—46no—
190C42×C13C22×C4112yes—
191C42×C13C22×C4112yes—
192C2×#520C2×C1311yescharacteristic
193#2357C2×C1313yescomplemented
194#2354C2×C1313yescomplemented
195#2351C2×C1311yescharacteristic, complemented
196Q8×C4⋊C4C2×C1311yescharacteristic, complemented
197#2345C2×C1313yescomplemented
198#2344C2×C1313yescomplemented
199#2341C2×C1311yescharacteristic
200#2341C2×C1311yescharacteristic
201#2319C2×C1313yescomplemented
202#2314C2×C1313yescomplemented
203#2298C2×C1313yescomplemented
204#2293C2×C1313yescomplemented
205#2276C2×C1311yescharacteristic, complemented
206C42×Q8C2×C1311yescharacteristic, complemented
207C23×C13—23no—
208C23×C13—23no—
209C23×C13—23no—
210C23×C13—23no—
211C23×C13—23no—
212C23×C13—23no—
213C23×C13C23×C416yes—
214C23×C13C2511yescharacteristic
215Q8×C13#117116yescomplemented
216D4×C13—224no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—23no—
222C2×C4×C13—23no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—23no—
229C2×C4×C13—21no—
230C2×C4×C13—23no—
231C2×C4×C13—224no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—23no—
235C2×C4×C13—23no—
236C2×C4×C13—23no—
237C2×C4×C13—23no—
238C2×C4×C13—23no—
239C2×C4×C13—23no—
240C2×C4×C13—23no—
241C2×C4×C13—23no—
242C2×C4×C13—21no—
243C2×C4×C13—23no—
244C2×C4×C13—23no—
245C2×C4×C13—23no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—23no—
249C2×C4×C13—21no—
250C2×C4×C13—424no—
251C2×C4×C13C23×C412yes—
252C2×C4×C13C23×C412yes—
253C2×C4×C13C23×C416yes—
254C2×C4×C13C23×C416yes—
255C2×C4×C13C23×C412yes—
256C2×C4×C13C23×C416yes—
257C2×C4×C13C2×#4116yes—
258C2×C4×C13C2×#4116yes—
259C2×C4×C13H(5,𝔽2)12yes—
260C2×C4×C132−1+412yes—
261C22×#41C22×C1311yescharacteristic
262#520C4×C13116yescomplemented
263C2×C4×Q8C22×C1311yescharacteristic
264C2×C4×Q8C22×C1311yescharacteristic
265C2×C4×Q8C22×C1311yescharacteristic
266C2×C4×Q8C22×C1311yescharacteristic
267C2×C4×Q8C22×C1311yescharacteristic
268C2×C4×Q8C22×C1311yescharacteristic
269C2×C4×D4C22×C1313yes—
270C2×C4×D4C22×C1313yes—
271C2×#117C22×C1316yes—
272C2×#117C22×C1313yes—
273C22×C4⋊C4C22×C1313yes—
274#390C22×C1313yes—
275#390C22×C1313yes—
276#390C22×C1313yes—
277#390C22×C1313yes—
278#389C22×C1313yes—
279#389C22×C1313yes—
280#389C22×C1313yes—
281#389C22×C1313yes—
282#388C22×C1316yes—
283#388C22×C1316yes—
284#388C22×C1313yes—
285#388C22×C1313yes—
286#388C22×C1313yes—
287#388C22×C1313yes—
288#387C22×C1313yes—
289#387C22×C1316yes—
290#387C22×C1313yes—
291#387C22×C1313yes—
292#387C22×C1311yescharacteristic
293#384C22×C1313yes—
294#382C22×C1313yes—
295#381C22×C1316yes—
296#380C22×C1313yes—
297#380C22×C1313yes—
298#380C22×C1316yes—
299C4×C4⋊C4C22×C1313yes—
300C4×C4⋊C4C22×C1313yes—
301C4×C4⋊C4C22×C1313yes—
302C4×C4⋊C4C22×C1313yes—
303C4×C4⋊C4C22×C1313yes—
304C4×C4⋊C4C22×C1313yes—
305C4×C4⋊C4C22×C1313yes—
306C4×C4⋊C4C22×C1313yes—
307C4×C22⋊C4C22×C1313yes—
308C4×C22⋊C4C22×C1313yes—
309C4×C22⋊C4C22×C1316yes—
310#376C22×C1313yes—
311C43C22×C1313yes—
312C22×C13—26no—
313C22×C13—26no—
314C22×C13—26no—
315C22×C13—43no—
316C22×C13—43no—
317C22×C13—43no—
318C22×C13—43no—
319C22×C13C24×C411yescharacteristic
320C22×C13C22×#4111yescharacteristic
321C22×C13C22×#4111yescharacteristic
322C22×C13C2×H(5,𝔽2)11yescharacteristic
323C22×C13C2×2−1+411yescharacteristic
324C22×C13#58511yescharacteristic
325C22×C13#58511yescharacteristic
326C4×C13—22no—
327C4×C13—26no—
328C4×C13—26no—
329C4×C13—22no—
330C4×C13—22no—
331C4×C13—22no—
332C4×C13—22no—
333C4×C13—41no—
334C4×C13—43no—
335C4×C13—43no—
336C4×C13—43no—
337C4×C13—41no—
338C4×C13—43no—
339C4×C13C2×#117112yes—
340C2×#41—24no—
341C2×#41—24no—
342C2×#41C2×C4×C1318yes—
343C22×Q8C23×C1311yescharacteristic
344C22×D4C23×C1313yes—
345C23×C4C23×C1313yes—
346C23×C4C23×C1316yes—
347C4×Q8—24no—
348C4×Q8—24no—
349C4×Q8—24no—
350C4×Q8—24no—
351C4×Q8C2×C4×C1318yes—
352C4×Q8C2×C4×C1318yes—
353C4×D4C2×C4×C13124yes—
354C4×D4C2×C4×C13124yes—
355#117—412no—
356#117C2×C4×C13124yes—
357C2×C4⋊C4C2×C4×C13124yes—
358C2×C4⋊C4C23×C1313yes—
359C2×C4⋊C4C23×C1313yes—
360C2×C4⋊C4C23×C1313yes—
361C2×C4⋊C4C23×C1313yes—
362C2×C4⋊C4C23×C1313yes—
363C2×C4⋊C4C23×C1311yescharacteristic
364C2×C4⋊C4C23×C1316yes—
365C2×C4⋊C4C23×C1313yes—
366C2×C4⋊C4C23×C1313yes—
367C2×C4⋊C4C23×C1313yes—
368C2×C4⋊C4C23×C1313yes—
369C2×C4⋊C4C23×C1313yes—
370C2×C4⋊C4C23×C1311yescharacteristic
371C2×C22⋊C4C23×C1313yes—
372C2×C22⋊C4C23×C1313yes—
373C2×C22⋊C4C23×C1316yes—
374C2×C22⋊C4C23×C1313yes—
375C2×C22⋊C4C23×C1316yes—
376C2×C22⋊C4C23×C1313yes—
377C2×C22⋊C4C23×C1313yes—
378C2×C22⋊C4C23×C1313yes—
379C2×C42C23×C1313yes—
380C2×C42C23×C1313yes—
381C2×C42C23×C1313yes—
382C2×C42C23×C1313yes—
383C2×C42C23×C1313yes—
384C2×C42C23×C1311yescharacteristic
385C2×C42C23×C1316yes—
386C2×C42C23×C1313yes—
387C2×C42C23×C1313yes—
388C2×C42C23×C1313yes—
389C2×C42C23×C1313yes—
390#95C23×C1311yescharacteristic
391#95C23×C1313yes—
392#95C23×C1313yes—
393#95C23×C1313yes—
394#95C23×C1311yescharacteristic
395#95C23×C1311yescharacteristic
396#95C23×C1313yes—
397#95C23×C1313yes—
398#95C23×C1313yes—
399#95C23×C1316yes—
400#95C23×C1316yes—
401#95C23×C1311yescharacteristic
402#95C23×C1313yes—
403#95C23×C1313yes—
404C2×C13—46no—
405C2×C13C22×#11711yescharacteristic
406C2×C13C4×H(5,𝔽2)11yescharacteristic
407C2×C13C4×2−1+411yescharacteristic
408C2×C13#351611yescharacteristic
409C2×C13#351711yescharacteristic
410C2×C13#352211yescharacteristic
411C2×C13#352411yescharacteristic
412C24C24×C1313yes—
413#41—232no—
414C2×Q8C22×C4×C1314yes—
415C2×Q8C13×#4114yes—
416C2×Q8C13×#4114yes—
417C2×D4—26no—
418C2×D4—26no—
419C2×D4C22×C4×C13112yes—
420C22×C4—26no—
421C22×C4—26no—
422C22×C4—46no—
423C22×C4—46no—
424C22×C4C22×C4×C13112yes—
425C22×C4C22×C4×C13124yes—
426C22×C4C24×C1311yescharacteristic
427C22×C4C24×C1311yescharacteristic
428C22×C4C24×C1313yes—
429C22×C4C24×C1313yes—
430C22×C4C24×C1313yes—
431C22×C4C24×C1313yes—
432C22×C4C24×C1311yescharacteristic
433C22×C4C24×C1311yescharacteristic
434C22×C4C24×C1313yes—
435C22×C4C24×C1311yescharacteristic
436C22×C4C24×C1313yes—
437C22×C4C24×C1311yescharacteristic
438C22×C4C24×C1311yescharacteristic
439C22×C4C24×C1313yes—
440C4⋊C4—26no—
441C4⋊C4—26no—
442C4⋊C4—26no—
443C4⋊C4—26no—
444C4⋊C4—26no—
445C4⋊C4—22no—
446C4⋊C4—46no—
447C4⋊C4—43no—
448C4⋊C4—43no—
449C4⋊C4C22×C4×C13112yes—
450C4⋊C4C22×C4×C13112yes—
451C4⋊C4C22×C4×C13112yes—
452C4⋊C4C22×C4×C1314yes—
453C22⋊C4—26no—
454C22⋊C4—26no—
455C22⋊C4—46no—
456C22⋊C4—46no—
457C22⋊C4—43no—
458C22⋊C4—43no—
459C22⋊C4C22×C4×C13112yes—
460C22⋊C4C22×C4×C13112yes—
461C42—26no—
462C42—26no—
463C42—26no—
464C42—26no—
465C42—26no—
466C42—22no—
467C42—46no—
468C42—43no—
469C42—43no—
470C42C22×C4×C13112yes—
471C42C22×C4×C13112yes—
472C13#3426311yescharacteristic, direct product factor, Sylow
473C23—23no—
474C23—23no—
475C23—23no—
476C23—23no—
477C23—23no—
478C23—23no—
479C23C23×C4×C1316yes—
480C23C25×C1311yescharacteristic
481Q8C13×#117116yescomplemented
482D4—224no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—23no—
488C2×C4—23no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—23no—
495C2×C4—21no—
496C2×C4—23no—
497C2×C4—224no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—23no—
501C2×C4—23no—
502C2×C4—23no—
503C2×C4—23no—
504C2×C4—23no—
505C2×C4—23no—
506C2×C4—23no—
507C2×C4—23no—
508C2×C4—21no—
509C2×C4—23no—
510C2×C4—23no—
511C2×C4—23no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—23no—
515C2×C4—21no—
516C2×C4—424no—
517C2×C4C23×C4×C1312yes—
518C2×C4C23×C4×C1312yes—
519C2×C4C23×C4×C1316yes—
520C2×C4C23×C4×C1316yes—
521C2×C4C23×C4×C1312yes—
522C2×C4C23×C4×C1316yes—
523C2×C4C2×C13×#4116yes—
524C2×C4C2×C13×#4116yes—
525C2×C4C13×H(5,𝔽2)12yes—
526C2×C4C13×2−1+412yes—
527C22—26no—
528C22—26no—
529C22—26no—
530C22—43no—
531C22—43no—
532C22—43no—
533C22—43no—
534C22C24×C4×C1311yescharacteristic
535C22C22×C13×#4111yescharacteristic
536C22C22×C13×#4111yescharacteristic
537C22C2×C13×H(5,𝔽2)11yescharacteristic
538C22C2×C13×2−1+411yescharacteristic
539C22C13×#58511yescharacteristic
540C22C13×#58511yescharacteristic
541C4—22no—
542C4—22no—
543C4—26no—
544C4—26no—
545C4—22no—
546C4—22no—
547C4—22no—
548C4—43no—
549C4—41no—
550C4—43no—
551C4—41no—
552C4—43no—
553C4—43no—
554C4C2×C13×#117112yes—
555C2—46no—
556C2C22×C13×#11711yescharacteristic
557C2C4×C13×H(5,𝔽2)11yescharacteristic
558C2C4×C13×2−1+411yescharacteristic
559C2C13×#351611yescharacteristic
560C2C13×#351711yescharacteristic
561C2C13×#352211yescharacteristic
562C2C13×#352411yescharacteristic
subgroupG/H
center, socleC23×C13C25
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
prime radicalC22×C13×#41C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2357C2semidirect
3. C13×#2354C2semidirect
4. C13×#2351C2semidirect
5. Q8×C13×C4⋊C4C2semidirect
6. C13×#2345C2semidirect
7. C13×#2344C2semidirect
10. C13×#2319C2semidirect
11. C13×#2314C2semidirect
12. C13×#2298C2semidirect
13. C13×#2293C2semidirect
14. C13×#2276C2semidirect
15. C42×Q8×C13C2semidirect
17. C13×#520C4semidirect
131. #34263C13direct (N × H)
193. #2357C2×C13semidirect
194. #2354C2×C13semidirect
195. #2351C2×C13semidirect
196. Q8×C4⋊C4C2×C13semidirect
197. #2345C2×C13semidirect
198. #2344C2×C13semidirect
201. #2319C2×C13semidirect
202. #2314C2×C13semidirect
203. #2298C2×C13semidirect
204. #2293C2×C13semidirect
205. #2276C2×C13semidirect
206. C42×Q8C2×C13semidirect
215. Q8×C13#117semidirect
262. #520C4×C13semidirect
472. C13#34263direct (N × H)
481. Q8C13×#117semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#5202
C13×#23572
C13×#23542
C13×#23512
Q8×C13×C4⋊C42
C13×#23452
C13×#23442
C13×#23412
C13×#23192
C13×#23142
C13×#22982
C13×#22932
C13×#22762
C42×Q8×C132
#3426313