Finite Group Databasebeta

← C13×#34262 #15720601

Subgroups — C13×#34262 #15720601

Order 3328.

2198 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#519C211yesmaximal, characteristic
2C13×#2356C213yesmaximal, complemented
3C13×#2355C213yesmaximal, complemented
4C13×#2351C211yesmaximal, characteristic, complemented
5Q8×C13×C4⋊C4C211yesmaximal, characteristic, complemented
6C13×#2347C213yesmaximal
7C13×#2346C213yesmaximal
8Q8×C13×C22⋊C4C211yesmaximal, characteristic
9Q8×C13×C22⋊C4C211yesmaximal, characteristic
10C13×#2320C213yesmaximal, complemented
11C13×#2314C213yesmaximal
12C13×#2298C213yesmaximal
13C13×#2295C213yesmaximal, complemented
14C13×#2276C211yesmaximal, characteristic, complemented
15C42×Q8×C13C211yesmaximal, characteristic, complemented
16C23×Q8×C13C2211yescharacteristic
17C13×#519C4116yescomplemented
18C2×C4×Q8×C13C2211yescharacteristic
19C2×C4×Q8×C13C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×Q8×C13C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×Q8×C13C2213yes—
24C2×C4×Q8×C13C2211yescharacteristic
25C2×C4×Q8×C13C2213yes—
26C2×C13×#117C2213yes—
27C2×C13×#117C2213yes—
28C13×#391C2213yes—
29C13×#391C2213yes—
30C13×#391C2213yes—
31C13×#391C2213yes—
32C13×#389C2213yes—
33C13×#389C2213yes—
34C13×#389C2213yes—
35C13×#389C2213yes—
36C13×#388C2211yescharacteristic
37C13×#388C2213yes—
38C13×#388C2213yes—
39C13×#388C2213yes—
40C13×#388C2216yes—
41C13×#387C2213yes—
42C13×#387C2216yes—
43C13×#387C2213yes—
44C13×#387C2213yes—
45C13×#387C2213yes—
46C13×#387C2216yes—
47C13×#384C2213yes—
48C13×#383C2216yes—
49C13×#382C2213yes—
50C13×#382C2216yes—
51C13×#380C2213yes—
52C13×#380C2213yes—
53C4×C13×C4⋊C4C2213yes—
54C4×C13×C4⋊C4C2213yes—
55C4×C13×C4⋊C4C2213yes—
56C4×C13×C4⋊C4C2213yes—
57C4×C13×C4⋊C4C2213yes—
58C4×C13×C4⋊C4C2213yes—
59C4×C13×C4⋊C4C2216yes—
60C4×C13×C4⋊C4C2213yes—
61C4×C13×C4⋊C4C2213yes—
62C4×C13×C22⋊C4C2213yes—
63C4×C13×C22⋊C4C2213yes—
64C13×#376C2213yes—
65C13×#376C2216yes—
66C43×C13C2213yes—
67C22×Q8×C13—24no—
68C22×Q8×C13—24no—
69C22×Q8×C13C2×C418yes—
70C22×Q8×C13C2313yes—
71C22×Q8×C13C2311yescharacteristic
72C23×C4×C13C2313yes—
73C4×Q8×C13—24no—
74C4×Q8×C13—24no—
75C4×Q8×C13—24no—
76C4×Q8×C13—24no—
77C4×Q8×C13C2×C4124yes—
78C4×Q8×C13C2×C4124yes—
79C4×Q8×C13C2×C418yes—
80C4×Q8×C13C2×C418yes—
81C13×#117C2×C4124yes—
82C13×#117C2×C4124yes—
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2313yes—
85C2×C13×C4⋊C4C2313yes—
86C2×C13×C4⋊C4C2313yes—
87C2×C13×C4⋊C4C2313yes—
88C2×C13×C4⋊C4C2313yes—
89C2×C13×C4⋊C4C2313yes—
90C2×C13×C4⋊C4C2316yes—
91C2×C13×C4⋊C4C2313yes—
92C2×C13×C4⋊C4C2313yes—
93C2×C13×C4⋊C4C2313yes—
94C2×C13×C4⋊C4C2313yes—
95C2×C13×C4⋊C4C2313yes—
96C2×C13×C22⋊C4C2311yescharacteristic
97C2×C13×C22⋊C4C2311yescharacteristic
98C2×C13×C22⋊C4C2313yes—
99C2×C13×C22⋊C4C2313yes—
100C2×C13×C22⋊C4C2311yescharacteristic
101C2×C13×C22⋊C4C2313yes—
102C2×C42×C13C2313yes—
103C2×C42×C13C2313yes—
104C2×C42×C13C2313yes—
105C2×C42×C13C2313yes—
106C2×C42×C13C2313yes—
107C2×C42×C13C2311yescharacteristic
108C2×C42×C13C2313yes—
109C2×C42×C13C2316yes—
110C2×C42×C13C2313yes—
111C2×C42×C13C2313yes—
112C2×C42×C13C2313yes—
113C2×C42×C13C2316yes—
114C13×#95C2313yes—
115C13×#95C2313yes—
116C13×#95C2313yes—
117C13×#95C2313yes—
118C13×#95C2316yes—
119C13×#95C2311yescharacteristic
120C13×#95C2313yes—
121C13×#95C2313yes—
122C13×#95C2313yes—
123C13×#95C2316yes—
124C13×#95C2313yes—
125C13×#95C2313yes—
126C13×#95C2313yes—
127C13×#95C2316yes—
128C13×#95C2316yes—
129C13×#95C2311yescharacteristic
130#34262C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13C2411yescharacteristic
132C2×Q8×C13—232no—
133C2×Q8×C13—26no—
134C2×Q8×C13—26no—
135C2×Q8×C13C22×C4112yes—
136C2×Q8×C13C22×C414yes—
137C2×Q8×C13#4114yes—
138C2×Q8×C13#4114yes—
139C22×C4×C13—26no—
140C22×C4×C13—26no—
141C22×C4×C13C22×C4112yes—
142C22×C4×C13C2411yescharacteristic
143C22×C4×C13C2411yescharacteristic
144C22×C4×C13C2413yes—
145C22×C4×C13C2413yes—
146C22×C4×C13C2413yes—
147C22×C4×C13C2413yes—
148C22×C4×C13C2413yes—
149C22×C4×C13C2413yes—
150C22×C4×C13C2411yescharacteristic
151C22×C4×C13C2411yescharacteristic
152C22×C4×C13C2413yes—
153C22×C4×C13C2411yescharacteristic
154C22×C4×C13C2411yescharacteristic
155C22×C4×C13C2413yes—
156C13×C4⋊C4—26no—
157C13×C4⋊C4—26no—
158C13×C4⋊C4—26no—
159C13×C4⋊C4—26no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—26no—
162C13×C4⋊C4—43no—
163C13×C4⋊C4—43no—
164C13×C4⋊C4—46no—
165C13×C4⋊C4C22×C4112yes—
166C13×C4⋊C4C22×C4112yes—
167C13×C4⋊C4C22×C4112yes—
168C13×C4⋊C4C22×C4112yes—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—43no—
172C13×C22⋊C4—43no—
173C13×C22⋊C4C22×C414yes—
174C13×C22⋊C4C22×C4112yes—
175C42×C13—26no—
176C42×C13—26no—
177C42×C13—26no—
178C42×C13—26no—
179C42×C13—22no—
180C42×C13—26no—
181C42×C13—43no—
182C42×C13—46no—
183C42×C13—43no—
184C42×C13C22×C4124yes—
185C42×C13C22×C4112yes—
186C42×C13C22×C4112yes—
187C2×#519C2×C1311yescharacteristic
188#2356C2×C1313yescomplemented
189#2355C2×C1313yescomplemented
190#2351C2×C1311yescharacteristic, complemented
191Q8×C4⋊C4C2×C1311yescharacteristic, complemented
192#2347C2×C1313yes—
193#2346C2×C1313yes—
194Q8×C22⋊C4C2×C1311yescharacteristic
195Q8×C22⋊C4C2×C1311yescharacteristic
196#2320C2×C1313yescomplemented
197#2314C2×C1313yes—
198#2298C2×C1313yes—
199#2295C2×C1313yescomplemented
200#2276C2×C1311yescharacteristic, complemented
201C42×Q8C2×C1311yescharacteristic, complemented
202C23×C13—21no—
203C23×C13—21no—
204C23×C13—21no—
205C23×C13—21no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13C23×C412yes—
209C23×C13C2511yescharacteristic
210Q8×C13—224no—
211Q8×C13#117116yes—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—23no—
215C2×C4×C13—23no—
216C2×C4×C13—21no—
217C2×C4×C13—23no—
218C2×C4×C13—21no—
219C2×C4×C13—23no—
220C2×C4×C13—21no—
221C2×C4×C13—23no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—23no—
226C2×C4×C13—224no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—23no—
230C2×C4×C13—23no—
231C2×C4×C13—23no—
232C2×C4×C13—23no—
233C2×C4×C13—23no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—23no—
237C2×C4×C13—21no—
238C2×C4×C13—23no—
239C2×C4×C13—23no—
240C2×C4×C13—23no—
241C2×C4×C13—23no—
242C2×C4×C13—23no—
243C2×C4×C13—23no—
244C2×C4×C13—21no—
245C2×C4×C13C23×C416yes—
246C2×C4×C13C23×C412yes—
247C2×C4×C13C23×C416yes—
248C2×C4×C13C23×C412yes—
249C2×C4×C13C23×C416yes—
250C2×C4×C13C23×C416yes—
251C2×C4×C13C2×#4116yes—
252C2×C4×C13C2×#4116yes—
253C2×C4×C132−1+412yes—
254C2×C4×C132−1+412yes—
255C23×Q8C22×C1311yescharacteristic
256#519C4×C13116yescomplemented
257C2×C4×Q8C22×C1311yescharacteristic
258C2×C4×Q8C22×C1311yescharacteristic
259C2×C4×Q8C22×C1311yescharacteristic
260C2×C4×Q8C22×C1311yescharacteristic
261C2×C4×Q8C22×C1313yes—
262C2×C4×Q8C22×C1311yescharacteristic
263C2×C4×Q8C22×C1313yes—
264C2×C4×Q8C22×C1311yescharacteristic
265C2×#117C22×C1313yes—
266C2×#117C22×C1313yes—
267#391C22×C1313yes—
268#391C22×C1313yes—
269#391C22×C1313yes—
270#391C22×C1313yes—
271#389C22×C1313yes—
272#389C22×C1313yes—
273#389C22×C1313yes—
274#389C22×C1313yes—
275#388C22×C1313yes—
276#388C22×C1316yes—
277#388C22×C1313yes—
278#388C22×C1313yes—
279#388C22×C1311yescharacteristic
280#387C22×C1316yes—
281#387C22×C1316yes—
282#387C22×C1313yes—
283#387C22×C1313yes—
284#387C22×C1313yes—
285#387C22×C1313yes—
286#384C22×C1313yes—
287#383C22×C1316yes—
288#382C22×C1313yes—
289#382C22×C1316yes—
290#380C22×C1313yes—
291#380C22×C1313yes—
292C4×C4⋊C4C22×C1313yes—
293C4×C4⋊C4C22×C1313yes—
294C4×C4⋊C4C22×C1313yes—
295C4×C4⋊C4C22×C1313yes—
296C4×C4⋊C4C22×C1313yes—
297C4×C4⋊C4C22×C1316yes—
298C4×C4⋊C4C22×C1313yes—
299C4×C4⋊C4C22×C1313yes—
300C4×C4⋊C4C22×C1313yes—
301C4×C22⋊C4C22×C1313yes—
302C4×C22⋊C4C22×C1313yes—
303#376C22×C1313yes—
304#376C22×C1316yes—
305C43C22×C1313yes—
306C22×C13—22no—
307C22×C13—22no—
308C22×C13—22no—
309C22×C13—41no—
310C22×C13—41no—
311C22×C13—41no—
312C22×C13—41no—
313C22×C13C24×C411yescharacteristic
314C22×C13C22×#4111yescharacteristic
315C22×C13C22×#4111yescharacteristic
316C22×C13C2×2−1+411yescharacteristic
317C22×C13C2×2−1+411yescharacteristic
318C22×C13#58511yescharacteristic
319C22×C13#58511yescharacteristic
320C4×C13—26no—
321C4×C13—22no—
322C4×C13—26no—
323C4×C13—26no—
324C4×C13—22no—
325C4×C13—22no—
326C4×C13—22no—
327C4×C13—43no—
328C4×C13—41no—
329C4×C13—43no—
330C4×C13—41no—
331C4×C13—43no—
332C4×C13—43no—
333C4×C13C2×#117112yes—
334C22×Q8—24no—
335C22×Q8—24no—
336C22×Q8C2×C4×C1318yes—
337C22×Q8C23×C1313yes—
338C22×Q8C23×C1311yescharacteristic
339C23×C4C23×C1313yes—
340C4×Q8—24no—
341C4×Q8—24no—
342C4×Q8—24no—
343C4×Q8—24no—
344C4×Q8C2×C4×C13124yes—
345C4×Q8C2×C4×C13124yes—
346C4×Q8C2×C4×C1318yes—
347C4×Q8C2×C4×C1318yes—
348#117C2×C4×C13124yes—
349#117C2×C4×C13124yes—
350C2×C4⋊C4C23×C1313yes—
351C2×C4⋊C4C23×C1313yes—
352C2×C4⋊C4C23×C1313yes—
353C2×C4⋊C4C23×C1313yes—
354C2×C4⋊C4C23×C1311yescharacteristic
355C2×C4⋊C4C23×C1313yes—
356C2×C4⋊C4C23×C1313yes—
357C2×C4⋊C4C23×C1316yes—
358C2×C4⋊C4C23×C1313yes—
359C2×C4⋊C4C23×C1313yes—
360C2×C4⋊C4C23×C1313yes—
361C2×C4⋊C4C23×C1313yes—
362C2×C4⋊C4C23×C1313yes—
363C2×C22⋊C4C23×C1311yescharacteristic
364C2×C22⋊C4C23×C1311yescharacteristic
365C2×C22⋊C4C23×C1313yes—
366C2×C22⋊C4C23×C1313yes—
367C2×C22⋊C4C23×C1311yescharacteristic
368C2×C22⋊C4C23×C1313yes—
369C2×C42C23×C1313yes—
370C2×C42C23×C1313yes—
371C2×C42C23×C1313yes—
372C2×C42C23×C1313yes—
373C2×C42C23×C1311yescharacteristic
374C2×C42C23×C1313yes—
375C2×C42C23×C1313yes—
376C2×C42C23×C1313yes—
377C2×C42C23×C1316yes—
378C2×C42C23×C1313yes—
379C2×C42C23×C1316yes—
380C2×C42C23×C1313yes—
381#95C23×C1311yescharacteristic
382#95C23×C1313yes—
383#95C23×C1313yes—
384#95C23×C1313yes—
385#95C23×C1313yes—
386#95C23×C1313yes—
387#95C23×C1316yes—
388#95C23×C1316yes—
389#95C23×C1313yes—
390#95C23×C1313yes—
391#95C23×C1313yes—
392#95C23×C1316yes—
393#95C23×C1311yescharacteristic
394#95C23×C1316yes—
395#95C23×C1313yes—
396#95C23×C1313yes—
397C2×C13—42no—
398C2×C13C22×#11711yescharacteristic
399C2×C13C4×2−1+411yescharacteristic
400C2×C13C4×2−1+411yescharacteristic
401C2×C13#351611yescharacteristic
402C2×C13#351811yescharacteristic
403C2×C13#352311yescharacteristic
404C2×C13#352411yescharacteristic
405C24C24×C1311yescharacteristic
406C2×Q8—232no—
407C2×Q8—26no—
408C2×Q8—26no—
409C2×Q8C22×C4×C13112yes—
410C2×Q8C22×C4×C1314yes—
411C2×Q8C13×#4114yes—
412C2×Q8C13×#4114yes—
413C22×C4—26no—
414C22×C4—26no—
415C22×C4C22×C4×C13112yes—
416C22×C4C24×C1311yescharacteristic
417C22×C4C24×C1311yescharacteristic
418C22×C4C24×C1313yes—
419C22×C4C24×C1313yes—
420C22×C4C24×C1313yes—
421C22×C4C24×C1313yes—
422C22×C4C24×C1313yes—
423C22×C4C24×C1311yescharacteristic
424C22×C4C24×C1313yes—
425C22×C4C24×C1313yes—
426C22×C4C24×C1311yescharacteristic
427C22×C4C24×C1311yescharacteristic
428C22×C4C24×C1311yescharacteristic
429C22×C4C24×C1313yes—
430C4⋊C4—26no—
431C4⋊C4—26no—
432C4⋊C4—26no—
433C4⋊C4—26no—
434C4⋊C4—22no—
435C4⋊C4—26no—
436C4⋊C4—43no—
437C4⋊C4—43no—
438C4⋊C4—46no—
439C4⋊C4C22×C4×C13112yes—
440C4⋊C4C22×C4×C13112yes—
441C4⋊C4C22×C4×C13112yes—
442C4⋊C4C22×C4×C13112yes—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—43no—
446C22⋊C4—43no—
447C22⋊C4C22×C4×C1314yes—
448C22⋊C4C22×C4×C13112yes—
449C42—26no—
450C42—26no—
451C42—26no—
452C42—26no—
453C42—22no—
454C42—26no—
455C42—43no—
456C42—46no—
457C42—43no—
458C42C22×C4×C13124yes—
459C42C22×C4×C13112yes—
460C42C22×C4×C13112yes—
461C13#3426211yescharacteristic, direct product factor, Sylow
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23C23×C4×C1312yes—
469C23C25×C1311yescharacteristic
470Q8—224no—
471Q8C13×#117116yes—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—23no—
475C2×C4—23no—
476C2×C4—21no—
477C2×C4—23no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—23no—
481C2×C4—21no—
482C2×C4—23no—
483C2×C4—21no—
484C2×C4—23no—
485C2×C4—21no—
486C2×C4—224no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—23no—
490C2×C4—23no—
491C2×C4—23no—
492C2×C4—23no—
493C2×C4—23no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—23no—
498C2×C4—23no—
499C2×C4—23no—
500C2×C4—23no—
501C2×C4—23no—
502C2×C4—23no—
503C2×C4—23no—
504C2×C4—21no—
505C2×C4C23×C4×C1316yes—
506C2×C4C23×C4×C1312yes—
507C2×C4C23×C4×C1316yes—
508C2×C4C23×C4×C1312yes—
509C2×C4C23×C4×C1316yes—
510C2×C4C23×C4×C1316yes—
511C2×C4C2×C13×#4116yes—
512C2×C4C2×C13×#4116yes—
513C2×C4C13×2−1+412yes—
514C2×C4C13×2−1+412yes—
515C22—22no—
516C22—22no—
517C22—22no—
518C22—41no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22C24×C4×C1311yescharacteristic
523C22C22×C13×#4111yescharacteristic
524C22C22×C13×#4111yescharacteristic
525C22C2×C13×2−1+411yescharacteristic
526C22C2×C13×2−1+411yescharacteristic
527C22C13×#58511yescharacteristic
528C22C13×#58511yescharacteristic
529C4—22no—
530C4—26no—
531C4—26no—
532C4—22no—
533C4—22no—
534C4—26no—
535C4—22no—
536C4—41no—
537C4—43no—
538C4—41no—
539C4—43no—
540C4—43no—
541C4—43no—
542C4C2×C13×#117112yes—
543C2—42no—
544C2C22×C13×#11711yescharacteristic
545C2C4×C13×2−1+411yescharacteristic
546C2C4×C13×2−1+411yescharacteristic
547C2C13×#351611yescharacteristic
548C2C13×#351811yescharacteristic
549C2C13×#352311yescharacteristic
550C2C13×#352411yescharacteristic
subgroupG/H
center, socleC23×C13C25
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
prime radicalC24×C13C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2356C2semidirect
3. C13×#2355C2semidirect
4. C13×#2351C2semidirect
5. Q8×C13×C4⋊C4C2semidirect
10. C13×#2320C2semidirect
13. C13×#2295C2semidirect
14. C13×#2276C2semidirect
15. C42×Q8×C13C2semidirect
17. C13×#519C4semidirect
130. #34262C13direct (N × H)
188. #2356C2×C13semidirect
189. #2355C2×C13semidirect
190. #2351C2×C13semidirect
191. Q8×C4⋊C4C2×C13semidirect
196. #2320C2×C13semidirect
199. #2295C2×C13semidirect
200. #2276C2×C13semidirect
201. C42×Q8C2×C13semidirect
256. #519C4×C13semidirect
461. C13#34262direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5192
C13×#23562
C13×#23552
C13×#23512
Q8×C13×C4⋊C42
C13×#23472
C13×#23462
Q8×C13×C22⋊C42
C13×#23202
C13×#23142
C13×#22982
C13×#22952
C13×#22762
C42×Q8×C132
#3426213