Finite Group Databasebeta

← C4×C13×#548 #15720497

Subgroups — C4×C13×#548 #15720497

Order 3328.

3232 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#548C211yesmaximal, characteristic
2C2×C4×C13×#41C211yesmaximal, characteristic, complemented
3C22×C4×Q8×C13C211yesmaximal, characteristic, complemented
4C13×#2367C213yesmaximal, complemented
5C13×#2362C213yesmaximal, complemented
6C13×#2361C213yesmaximal, complemented
7C13×#2352C213yesmaximal, complemented
8C13×#2351C211yesmaximal, characteristic, complemented
9C13×#2341C211yesmaximal, characteristic, complemented
10Q8×C13×C22⋊C4C211yesmaximal, characteristic, complemented
11C4×C13×#124C213yesmaximal, complemented
12C4×C13×C22⋊Q8C213yesmaximal, complemented
13C4×C13×#121C213yesmaximal, complemented
14C42×Q8×C13C211yesmaximal, characteristic, complemented
15C42×D4×C13C213yesmaximal, complemented
16C22×C13×#41C2211yescharacteristic
17C23×Q8×C13C2211yescharacteristic
18C13×#548C4116yesdirect product factor
19C2×C13×#124C2213yes—
20C2×C13×C22⋊Q8C2213yes—
21C2×C13×#121C2213yes—
22C4×C13×#41—28no—
23C2×C4×Q8×C13—28no—
24C2×C4×Q8×C13C2211yescharacteristic
25C2×C4×Q8×C13C2213yes—
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×Q8×C13C2213yes—
29C2×C4×Q8×C13C2211yescharacteristic
30C2×C4×Q8×C13C2211yescharacteristic
31C2×C4×D4×C13C2213yes—
32C2×C4×D4×C13C2213yes—
33C2×C4×D4×C13C2213yes—
34C2×C4×D4×C13C2213yes—
35C2×C4×D4×C13C2213yes—
36C2×C13×#117C2213yes—
37C22×C13×C4⋊C4C2213yes—
38C22×C42×C13C2213yes—
39C22×C42×C13C2213yes—
40C13×#391C2213yes—
41C13×#391C2213yes—
42C13×#390C2213yes—
43C13×#390C2213yes—
44C13×#389C2213yes—
45C13×#389C2213yes—
46C13×#388C2216yes—
47C13×#388C2216yes—
48C13×#388C2216yes—
49C13×#387C2216yes—
50C13×#386C2216yes—
51C13×#385C2216yes—
52C13×#382C2213yes—
53C13×#380C2213yes—
54C13×#380C2213yes—
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×C22⋊C4C2211yescharacteristic
62C4×C13×C22⋊C4C2213yes—
63C4×C13×C22⋊C4C2213yes—
64C4×C13×C22⋊C4C2213yes—
65C4×C13×C22⋊C4C2213yes—
66C4×C13×C22⋊C4C2213yes—
67C4×C13×C22⋊C4C2216yes—
68C43×C13C2213yes—
69C2×C13×#41—24no—
70C2×C13×#41—24no—
71C2×C13×#41C2×C418yescomplemented
72C22×Q8×C13—24no—
73C22×Q8×C13—24no—
74C22×Q8×C13C2×C418yescomplemented
75C22×Q8×C13C2313yes—
76C22×Q8×C13C2311yescharacteristic
77C22×D4×C13C2313yes—
78C22×D4×C13C2313yes—
79C23×C4×C13C2313yes—
80C23×C4×C13C2313yes—
81C23×C4×C13C2313yes—
82C23×C4×C13C2313yes—
83C23×C4×C13C2313yes—
84C23×C4×C13C2311yescharacteristic
85C13×#124C2×C4124yescomplemented
86C13×C22⋊Q8C2×C4124yescomplemented
87C13×#121C2×C4124yescomplemented
88C4×Q8×C13—24no—
89C4×Q8×C13—24no—
90C4×Q8×C13—24no—
91C4×Q8×C13—212no—
92C4×Q8×C13—212no—
93C4×Q8×C13C2×C418yescomplemented
94C4×Q8×C13D418yescomplemented
95C4×D4×C13—212no—
96C4×D4×C13—212no—
97C4×D4×C13—212no—
98C4×D4×C13—212no—
99C4×D4×C13C2×C4124yescomplemented
100C13×#117—212no—
101C2×C13×C4⋊C4—212no—
102C2×C13×C4⋊C4C2313yes—
103C2×C13×C4⋊C4C2313yes—
104C2×C13×C4⋊C4C2313yes—
105C2×C13×C4⋊C4C2313yes—
106C2×C13×C4⋊C4C2313yes—
107C2×C13×C4⋊C4C2316yes—
108C2×C13×C4⋊C4C2313yes—
109C2×C13×C4⋊C4C2313yes—
110C2×C13×C4⋊C4C2313yes—
111C2×C13×C22⋊C4C2313yes—
112C2×C13×C22⋊C4C2313yes—
113C2×C13×C22⋊C4C2313yes—
114C2×C13×C22⋊C4C2316yes—
115C2×C13×C22⋊C4C2316yes—
116C2×C13×C22⋊C4C2311yescharacteristic
117C2×C13×C22⋊C4C2313yes—
118C2×C13×C22⋊C4C2316yes—
119C2×C13×C22⋊C4C2311yescharacteristic
120C2×C42×C13—212no—
121C2×C42×C13—212no—
122C2×C42×C13C2313yes—
123C2×C42×C13C2313yes—
124C2×C42×C13C2313yes—
125C2×C42×C13C2313yes—
126C2×C42×C13C2313yes—
127C2×C42×C13C2313yes—
128C2×C42×C13C2311yescharacteristic
129C2×C42×C13C2313yes—
130C2×C42×C13C2313yes—
131C2×C42×C13C2311yescharacteristic
132C2×C42×C13C2313yes—
133C2×C42×C13C2313yes—
134C2×C42×C13C2313yes—
135C13×#95C2311yescharacteristic
136C13×#95C2311yescharacteristic
137C13×#95C2313yes—
138C13×#95C2313yes—
139C13×#95C2313yes—
140C13×#95C2313yes—
141C13×#95C2316yes—
142C13×#95C2316yes—
143C13×#95C2316yes—
144C4×#548C1311yesmaximal, characteristic, direct product factor, Sylow
145C24×C13C2413yes—
146C24×C13C2411yescharacteristic
147C13×#41—232no—
148C2×Q8×C13—232no—
149C2×Q8×C13—26no—
150C2×Q8×C13—26no—
151C2×Q8×C13C22×C4112yes—
152C2×Q8×C13C22×C414yes—
153C2×Q8×C13C2×D414yes—
154C2×Q8×C13#4114yes—
155C2×D4×C13—26no—
156C2×D4×C13—26no—
157C2×D4×C13—26no—
158C2×D4×C13—26no—
159C2×D4×C13C22×C4112yes—
160C2×D4×C13C22×C4112yes—
161C22×C4×C13—22no—
162C22×C4×C13—26no—
163C22×C4×C13—26no—
164C22×C4×C13—26no—
165C22×C4×C13—26no—
166C22×C4×C13—22no—
167C22×C4×C13—26no—
168C22×C4×C13—26no—
169C22×C4×C13—26no—
170C22×C4×C13—26no—
171C22×C4×C13—26no—
172C22×C4×C13—26no—
173C22×C4×C13—26no—
174C22×C4×C13—43no—
175C22×C4×C13—43no—
176C22×C4×C13C22×C4112yes—
177C22×C4×C13C22×C4112yes—
178C22×C4×C13#4114yescomplemented
179C22×C4×C13C2413yes—
180C22×C4×C13C2413yes—
181C22×C4×C13C2413yes—
182C22×C4×C13C2411yescharacteristic
183C22×C4×C13C2411yescharacteristic
184C22×C4×C13C2413yes—
185C22×C4×C13C2413yes—
186C22×C4×C13C2413yes—
187C22×C4×C13C2411yescharacteristic
188C22×C4×C13C2411yescharacteristic
189C22×C4×C13C2411yescharacteristic
190C22×C4×C13C2413yes—
191C22×C4×C13C2411yescharacteristic
192C13×C4⋊C4—212no—
193C13×C4⋊C4—26no—
194C13×C4⋊C4—26no—
195C13×C4⋊C4—26no—
196C13×C4⋊C4—26no—
197C13×C4⋊C4—26no—
198C13×C4⋊C4C22×C4112yes—
199C13×C4⋊C4C22×C4112yes—
200C13×C4⋊C4C2×D4112yes—
201C13×C22⋊C4—26no—
202C13×C22⋊C4—212no—
203C13×C22⋊C4—26no—
204C13×C22⋊C4—26no—
205C13×C22⋊C4—46no—
206C13×C22⋊C4C22×C414yes—
207C13×C22⋊C4C22×C4112yes—
208C13×C22⋊C4C22×C4124yes—
209C13×C22⋊C4#4114yescomplemented
210C42×C13—22no—
211C42×C13—26no—
212C42×C13—26no—
213C42×C13—26no—
214C42×C13—26no—
215C42×C13—26no—
216C42×C13—26no—
217C42×C13—26no—
218C42×C13—26no—
219C42×C13—22no—
220C42×C13—43no—
221C42×C13C22×C4112yes—
222C42×C13C2×D4112yes—
223C2×#548C2×C1311yescharacteristic
224C2×C4×#41C2×C1311yescharacteristic, complemented
225C22×C4×Q8C2×C1311yescharacteristic, complemented
226#2367C2×C1313yescomplemented
227#2362C2×C1313yescomplemented
228#2361C2×C1313yescomplemented
229#2352C2×C1313yescomplemented
230#2351C2×C1311yescharacteristic, complemented
231#2341C2×C1311yescharacteristic, complemented
232Q8×C22⋊C4C2×C1311yescharacteristic, complemented
233C4×#124C2×C1313yescomplemented
234C4×C22⋊Q8C2×C1313yescomplemented
235C4×#121C2×C1313yescomplemented
236C42×Q8C2×C1311yescharacteristic, complemented
237C42×D4C2×C1313yescomplemented
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—23no—
243C23×C13—23no—
244C23×C13—23no—
245C23×C13—23no—
246C23×C13—23no—
247C23×C13—23no—
248C23×C13C23×C416yes—
249C23×C13C23×C412yes—
250C23×C13C2×#4112yes—
251C23×C13C2×#4112yes—
252C23×C13C2511yescharacteristic
253Q8×C13—224no—
254Q8×C13C4×D4116yescomplemented
255D4×C13—224no—
256D4×C13—224no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—23no—
261C2×C4×C13—21no—
262C2×C4×C13—23no—
263C2×C4×C13—23no—
264C2×C4×C13—23no—
265C2×C4×C13—21no—
266C2×C4×C13—23no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—23no—
272C2×C4×C13—21no—
273C2×C4×C13—224no—
274C2×C4×C13—224no—
275C2×C4×C13—28no—
276C2×C4×C13—23no—
277C2×C4×C13—23no—
278C2×C4×C13—23no—
279C2×C4×C13—23no—
280C2×C4×C13—23no—
281C2×C4×C13—23no—
282C2×C4×C13—23no—
283C2×C4×C13—23no—
284C2×C4×C13—23no—
285C2×C4×C13—412no—
286C2×C4×C13—412no—
287C2×C4×C13—412no—
288C2×C4×C13C23×C412yes—
289C2×C4×C13C23×C416yes—
290C2×C4×C13C23×C416yes—
291C2×C4×C13C23×C412yes—
292C2×C4×C13C23×C416yes—
293C2×C4×C13C22×D416yes—
294C2×C4×C13C22×D416yes—
295C2×C4×C13C22×D412yes—
296C2×C4×C13C2×#4112yes—
297C2×C4×C13C2×#4112yes—
298C2×C4×C13C2×#4112yes—
299C2×C4×C13C2×#4116yes—
300C2×C4×C13C2×#4112yes—
301C2×C4×C132−1+412yes—
302C22×#41C22×C1311yescharacteristic
303C23×Q8C22×C1311yescharacteristic
304#548C4×C13116yesdirect product factor
305C2×#124C22×C1313yes—
306C2×C22⋊Q8C22×C1313yes—
307C2×#121C22×C1313yes—
308C4×#41—28no—
309C2×C4×Q8—28no—
310C2×C4×Q8C22×C1311yescharacteristic
311C2×C4×Q8C22×C1311yescharacteristic
312C2×C4×Q8C22×C1311yescharacteristic
313C2×C4×Q8C22×C1313yes—
314C2×C4×Q8C22×C1313yes—
315C2×C4×Q8C22×C1311yescharacteristic
316C2×C4×Q8C22×C1311yescharacteristic
317C2×C4×D4C22×C1313yes—
318C2×C4×D4C22×C1313yes—
319C2×C4×D4C22×C1313yes—
320C2×C4×D4C22×C1313yes—
321C2×C4×D4C22×C1313yes—
322C2×#117C22×C1313yes—
323C22×C4⋊C4C22×C1313yes—
324C22×C42C22×C1313yes—
325C22×C42C22×C1313yes—
326#391C22×C1313yes—
327#391C22×C1313yes—
328#390C22×C1313yes—
329#390C22×C1313yes—
330#389C22×C1313yes—
331#389C22×C1313yes—
332#388C22×C1316yes—
333#388C22×C1316yes—
334#388C22×C1316yes—
335#387C22×C1316yes—
336#386C22×C1316yes—
337#385C22×C1316yes—
338#382C22×C1313yes—
339#380C22×C1313yes—
340#380C22×C1313yes—
341C4×C4⋊C4C22×C1313yes—
342C4×C4⋊C4C22×C1313yes—
343C4×C4⋊C4C22×C1313yes—
344C4×C4⋊C4C22×C1313yes—
345C4×C4⋊C4C22×C1313yes—
346C4×C4⋊C4C22×C1313yes—
347C4×C22⋊C4C22×C1313yes—
348C4×C22⋊C4C22×C1313yes—
349C4×C22⋊C4C22×C1313yes—
350C4×C22⋊C4C22×C1313yes—
351C4×C22⋊C4C22×C1311yescharacteristic
352C4×C22⋊C4C22×C1313yes—
353C4×C22⋊C4C22×C1316yes—
354C43C22×C1313yes—
355C22×C13—22no—
356C22×C13—22no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—22no—
360C22×C13—22no—
361C22×C13—26no—
362C22×C13—26no—
363C22×C13—26no—
364C22×C13—43no—
365C22×C13—43no—
366C22×C13—43no—
367C22×C13—43no—
368C22×C13C4×#4114yescomplemented
369C22×C13C24×C411yescharacteristic
370C22×C13C23×D411yescharacteristic
371C22×C13C22×#4111yescharacteristic
372C22×C13C22×#4111yescharacteristic
373C22×C13C22×#4111yescharacteristic
374C22×C13C2×2−1+411yescharacteristic
375C22×C13#58511yescharacteristic
376C4×C13—22no—
377C4×C13—26no—
378C4×C13—26no—
379C4×C13—22no—
380C4×C13—22no—
381C4×C13—22no—
382C4×C13—26no—
383C4×C13—22no—
384C4×C13—43no—
385C4×C13—43no—
386C4×C13—43no—
387C4×C13C2×C4×D4112yes—
388C4×C13#54814yesdirect product factor
389C2×#41—24no—
390C2×#41—24no—
391C2×#41C2×C4×C1318yescomplemented
392C22×Q8—24no—
393C22×Q8—24no—
394C22×Q8C2×C4×C1318yescomplemented
395C22×Q8C23×C1313yes—
396C22×Q8C23×C1311yescharacteristic
397C22×D4C23×C1313yes—
398C22×D4C23×C1313yes—
399C23×C4C23×C1313yes—
400C23×C4C23×C1313yes—
401C23×C4C23×C1313yes—
402C23×C4C23×C1313yes—
403C23×C4C23×C1313yes—
404C23×C4C23×C1311yescharacteristic
405#124C2×C4×C13124yescomplemented
406C22⋊Q8C2×C4×C13124yescomplemented
407#121C2×C4×C13124yescomplemented
408C4×Q8—24no—
409C4×Q8—24no—
410C4×Q8—24no—
411C4×Q8—212no—
412C4×Q8—212no—
413C4×Q8C2×C4×C1318yescomplemented
414C4×Q8D4×C1318yescomplemented
415C4×D4—212no—
416C4×D4—212no—
417C4×D4—212no—
418C4×D4—212no—
419C4×D4C2×C4×C13124yescomplemented
420#117—212no—
421C2×C4⋊C4—212no—
422C2×C4⋊C4C23×C1313yes—
423C2×C4⋊C4C23×C1316yes—
424C2×C4⋊C4C23×C1313yes—
425C2×C4⋊C4C23×C1313yes—
426C2×C4⋊C4C23×C1313yes—
427C2×C4⋊C4C23×C1313yes—
428C2×C4⋊C4C23×C1313yes—
429C2×C4⋊C4C23×C1313yes—
430C2×C4⋊C4C23×C1313yes—
431C2×C22⋊C4C23×C1316yes—
432C2×C22⋊C4C23×C1313yes—
433C2×C22⋊C4C23×C1313yes—
434C2×C22⋊C4C23×C1313yes—
435C2×C22⋊C4C23×C1316yes—
436C2×C22⋊C4C23×C1311yescharacteristic
437C2×C22⋊C4C23×C1313yes—
438C2×C22⋊C4C23×C1316yes—
439C2×C22⋊C4C23×C1311yescharacteristic
440C2×C42—212no—
441C2×C42—212no—
442C2×C42C23×C1313yes—
443C2×C42C23×C1313yes—
444C2×C42C23×C1313yes—
445C2×C42C23×C1313yes—
446C2×C42C23×C1313yes—
447C2×C42C23×C1313yes—
448C2×C42C23×C1313yes—
449C2×C42C23×C1313yes—
450C2×C42C23×C1311yescharacteristic
451C2×C42C23×C1311yescharacteristic
452C2×C42C23×C1313yes—
453C2×C42C23×C1313yes—
454C2×C42C23×C1313yes—
455#95C23×C1311yescharacteristic
456#95C23×C1311yescharacteristic
457#95C23×C1313yes—
458#95C23×C1313yes—
459#95C23×C1313yes—
460#95C23×C1313yes—
461#95C23×C1316yes—
462#95C23×C1316yes—
463#95C23×C1316yes—
464C2×C13—24no—
465C2×C13—46no—
466C2×C13C22×C4×D411yescharacteristic
467C2×C13C2×C4×#4111yescharacteristic
468C2×C13C4×2−1+411yescharacteristic
469C2×C13C2×#54811yescharacteristic
470C2×C13D4×#4111yescharacteristic
471C2×C13#348011yescharacteristic
472C2×C13#348211yescharacteristic
473C24C24×C1313yes—
474C24C24×C1311yescharacteristic
475#41—232no—
476C2×Q8—232no—
477C2×Q8—26no—
478C2×Q8—26no—
479C2×Q8C22×C4×C13112yes—
480C2×Q8C22×C4×C1314yes—
481C2×Q8C2×D4×C1314yes—
482C2×Q8C13×#4114yes—
483C2×D4—26no—
484C2×D4—26no—
485C2×D4—26no—
486C2×D4—26no—
487C2×D4C22×C4×C13112yes—
488C2×D4C22×C4×C13112yes—
489C22×C4—22no—
490C22×C4—26no—
491C22×C4—26no—
492C22×C4—26no—
493C22×C4—26no—
494C22×C4—22no—
495C22×C4—26no—
496C22×C4—26no—
497C22×C4—26no—
498C22×C4—26no—
499C22×C4—26no—
500C22×C4—26no—
501C22×C4—26no—
502C22×C4—43no—
503C22×C4—43no—
504C22×C4C22×C4×C13112yes—
505C22×C4C22×C4×C13112yes—
506C22×C4C13×#4114yescomplemented
507C22×C4C24×C1313yes—
508C22×C4C24×C1313yes—
509C22×C4C24×C1313yes—
510C22×C4C24×C1311yescharacteristic
511C22×C4C24×C1311yescharacteristic
512C22×C4C24×C1313yes—
513C22×C4C24×C1313yes—
514C22×C4C24×C1313yes—
515C22×C4C24×C1311yescharacteristic
516C22×C4C24×C1311yescharacteristic
517C22×C4C24×C1311yescharacteristic
518C22×C4C24×C1313yes—
519C22×C4C24×C1311yescharacteristic
520C4⋊C4—212no—
521C4⋊C4—26no—
522C4⋊C4—26no—
523C4⋊C4—26no—
524C4⋊C4—26no—
525C4⋊C4—26no—
526C4⋊C4C22×C4×C13112yes—
527C4⋊C4C22×C4×C13112yes—
528C4⋊C4C2×D4×C13112yes—
529C22⋊C4—26no—
530C22⋊C4—212no—
531C22⋊C4—26no—
532C22⋊C4—26no—
533C22⋊C4—46no—
534C22⋊C4C22×C4×C1314yes—
535C22⋊C4C22×C4×C13112yes—
536C22⋊C4C22×C4×C13124yes—
537C22⋊C4C13×#4114yescomplemented
538C42—22no—
539C42—26no—
540C42—26no—
541C42—26no—
542C42—26no—
543C42—26no—
544C42—26no—
545C42—26no—
546C42—26no—
547C42—22no—
548C42—43no—
549C42C22×C4×C13112yes—
550C42C2×D4×C13112yes—
551C13C4×#54811yescharacteristic, direct product factor, Sylow
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—23no—
557C23—23no—
558C23—23no—
559C23—23no—
560C23—23no—
561C23—23no—
562C23C23×C4×C1316yes—
563C23C23×C4×C1312yes—
564C23C2×C13×#4112yes—
565C23C2×C13×#4112yes—
566C23C25×C1311yescharacteristic
567Q8—224no—
568Q8C4×D4×C13116yescomplemented
569D4—224no—
570D4—224no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—23no—
575C2×C4—21no—
576C2×C4—23no—
577C2×C4—23no—
578C2×C4—23no—
579C2×C4—21no—
580C2×C4—23no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—23no—
586C2×C4—21no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—28no—
590C2×C4—23no—
591C2×C4—23no—
592C2×C4—23no—
593C2×C4—23no—
594C2×C4—23no—
595C2×C4—23no—
596C2×C4—23no—
597C2×C4—23no—
598C2×C4—23no—
599C2×C4—412no—
600C2×C4—412no—
601C2×C4—412no—
602C2×C4C23×C4×C1312yes—
603C2×C4C23×C4×C1316yes—
604C2×C4C23×C4×C1316yes—
605C2×C4C23×C4×C1312yes—
606C2×C4C23×C4×C1316yes—
607C2×C4C22×D4×C1316yes—
608C2×C4C22×D4×C1316yes—
609C2×C4C22×D4×C1312yes—
610C2×C4C2×C13×#4112yes—
611C2×C4C2×C13×#4112yes—
612C2×C4C2×C13×#4112yes—
613C2×C4C2×C13×#4116yes—
614C2×C4C2×C13×#4112yes—
615C2×C4C13×2−1+412yes—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—26no—
623C22—26no—
624C22—26no—
625C22—43no—
626C22—43no—
627C22—43no—
628C22—43no—
629C22C4×C13×#4114yescomplemented
630C22C24×C4×C1311yescharacteristic
631C22C23×D4×C1311yescharacteristic
632C22C22×C13×#4111yescharacteristic
633C22C22×C13×#4111yescharacteristic
634C22C22×C13×#4111yescharacteristic
635C22C2×C13×2−1+411yescharacteristic
636C22C13×#58511yescharacteristic
637C4—22no—
638C4—26no—
639C4—26no—
640C4—22no—
641C4—22no—
642C4—22no—
643C4—26no—
644C4—22no—
645C4—43no—
646C4—43no—
647C4—43no—
648C4C2×C4×D4×C13112yes—
649C4C13×#54814yesdirect product factor
650C2—24no—
651C2—46no—
652C2C22×C4×D4×C1311yescharacteristic
653C2C2×C4×C13×#4111yescharacteristic
654C2C4×C13×2−1+411yescharacteristic
655C2C2×C13×#54811yescharacteristic
656C2D4×C13×#4111yescharacteristic
657C2C13×#348011yescharacteristic
658C2C13×#348211yescharacteristic
subgroupG/H
centerC22×C4×C13C24
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
socleC23×C13C25
prime radicalC2×C13×#548C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C13×#41C2semidirect
3. C22×C4×Q8×C13C2semidirect
4. C13×#2367C2semidirect
5. C13×#2362C2semidirect
6. C13×#2361C2semidirect
7. C13×#2352C2semidirect
8. C13×#2351C2semidirect
9. C13×#2341C2semidirect
10. Q8×C13×C22⋊C4C2semidirect
11. C4×C13×#124C2semidirect
12. C4×C13×C22⋊Q8C2semidirect
13. C4×C13×#121C2semidirect
14. C42×Q8×C13C2semidirect
15. C42×D4×C13C2semidirect
18. C13×#548C4direct (N × H)
71. C2×C13×#41C2×C4semidirect
74. C22×Q8×C13C2×C4semidirect
85. C13×#124C2×C4semidirect
86. C13×C22⋊Q8C2×C4semidirect
87. C13×#121C2×C4semidirect
93. C4×Q8×C13C2×C4semidirect
94. C4×Q8×C13D4semidirect
99. C4×D4×C13C2×C4semidirect
144. C4×#548C13direct (N × H)
178. C22×C4×C13#41semidirect
209. C13×C22⋊C4#41semidirect
224. C2×C4×#41C2×C13semidirect
225. C22×C4×Q8C2×C13semidirect
226. #2367C2×C13semidirect
227. #2362C2×C13semidirect
228. #2361C2×C13semidirect
229. #2352C2×C13semidirect
230. #2351C2×C13semidirect
231. #2341C2×C13semidirect
232. Q8×C22⋊C4C2×C13semidirect
233. C4×#124C2×C13semidirect
234. C4×C22⋊Q8C2×C13semidirect
235. C4×#121C2×C13semidirect
236. C42×Q8C2×C13semidirect
237. C42×D4C2×C13semidirect
254. Q8×C13C4×D4semidirect
304. #548C4×C13direct (N × H)
368. C22×C13C4×#41semidirect
388. C4×C13#548direct (N × H)
391. C2×#41C2×C4×C13semidirect
394. C22×Q8C2×C4×C13semidirect
405. #124C2×C4×C13semidirect
406. C22⋊Q8C2×C4×C13semidirect
407. #121C2×C4×C13semidirect
413. C4×Q8C2×C4×C13semidirect
414. C4×Q8D4×C13semidirect
419. C4×D4C2×C4×C13semidirect
506. C22×C4C13×#41semidirect
537. C22⋊C4C13×#41semidirect
551. C13C4×#548direct (N × H)
568. Q8C4×D4×C13semidirect
629. C22C4×C13×#41semidirect
649. C4C13×#548direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5482
C2×C4×C13×#412
C22×C4×Q8×C132
C13×#23672
C13×#23622
C13×#23612
C13×#23522
C13×#23512
C13×#23412
Q8×C13×C22⋊C42
C4×C13×#1242
C4×C13×C22⋊Q82
C4×C13×#1212
C42×Q8×C132
C42×D4×C132
C4×#54813