Finite Group Databasebeta

← C13×#62788 #15749127

Subgroups — C13×#62788 #15749127

Order 3328.

7094 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3523C214yesmaximal, complemented
2C13×#3522C214yesmaximal, complemented
3C13×#3516C218yesmaximal, complemented
4C13×#3507C216yesmaximal, complemented
5C13×#3502C211yesmaximal, characteristic, complemented
6C13×#3497C211yesmaximal, characteristic, complemented
7C13×#3492C216yesmaximal, complemented
8C13×#3486C212yesmaximal, complemented
9C13×#3482C218yesmaximal, complemented
10C13×#3480C214yesmaximal, complemented
11Q8×C13×#41C214yesmaximal, complemented
12C13×#3461C216yesmaximal, complemented
13C13×#3444C216yesmaximal, complemented
14C4×C13×2−1+4C212yesmaximal, complemented
15C22×C4×Q8×C13C211yesmaximal, characteristic, complemented
16C2×C13×2−1+4C2212yes—
17C23×Q8×C13C2211yescharacteristic
18C13×#559C22112yescomplemented
19Q82×C13C2214yescomplemented
20C13×#557C22112yescomplemented
21C13×#557C2214yescomplemented
22C13×#557C2218yescomplemented
23C13×#556C22112yescomplemented
24C13×#556C22124yescomplemented
25C13×#554C22124yes—
26C13×#554C22112yescomplemented
27C13×#553C22124yes—
28C13×#552C22124yes—
29C13×#552C22124yescomplemented
30C13×#550C2214yescomplemented
31D4×Q8×C13C2218yes—
32D4×Q8×C13C2218yes—
33D4×Q8×C13C2214yescomplemented
34C13×#548C2218yes—
35C13×#548C2218yes—
36C13×#548C2218yescomplemented
37C13×#547C22124yes—
38C13×#544C2216yes—
39C13×#542C22124yescomplemented
40C13×#541C22124yescomplemented
41C13×#539C22124yes—
42C13×#537C2216yes—
43C13×#536C22112yes—
44C13×#533C2216yes—
45C13×#533C2216yes—
46C13×#533C2216yes—
47C13×#533C22124yescomplemented
48C13×#532C2216yes—
49C13×#532C2216yes—
50C13×#532C2216yes—
51C13×#529C22112yes—
52C13×#529C22112yes—
53C13×#529C22112yes—
54C13×#529C22112yes—
55C13×#529C22112yes—
56C13×#529C22112yes—
57C13×#529C22124yescomplemented
58C13×#525C2214yes—
59C13×#525C22112yes—
60C13×#525C22112yes—
61C13×#520C22112yes—
62C13×#520C2218yescomplemented
63C13×#519C2212yes—
64C13×#519C2218yescomplemented
65C4×C13×#41C22112yes—
66C4×C13×#41C22112yes—
67C4×C13×#41C22112yes—
68C4×C13×#41C2218yescomplemented
69C2×C4×Q8×C13C2214yes—
70C2×C4×Q8×C13C2211yescharacteristic
71C2×C4×Q8×C13C2213yes—
72C2×C4×Q8×C13C2214yes—
73C2×C4×Q8×C13C2214yes—
74C2×C4×Q8×C13C2211yescharacteristic
75C2×C4×Q8×C13C2213yes—
76C2×C4×Q8×C13C2214yes—
77C2×C4×Q8×C13C2218yescomplemented
78C22×C13×C4⋊C4C2213yes—
79C22×C42×C13C2213yes—
80C13×2−1+4—216no—
81C2×C13×#41C2314yes—
82C2×C13×#41C23112yes—
83C2×C13×#41C2318yes—
84C2×C13×#41C23112yes—
85C22×Q8×C13—28no—
86C22×Q8×C13C2313yes—
87C22×Q8×C13C2314yes—
88C22×Q8×C13C2314yes—
89C22×Q8×C13C2318yes—
90C22×Q8×C13C2311yescharacteristic
91C23×C4×C13C2311yescharacteristic
92C23×C4×C13C2313yes—
93C23×C4×C13C2313yes—
94C13×C4⋊Q8C2316yes—
95C13×C4⋊Q8C2316yes—
96C13×C4⋊Q8C2316yes—
97C13×C4⋊Q8C23124yes—
98C13×C4⋊Q8C23124yes—
99C13×#127C2316yes—
100C13×#126C23124yes—
101C13×#126C23124yes—
102C13×#126C23148yes—
103C13×#125C23112yes—
104C13×#125C23112yes—
105C13×#125C23112yes—
106C13×#125C23124yes—
107C13×#125C23148yes—
108C13×#124C23112yes—
109C13×#124C23112yes—
110C13×#124C23112yes—
111C13×#124C23124yes—
112C13×#123C2318yes—
113C13×#123C23124yes—
114C13×#123C23124yes—
115C13×#123C23148yes—
116C13×C22⋊Q8C2314yes—
117C13×C22⋊Q8C2314yes—
118C13×C22⋊Q8C23112yes—
119C13×C22⋊Q8C23112yes—
120C13×C22⋊Q8C23112yes—
121C13×C22⋊Q8C23112yes—
122C13×C22⋊Q8C23124yes—
123C13×C22⋊Q8C23124yes—
124C13×C22⋊Q8C23124yes—
125C13×C22⋊Q8C23148yes—
126C13×#121C2314yes—
127C13×#121C2314yes—
128C13×#121C23112yes—
129C13×#121C23112yes—
130C13×#121C23112yes—
131C13×#121C23112yes—
132C13×#121C23124yes—
133C13×#120C2318yes—
134C4×Q8×C13C2314yes—
135C4×Q8×C13C2314yes—
136C4×Q8×C13C23112yes—
137C4×Q8×C13C23112yes—
138C4×Q8×C13C2314yes—
139C4×Q8×C13C2314yes—
140C4×Q8×C13C23112yes—
141C4×Q8×C13C23112yes—
142C4×Q8×C13C23112yes—
143C4×Q8×C13C2318yes—
144C4×Q8×C13C23124yes—
145C4×Q8×C13C23112yes—
146C4×Q8×C13C23112yes—
147C4×Q8×C13C23112yes—
148C4×Q8×C13C23112yes—
149C4×Q8×C13C23112yes—
150C4×Q8×C13C2318yes—
151C4×D4×C13C2318yes—
152C4×D4×C13C2318yes—
153C4×D4×C13C23112yes—
154C4×D4×C13C23124yes—
155C4×D4×C13C23112yes—
156C4×D4×C13C23124yes—
157C4×D4×C13C23124yes—
158C4×D4×C13C23124yes—
159C4×D4×C13C23112yes—
160C4×D4×C13C23112yes—
161C4×D4×C13C23112yes—
162C4×D4×C13C23112yes—
163C4×D4×C13C23124yes—
164C13×#117C2314yes—
165C13×#117C23112yes—
166C13×#117C23124yes—
167C13×#117C23112yes—
168C13×#117C23124yes—
169C13×#117C23124yes—
170C13×#117C23124yes—
171C2×C13×C4⋊C4C2313yes—
172C2×C13×C4⋊C4C2313yes—
173C2×C13×C4⋊C4C2316yes—
174C2×C13×C4⋊C4C23112yes—
175C2×C13×C4⋊C4C23112yes—
176C2×C13×C4⋊C4C23124yes—
177C2×C42×C13C2313yes—
178C2×C42×C13C2316yes—
179C2×C42×C13C2316yes—
180C2×C42×C13C2316yes—
181C2×C42×C13C2313yes—
182C2×C42×C13C2313yes—
183C2×C42×C13C2316yes—
184C2×C42×C13C2313yes—
185C2×C42×C13C23124yes—
186#62788C1311yesmaximal, characteristic, direct product factor, Sylow
187C24×C13C2411yescharacteristic
188C13×#41—232no—
189C13×#41—248no—
190C13×#41—216no—
191C13×#41—424no—
192C2×Q8×C13—216no—
193C2×Q8×C13—216no—
194C2×Q8×C13—232no—
195C2×Q8×C13—212no—
196C2×Q8×C13#4118yescomplemented
197C2×Q8×C13C2414yes—
198C2×Q8×C13C24112yes—
199C2×Q8×C13C24112yes—
200C2×Q8×C13C24112yes—
201C2×Q8×C13C2414yes—
202C2×D4×C13C2418yes—
203C2×D4×C13C2414yes—
204C2×D4×C13C2418yes—
205C2×D4×C13C2418yes—
206C2×D4×C13C24112yes—
207C2×D4×C13C24112yes—
208C22×C4×C13—212no—
209C22×C4×C13—24no—
210C22×C4×C13—46no—
211C22×C4×C13C2411yescharacteristic
212C22×C4×C13C2411yescharacteristic
213C22×C4×C13C2411yescharacteristic
214C22×C4×C13C2416yes—
215C22×C4×C13C2416yes—
216C22×C4×C13C2416yes—
217C22×C4×C13C2413yes—
218C22×C4×C13C24124yes—
219C22×C4×C13C2411yescharacteristic
220C22×C4×C13C2411yescharacteristic
221C22×C4×C13C2418yes—
222C22×C4×C13C2413yes—
223C22×C4×C13C2416yes—
224C22×C4×C13C2413yes—
225C22×C4×C13C24124yes—
226C22×C4×C13C2413yes—
227C22×C4×C13C2411yescharacteristic
228C13×C4⋊C4C24112yes—
229C13×C4⋊C4C24112yes—
230C13×C4⋊C4C24124yes—
231C13×C4⋊C4C24112yes—
232C13×C4⋊C4C24124yes—
233C13×C4⋊C4C24112yes—
234C13×C4⋊C4C2418yes—
235C13×C4⋊C4C2418yes—
236C13×C4⋊C4C2414yes—
237C13×C4⋊C4C2414yes—
238C13×C4⋊C4C24112yes—
239C13×C4⋊C4C24112yes—
240C13×C4⋊C4C24124yes—
241C13×C4⋊C4C24124yes—
242C13×C4⋊C4C24124yes—
243C13×C22⋊C4C2418yes—
244C13×C22⋊C4C2418yes—
245C13×C22⋊C4C24124yes—
246C13×C22⋊C4C2418yes—
247C13×C22⋊C4C2418yes—
248C13×C22⋊C4C2418yes—
249C13×C22⋊C4C24124yes—
250C13×C22⋊C4C24124yes—
251C13×C22⋊C4C24124yes—
252C42×C13C2416yes—
253C42×C13C2416yes—
254C42×C13C2416yes—
255C42×C13C2416yes—
256C42×C13C2416yes—
257C42×C13C2416yes—
258C42×C13C24124yes—
259C42×C13C24124yes—
260C42×C13C2416yes—
261C42×C13C2416yes—
262C42×C13C2418yes—
263#3523C2×C1314yescomplemented
264#3522C2×C1314yescomplemented
265#3516C2×C1318yescomplemented
266#3507C2×C1316yescomplemented
267#3502C2×C1311yescharacteristic, complemented
268#3497C2×C1311yescharacteristic, complemented
269#3492C2×C1316yescomplemented
270#3486C2×C1312yescomplemented
271#3482C2×C1318yescomplemented
272#3480C2×C1314yescomplemented
273Q8×#41C2×C1314yescomplemented
274#3461C2×C1316yescomplemented
275#3444C2×C1316yescomplemented
276C4×2−1+4C2×C1312yescomplemented
277C22×C4×Q8C2×C1311yescharacteristic, complemented
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13C2518yes—
282C23×C13C2511yescharacteristic
283C23×C13C2511yescharacteristic
284C23×C13C2511yescharacteristic
285Q8×C13—224no—
286Q8×C13—224no—
287Q8×C13—28no—
288Q8×C13—412no—
289Q8×C13C2×#41116yes—
290D4×C13—216no—
291D4×C13—216no—
292D4×C13—216no—
293D4×C13—224no—
294D4×C13—28no—
295D4×C13—412no—
296C2×C4×C13—26no—
297C2×C4×C13—22no—
298C2×C4×C13—212no—
299C2×C4×C13—212no—
300C2×C4×C13—212no—
301C2×C4×C13—248no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—216no—
307C2×C4×C13—43no—
308C2×C4×C13—46no—
309C2×C4×C13—43no—
310C2×C4×C13—424no—
311C2×C4×C13C2×#41112yes—
312C2×C4×C132−1+414yescomplemented
313C2×C4×C13C2511yescharacteristic
314C2×C4×C13C2511yescharacteristic
315C2×C4×C13C2516yes—
316C2×C4×C13C2518yes—
317C2×C4×C13C2516yes—
318C2×C4×C13C2518yes—
319C2×C4×C13C2518yes—
320C2×C4×C13C2516yes—
321C2×C4×C13C2516yes—
322C2×C4×C13C2511yescharacteristic
323C2×C4×C13C2511yescharacteristic
324C2×2−1+4C22×C1312yes—
325C23×Q8C22×C1311yescharacteristic
326#559C22×C13112yescomplemented
327Q82C22×C1314yescomplemented
328#557C22×C13112yescomplemented
329#557C22×C1314yescomplemented
330#557C22×C1318yescomplemented
331#556C22×C13112yescomplemented
332#556C22×C13124yescomplemented
333#554C22×C13124yes—
334#554C22×C13112yescomplemented
335#553C22×C13124yes—
336#552C22×C13124yes—
337#552C22×C13124yescomplemented
338#550C22×C1314yescomplemented
339D4×Q8C22×C1318yes—
340D4×Q8C22×C1318yes—
341D4×Q8C22×C1314yescomplemented
342#548C22×C1318yes—
343#548C22×C1318yes—
344#548C22×C1318yescomplemented
345#547C22×C13124yes—
346#544C22×C1316yes—
347#542C22×C13124yescomplemented
348#541C22×C13124yescomplemented
349#539C22×C13124yes—
350#537C22×C1316yes—
351#536C22×C13112yes—
352#533C22×C1316yes—
353#533C22×C1316yes—
354#533C22×C1316yes—
355#533C22×C13124yescomplemented
356#532C22×C1316yes—
357#532C22×C1316yes—
358#532C22×C1316yes—
359#529C22×C13112yes—
360#529C22×C13112yes—
361#529C22×C13112yes—
362#529C22×C13112yes—
363#529C22×C13112yes—
364#529C22×C13112yes—
365#529C22×C13124yescomplemented
366#525C22×C1314yes—
367#525C22×C13112yes—
368#525C22×C13112yes—
369#520C22×C13112yes—
370#520C22×C1318yescomplemented
371#519C22×C1312yes—
372#519C22×C1318yescomplemented
373C4×#41C22×C13112yes—
374C4×#41C22×C13112yes—
375C4×#41C22×C13112yes—
376C4×#41C22×C1318yescomplemented
377C2×C4×Q8C22×C1311yescharacteristic
378C2×C4×Q8C22×C1313yes—
379C2×C4×Q8C22×C1314yes—
380C2×C4×Q8C22×C1314yes—
381C2×C4×Q8C22×C1311yescharacteristic
382C2×C4×Q8C22×C1313yes—
383C2×C4×Q8C22×C1314yes—
384C2×C4×Q8C22×C1314yes—
385C2×C4×Q8C22×C1318yescomplemented
386C22×C4⋊C4C22×C1313yes—
387C22×C42C22×C1313yes—
388C22×C13—28no—
389C22×C13—21no—
390C22×C13—21no—
391C22×C13—21no—
392C22×C13—21no—
393C22×C13—21no—
394C22×C13—21no—
395C22×C13—28no—
396C22×C13—28no—
397C22×C13—28no—
398C22×C13C22×#4112yes—
399C22×C13C2×2−1+412yes—
400C22×C13#58512yes—
401C22×C13C2611yescharacteristic
402C4×C13—28no—
403C4×C13—26no—
404C4×C13—21no—
405C4×C13—21no—
406C4×C13—28no—
407C4×C13—26no—
408C4×C13—26no—
409C4×C13—28no—
410C4×C13C22×#41112yes—
411C4×C13C2×2−1+412yes—
412C4×C13C2×2−1+412yes—
4132−1+4—216no—
414C2×#41C23×C1314yes—
415C2×#41C23×C13112yes—
416C2×#41C23×C1318yes—
417C2×#41C23×C13112yes—
418C22×Q8—28no—
419C22×Q8C23×C1313yes—
420C22×Q8C23×C1314yes—
421C22×Q8C23×C1314yes—
422C22×Q8C23×C1318yes—
423C22×Q8C23×C1311yescharacteristic
424C23×C4C23×C1313yes—
425C23×C4C23×C1311yescharacteristic
426C23×C4C23×C1313yes—
427C4⋊Q8C23×C1316yes—
428C4⋊Q8C23×C1316yes—
429C4⋊Q8C23×C1316yes—
430C4⋊Q8C23×C13124yes—
431C4⋊Q8C23×C13124yes—
432#127C23×C1316yes—
433#126C23×C13124yes—
434#126C23×C13124yes—
435#126C23×C13148yes—
436#125C23×C13112yes—
437#125C23×C13112yes—
438#125C23×C13112yes—
439#125C23×C13124yes—
440#125C23×C13148yes—
441#124C23×C13112yes—
442#124C23×C13112yes—
443#124C23×C13112yes—
444#124C23×C13124yes—
445#123C23×C1318yes—
446#123C23×C13124yes—
447#123C23×C13124yes—
448#123C23×C13148yes—
449C22⋊Q8C23×C1314yes—
450C22⋊Q8C23×C1314yes—
451C22⋊Q8C23×C13112yes—
452C22⋊Q8C23×C13112yes—
453C22⋊Q8C23×C13112yes—
454C22⋊Q8C23×C13112yes—
455C22⋊Q8C23×C13124yes—
456C22⋊Q8C23×C13124yes—
457C22⋊Q8C23×C13124yes—
458C22⋊Q8C23×C13148yes—
459#121C23×C1314yes—
460#121C23×C1314yes—
461#121C23×C13112yes—
462#121C23×C13112yes—
463#121C23×C13112yes—
464#121C23×C13112yes—
465#121C23×C13124yes—
466#120C23×C1318yes—
467C4×Q8C23×C1314yes—
468C4×Q8C23×C1314yes—
469C4×Q8C23×C13112yes—
470C4×Q8C23×C13112yes—
471C4×Q8C23×C1314yes—
472C4×Q8C23×C1314yes—
473C4×Q8C23×C13112yes—
474C4×Q8C23×C13112yes—
475C4×Q8C23×C13112yes—
476C4×Q8C23×C1318yes—
477C4×Q8C23×C13124yes—
478C4×Q8C23×C13112yes—
479C4×Q8C23×C13112yes—
480C4×Q8C23×C13112yes—
481C4×Q8C23×C13112yes—
482C4×Q8C23×C13112yes—
483C4×Q8C23×C1318yes—
484C4×D4C23×C1318yes—
485C4×D4C23×C1318yes—
486C4×D4C23×C13112yes—
487C4×D4C23×C13124yes—
488C4×D4C23×C13112yes—
489C4×D4C23×C13124yes—
490C4×D4C23×C13124yes—
491C4×D4C23×C13124yes—
492C4×D4C23×C13112yes—
493C4×D4C23×C13112yes—
494C4×D4C23×C13112yes—
495C4×D4C23×C13112yes—
496C4×D4C23×C13124yes—
497#117C23×C1314yes—
498#117C23×C13112yes—
499#117C23×C13124yes—
500#117C23×C13112yes—
501#117C23×C13124yes—
502#117C23×C13124yes—
503#117C23×C13124yes—
504C2×C4⋊C4C23×C1313yes—
505C2×C4⋊C4C23×C1313yes—
506C2×C4⋊C4C23×C1316yes—
507C2×C4⋊C4C23×C13112yes—
508C2×C4⋊C4C23×C13112yes—
509C2×C4⋊C4C23×C13124yes—
510C2×C42C23×C1313yes—
511C2×C42C23×C1316yes—
512C2×C42C23×C1316yes—
513C2×C42C23×C1313yes—
514C2×C42C23×C1316yes—
515C2×C42C23×C1313yes—
516C2×C42C23×C1316yes—
517C2×C42C23×C1313yes—
518C2×C42C23×C13124yes—
519C2×C13—22no—
520C2×C13—22no—
521C2×C13—22no—
522C2×C13—48no—
523C2×C13C23×#4111yescharacteristic
524C2×C13C22×2−1+411yescharacteristic
525C2×C13C2×#58511yescharacteristic
526C24C24×C1311yescharacteristic
527#41—232no—
528#41—248no—
529#41—216no—
530#41—424no—
531C2×Q8—216no—
532C2×Q8—216no—
533C2×Q8—232no—
534C2×Q8—212no—
535C2×Q8C13×#4118yescomplemented
536C2×Q8C24×C1314yes—
537C2×Q8C24×C13112yes—
538C2×Q8C24×C13112yes—
539C2×Q8C24×C13112yes—
540C2×Q8C24×C1314yes—
541C2×D4C24×C1318yes—
542C2×D4C24×C1314yes—
543C2×D4C24×C1318yes—
544C2×D4C24×C1318yes—
545C2×D4C24×C13112yes—
546C2×D4C24×C13112yes—
547C22×C4—212no—
548C22×C4—24no—
549C22×C4—46no—
550C22×C4C24×C1311yescharacteristic
551C22×C4C24×C1311yescharacteristic
552C22×C4C24×C1311yescharacteristic
553C22×C4C24×C1311yescharacteristic
554C22×C4C24×C1311yescharacteristic
555C22×C4C24×C1318yes—
556C22×C4C24×C1316yes—
557C22×C4C24×C1316yes—
558C22×C4C24×C1316yes—
559C22×C4C24×C1313yes—
560C22×C4C24×C13124yes—
561C22×C4C24×C1313yes—
562C22×C4C24×C1316yes—
563C22×C4C24×C1313yes—
564C22×C4C24×C13124yes—
565C22×C4C24×C1313yes—
566C22×C4C24×C1311yescharacteristic
567C4⋊C4C24×C13112yes—
568C4⋊C4C24×C13112yes—
569C4⋊C4C24×C13124yes—
570C4⋊C4C24×C13112yes—
571C4⋊C4C24×C13124yes—
572C4⋊C4C24×C13112yes—
573C4⋊C4C24×C1318yes—
574C4⋊C4C24×C1318yes—
575C4⋊C4C24×C1314yes—
576C4⋊C4C24×C1314yes—
577C4⋊C4C24×C13112yes—
578C4⋊C4C24×C13112yes—
579C4⋊C4C24×C13124yes—
580C4⋊C4C24×C13124yes—
581C4⋊C4C24×C13124yes—
582C22⋊C4C24×C1318yes—
583C22⋊C4C24×C1318yes—
584C22⋊C4C24×C13124yes—
585C22⋊C4C24×C1318yes—
586C22⋊C4C24×C1318yes—
587C22⋊C4C24×C1318yes—
588C22⋊C4C24×C13124yes—
589C22⋊C4C24×C13124yes—
590C22⋊C4C24×C13124yes—
591C42C24×C1316yes—
592C42C24×C1316yes—
593C42C24×C1316yes—
594C42C24×C1318yes—
595C42C24×C1316yes—
596C42C24×C1316yes—
597C42C24×C1316yes—
598C42C24×C1316yes—
599C42C24×C1316yes—
600C42C24×C13124yes—
601C42C24×C13124yes—
602C13#6278811yescharacteristic, direct product factor, Sylow
603C23—22no—
604C23—22no—
605C23—22no—
606C23C25×C1318yes—
607C23C25×C1311yescharacteristic
608C23C25×C1311yescharacteristic
609C23C25×C1311yescharacteristic
610Q8—224no—
611Q8—224no—
612Q8—28no—
613Q8—412no—
614Q8C2×C13×#41116yes—
615D4—216no—
616D4—216no—
617D4—216no—
618D4—224no—
619D4—28no—
620D4—412no—
621C2×C4—26no—
622C2×C4—22no—
623C2×C4—212no—
624C2×C4—212no—
625C2×C4—212no—
626C2×C4—248no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—216no—
632C2×C4—43no—
633C2×C4—46no—
634C2×C4—43no—
635C2×C4—424no—
636C2×C4C2×C13×#41112yes—
637C2×C4C13×2−1+414yescomplemented
638C2×C4C25×C1311yescharacteristic
639C2×C4C25×C1311yescharacteristic
640C2×C4C25×C1316yes—
641C2×C4C25×C1318yes—
642C2×C4C25×C1316yes—
643C2×C4C25×C1318yes—
644C2×C4C25×C1318yes—
645C2×C4C25×C1316yes—
646C2×C4C25×C1316yes—
647C2×C4C25×C1311yescharacteristic
648C2×C4C25×C1311yescharacteristic
649C22—28no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—28no—
657C22—28no—
658C22—28no—
659C22C22×C13×#4112yes—
660C22C2×C13×2−1+412yes—
661C22C13×#58512yes—
662C22C26×C1311yescharacteristic
663C4—28no—
664C4—26no—
665C4—21no—
666C4—21no—
667C4—28no—
668C4—26no—
669C4—26no—
670C4—28no—
671C4C22×C13×#41112yes—
672C4C2×C13×2−1+412yes—
673C4C2×C13×2−1+412yes—
674C2—22no—
675C2—22no—
676C2—22no—
677C2—48no—
678C2C23×C13×#4111yescharacteristic
679C2C22×C13×2−1+411yescharacteristic
680C2C2×C13×#58511yescharacteristic
subgroupG/H
centerC2×C4×C13C25
commutator, Frattini, cosocleC22C26×C13
socleC22×C13C26
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3523C2semidirect
2. C13×#3522C2semidirect
3. C13×#3516C2semidirect
4. C13×#3507C2semidirect
5. C13×#3502C2semidirect
6. C13×#3497C2semidirect
7. C13×#3492C2semidirect
8. C13×#3486C2semidirect
9. C13×#3482C2semidirect
10. C13×#3480C2semidirect
11. Q8×C13×#41C2semidirect
12. C13×#3461C2semidirect
13. C13×#3444C2semidirect
14. C4×C13×2−1+4C2semidirect
15. C22×C4×Q8×C13C2semidirect
18. C13×#559C22semidirect
19. Q82×C13C22semidirect
20. C13×#557C22semidirect
21. C13×#557C22semidirect
22. C13×#557C22semidirect
23. C13×#556C22semidirect
24. C13×#556C22semidirect
26. C13×#554C22semidirect
29. C13×#552C22semidirect
30. C13×#550C22semidirect
33. D4×Q8×C13C22semidirect
36. C13×#548C22semidirect
39. C13×#542C22semidirect
40. C13×#541C22semidirect
47. C13×#533C22semidirect
57. C13×#529C22semidirect
62. C13×#520C22semidirect
64. C13×#519C22semidirect
68. C4×C13×#41C22semidirect
77. C2×C4×Q8×C13C22semidirect
186. #62788C13direct (N × H)
196. C2×Q8×C13#41semidirect
263. #3523C2×C13semidirect
264. #3522C2×C13semidirect
265. #3516C2×C13semidirect
266. #3507C2×C13semidirect
267. #3502C2×C13semidirect
268. #3497C2×C13semidirect
269. #3492C2×C13semidirect
270. #3486C2×C13semidirect
271. #3482C2×C13semidirect
272. #3480C2×C13semidirect
273. Q8×#41C2×C13semidirect
274. #3461C2×C13semidirect
275. #3444C2×C13semidirect
276. C4×2−1+4C2×C13semidirect
277. C22×C4×Q8C2×C13semidirect
312. C2×C4×C132−1+4semidirect
326. #559C22×C13semidirect
327. Q82C22×C13semidirect
328. #557C22×C13semidirect
329. #557C22×C13semidirect
330. #557C22×C13semidirect
331. #556C22×C13semidirect
332. #556C22×C13semidirect
334. #554C22×C13semidirect
337. #552C22×C13semidirect
338. #550C22×C13semidirect
341. D4×Q8C22×C13semidirect
344. #548C22×C13semidirect
347. #542C22×C13semidirect
348. #541C22×C13semidirect
355. #533C22×C13semidirect
365. #529C22×C13semidirect
370. #520C22×C13semidirect
372. #519C22×C13semidirect
376. C4×#41C22×C13semidirect
385. C2×C4×Q8C22×C13semidirect
535. C2×Q8C13×#41semidirect
602. C13#62788direct (N × H)
637. C2×C4C13×2−1+4semidirect

Maximal subgroups

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

subgroupindex
C13×#35232
C13×#35222
C13×#35162
C13×#35072
C13×#35022
C13×#34972
C13×#34922
C13×#34862
C13×#34822
C13×#34802
Q8×C13×#412
C13×#34612
C13×#34442
C4×C13×2−1+42
C22×C4×Q8×C132
#6278813