Finite Group Databasebeta

← C13×#62865 #15749204

Subgroups — C13×#62865 #15749204

Order 3328.

6414 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3564C218yesmaximal, complemented
2C13×#3563C218yesmaximal, complemented
3C13×#3553C218yesmaximal, complemented
4C13×#3552C218yesmaximal, complemented
5C13×#3538C218yesmaximal, complemented
6C13×#3535C218yesmaximal, complemented
7C13×#3505C214yesmaximal, complemented
8C13×#3501C214yesmaximal, complemented
9C13×#3491C214yesmaximal, complemented
10C2×C13×#544C211yesmaximal, characteristic, complemented
11C2×C13×#539C212yesmaximal, complemented
12C13×#564C2218yescomplemented
13C13×#563C22116yescomplemented
14C13×#563C2218yescomplemented
15C13×#563C22116yescomplemented
16C13×#563C2218yescomplemented
17C13×#562C2218yescomplemented
18C13×#557C2218yescomplemented
19C13×#556C2218yescomplemented
20C13×#554C22116yescomplemented
21C13×#554C22116yescomplemented
22C13×#554C2218yescomplemented
23C13×#554C2218yescomplemented
24C13×#553C22116yescomplemented
25C13×#553C2218yescomplemented
26C13×#552C22116yescomplemented
27C13×#552C22116yescomplemented
28C13×#552C22116yescomplemented
29C13×#552C2218yescomplemented
30C13×#552C22116yescomplemented
31C13×#551C22116yescomplemented
32C13×#551C22116yescomplemented
33C13×#551C22116yescomplemented
34D4×Q8×C13C2218yescomplemented
35D4×Q8×C13C2218yescomplemented
36D4×Q8×C13C2218yescomplemented
37C13×#548C2218yescomplemented
38C13×#547C2218yescomplemented
39C13×#546C2218yescomplemented
40C13×#544C2218yescomplemented
41C13×#544C22116yescomplemented
42C13×#544C2218yescomplemented
43C13×#544C2218yescomplemented
44C13×#543C2214yes—
45C13×#543C2218yescomplemented
46C13×#542C22116yescomplemented
47C13×#541C22116yescomplemented
48C13×#541C22116yescomplemented
49C13×#541C22116yescomplemented
50C13×#539C2218yes—
51C13×#539C2218yes—
52C13×#539C2218yes—
53C13×#539C22116yescomplemented
54C13×#539C22116yescomplemented
55C13×#539C2218yescomplemented
56C13×#539C22116yescomplemented
57C13×#539C2218yescomplemented
58C13×#538C2218yes—
59C13×#536C22116yescomplemented
60C13×#534C2214yes—
61C13×#533C2218yescomplemented
62C2×C13×C4⋊Q8C2214yescomplemented
63C13×#529C2218yes—
64C13×#529C2218yescomplemented
65C13×#529C2218yescomplemented
66C2×C13×#126C2214yescomplemented
67C2×C13×#125C2214yescomplemented
68C2×C13×#125C2214yescomplemented
69C13×#525C2218yes—
70C2×C13×#123C2214yes—
71C2×C13×#123C2214yescomplemented
72C2×C13×C22⋊Q8C2212yes—
73C2×C13×C22⋊Q8C2214yes—
74C2×C13×C22⋊Q8C2218yescomplemented
75C2×C13×C22⋊Q8C2214yescomplemented
76C2×C13×#121C2212yes—
77C13×#518C2218yes—
78C2×C4×D4×C13C2214yes—
79C2×C13×#117C2212yes—
80C22×C13×C4⋊C4C2211yescharacteristic
81C2×C13×#41C2318yes—
82C22×Q8×C13C2312yes—
83C22×Q8×C13C2314yes—
84C22×Q8×C13C2318yes—
85C22×D4×C13C2314yes—
86C22×D4×C13C2312yes—
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2312yes—
89C23×C4×C13C2314yes—
90C13×C4⋊Q8C23116yes—
91C13×C4⋊Q8C2318yes—
92C13×C4⋊Q8C2318yes—
93C13×C4⋊Q8C2318yes—
94C13×C4⋊Q8C2318yes—
95C13×C4⋊Q8C23116yes—
96C13×C4⋊Q8C23116yes—
97C13×#126C23116yes—
98C13×#126C23116yes—
99C13×#126C23116yes—
100C13×#126C23116yes—
101C13×#126C23116yes—
102C13×#126C23116yes—
103C13×#126C23116yes—
104C13×#126C23116yes—
105C13×#126C23116yes—
106C13×#125C23116yes—
107C13×#125C23116yes—
108C13×#125C23116yes—
109C13×#125C2318yes—
110C13×#125C2318yes—
111C13×#125C2318yes—
112C13×#125C2318yes—
113C13×#125C2318yes—
114C13×#125C23116yes—
115C13×#125C23116yes—
116C13×#125C23116yes—
117C13×#125C23116yes—
118C13×#125C23116yes—
119C13×#125C23116yes—
120C13×#124C2318yes—
121C13×#124C2318yes—
122C13×#124C2318yes—
123C13×#124C23116yes—
124C13×#123C23116yes—
125C13×#123C23116yes—
126C13×#123C23116yes—
127C13×#123C23116yes—
128C13×#123C23116yes—
129C13×#123C23116yes—
130C13×#123C23116yes—
131C13×#123C23116yes—
132C13×#123C23116yes—
133C13×#123C23116yes—
134C13×C22⋊Q8C2318yes—
135C13×C22⋊Q8C2318yes—
136C13×C22⋊Q8C2318yes—
137C13×C22⋊Q8C2318yes—
138C13×C22⋊Q8C2318yes—
139C13×C22⋊Q8C2318yes—
140C13×C22⋊Q8C23116yes—
141C13×C22⋊Q8C23116yes—
142C13×C22⋊Q8C23116yes—
143C13×C22⋊Q8C2318yes—
144C13×C22⋊Q8C2318yes—
145C13×C22⋊Q8C23116yes—
146C13×C22⋊Q8C2318yes—
147C13×C22⋊Q8C2318yes—
148C13×C22⋊Q8C2318yes—
149C13×C22⋊Q8C23116yes—
150C13×C22⋊Q8C23116yes—
151C13×C22⋊Q8C23116yes—
152C13×C22⋊Q8C23116yes—
153C13×C22⋊Q8C23116yes—
154C13×C22⋊Q8C23116yes—
155C13×C22⋊Q8C23116yes—
156C13×C22⋊Q8C23116yes—
157C13×#121C2318yes—
158C13×#121C2318yes—
159C13×#121C2318yes—
160C13×#121C2318yes—
161C13×#121C2318yes—
162C13×#121C23116yes—
163C13×#120C23116yes—
164C4×Q8×C13C2318yes—
165C4×Q8×C13C2318yes—
166C4×Q8×C13C2318yes—
167C4×Q8×C13C2318yes—
168C4×Q8×C13C2318yes—
169C4×Q8×C13C23116yes—
170C4×D4×C13C2318yes—
171C4×D4×C13C2318yes—
172C4×D4×C13C2318yes—
173C4×D4×C13C2318yes—
174C4×D4×C13C23116yes—
175C4×D4×C13C23116yes—
176C4×D4×C13C23116yes—
177C4×D4×C13C23116yes—
178C4×D4×C13C23116yes—
179C4×D4×C13C2318yes—
180C4×D4×C13C2318yes—
181C4×D4×C13C2318yes—
182C13×#117C23116yes—
183C13×#117C23116yes—
184C13×#117C2318yes—
185C13×#117C23116yes—
186C13×#117C23116yes—
187C13×#117C23116yes—
188C2×C13×C4⋊C4C2314yes—
189C2×C13×C4⋊C4C2314yes—
190C2×C13×C4⋊C4C2314yes—
191C2×C13×C4⋊C4C2312yes—
192C2×C13×C4⋊C4C2312yes—
193C2×C13×C4⋊C4C2314yes—
194C2×C13×C4⋊C4C2312yes—
195C2×C13×C4⋊C4C2314yes—
196C2×C13×C4⋊C4C2314yes—
197C2×C13×C4⋊C4C2318yes—
198C2×C13×C4⋊C4C2312yes—
199C2×C13×C4⋊C4C2314yes—
200C2×C13×C4⋊C4C2318yes—
201C2×C13×C4⋊C4C23116yes—
202C2×C13×C4⋊C4C2314yes—
203C2×C13×C22⋊C4C2314yes—
204C2×C13×C22⋊C4C2314yes—
205C2×C13×C22⋊C4C2314yes—
206C2×C13×C22⋊C4C23116yes—
207C2×C13×C22⋊C4C2314yes—
208C2×C13×C22⋊C4C2314yes—
209C2×C13×C22⋊C4C2314yes—
210C2×C42×C13C2314yes—
211C2×C42×C13C2314yes—
212#62865C1311yesmaximal, characteristic, direct product factor, Sylow
213C24×C13C2414yes—
214C24×C13C2411yescharacteristic
215C13×#41—88no—
216C2×Q8×C13—82no—
217C2×Q8×C13—84no—
218C2×Q8×C13—88no—
219C2×Q8×C13C2418yes—
220C2×Q8×C13C2418yes—
221C2×Q8×C13C2418yes—
222C2×Q8×C13C2418yes—
223C2×Q8×C13C2418yes—
224C2×D4×C13—216no—
225C2×D4×C13—82no—
226C2×D4×C13C2418yes—
227C2×D4×C13C2418yes—
228C2×D4×C13C2418yes—
229C2×D4×C13C2418yes—
230C2×D4×C13C2418yes—
231C22×C4×C13—24no—
232C22×C4×C13—82no—
233C22×C4×C13—84no—
234C22×C4×C13C2412yes—
235C22×C4×C13C2414yes—
236C22×C4×C13C2414yes—
237C22×C4×C13C2414yes—
238C22×C4×C13C2414yes—
239C22×C4×C13C2414yes—
240C22×C4×C13C2414yes—
241C22×C4×C13C2414yes—
242C22×C4×C13C2412yes—
243C22×C4×C13C24116yes—
244C22×C4×C13C24116yes—
245C22×C4×C13C2414yes—
246C22×C4×C13C2412yes—
247C22×C4×C13C2418yes—
248C22×C4×C13C2418yes—
249C13×C4⋊C4C2414yes—
250C13×C4⋊C4C2418yes—
251C13×C4⋊C4C2414yes—
252C13×C4⋊C4C2418yes—
253C13×C4⋊C4C24116yes—
254C13×C4⋊C4C24116yes—
255C13×C4⋊C4C2418yes—
256C13×C4⋊C4C2418yes—
257C13×C4⋊C4C2418yes—
258C13×C4⋊C4C2418yes—
259C13×C4⋊C4C2418yes—
260C13×C4⋊C4C24116yes—
261C13×C4⋊C4C2418yes—
262C13×C4⋊C4C24116yes—
263C13×C4⋊C4C24116yes—
264C13×C4⋊C4C24116yes—
265C13×C4⋊C4C24116yes—
266C13×C4⋊C4C2418yes—
267C13×C4⋊C4C2418yes—
268C13×C4⋊C4C2418yes—
269C13×C4⋊C4C24116yes—
270C13×C4⋊C4C24116yes—
271C13×C4⋊C4C2418yes—
272C13×C4⋊C4C2418yes—
273C13×C22⋊C4C2418yes—
274C13×C22⋊C4C24116yes—
275C13×C22⋊C4C24116yes—
276C13×C22⋊C4C24116yes—
277C13×C22⋊C4C24116yes—
278C13×C22⋊C4C2418yes—
279C13×C22⋊C4C2418yes—
280C13×C22⋊C4C24116yes—
281C13×C22⋊C4C24116yes—
282C13×C22⋊C4C2418yes—
283C13×C22⋊C4C24116yes—
284C13×C22⋊C4C24116yes—
285C42×C13C2418yes—
286C42×C13C2418yes—
287C42×C13C2418yes—
288C42×C13C2418yes—
289C42×C13C24116yes—
290C42×C13C24116yes—
291#3564C2×C1318yescomplemented
292#3563C2×C1318yescomplemented
293#3553C2×C1318yescomplemented
294#3552C2×C1318yescomplemented
295#3538C2×C1318yescomplemented
296#3535C2×C1318yescomplemented
297#3505C2×C1314yescomplemented
298#3501C2×C1314yescomplemented
299#3491C2×C1314yescomplemented
300C2×#544C2×C1311yescharacteristic, complemented
301C2×#539C2×C1312yescomplemented
302C23×C13—28no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—44no—
306C23×C13—44no—
307C23×C132−1+414yes—
308C23×C13C2518yes—
309C23×C13C2512yes—
310C23×C13C2511yescharacteristic
311Q8×C13—48no—
312Q8×C13—48no—
313Q8×C13—48no—
314Q8×C13—48no—
315Q8×C13—48no—
316D4×C13—216no—
317D4×C13—216no—
318D4×C13—48no—
319D4×C13—48no—
320D4×C13—48no—
321C2×C4×C13—28no—
322C2×C4×C13—24no—
323C2×C4×C13—28no—
324C2×C4×C13—44no—
325C2×C4×C13—42no—
326C2×C4×C13—44no—
327C2×C4×C13—42no—
328C2×C4×C13—44no—
329C2×C4×C13—48no—
330C2×C4×C13—48no—
331C2×C4×C13—44no—
332C2×C4×C13—416no—
333C2×C4×C13—44no—
334C2×C4×C13—44no—
335C2×C4×C13—416no—
336C2×C4×C13C2518yes—
337C2×C4×C13C2514yes—
338C2×C4×C13C2518yes—
339C2×C4×C13C2518yes—
340C2×C4×C13C2518yes—
341C2×C4×C13C2514yes—
342C2×C4×C13C2518yes—
343C2×C4×C13C2514yes—
344#564C22×C1318yescomplemented
345#563C22×C13116yescomplemented
346#563C22×C1318yescomplemented
347#563C22×C13116yescomplemented
348#563C22×C1318yescomplemented
349#562C22×C1318yescomplemented
350#557C22×C1318yescomplemented
351#556C22×C1318yescomplemented
352#554C22×C13116yescomplemented
353#554C22×C13116yescomplemented
354#554C22×C1318yescomplemented
355#554C22×C1318yescomplemented
356#553C22×C13116yescomplemented
357#553C22×C1318yescomplemented
358#552C22×C13116yescomplemented
359#552C22×C13116yescomplemented
360#552C22×C1318yescomplemented
361#552C22×C13116yescomplemented
362#552C22×C13116yescomplemented
363#551C22×C13116yescomplemented
364#551C22×C13116yescomplemented
365#551C22×C13116yescomplemented
366D4×Q8C22×C1318yescomplemented
367D4×Q8C22×C1318yescomplemented
368D4×Q8C22×C1318yescomplemented
369#548C22×C1318yescomplemented
370#547C22×C1318yescomplemented
371#546C22×C1318yescomplemented
372#544C22×C1318yescomplemented
373#544C22×C1318yescomplemented
374#544C22×C1318yescomplemented
375#544C22×C13116yescomplemented
376#543C22×C1314yes—
377#543C22×C1318yescomplemented
378#542C22×C13116yescomplemented
379#541C22×C13116yescomplemented
380#541C22×C13116yescomplemented
381#541C22×C13116yescomplemented
382#539C22×C1318yes—
383#539C22×C1318yes—
384#539C22×C1318yes—
385#539C22×C13116yescomplemented
386#539C22×C1318yescomplemented
387#539C22×C1318yescomplemented
388#539C22×C13116yescomplemented
389#539C22×C13116yescomplemented
390#538C22×C1318yes—
391#536C22×C13116yescomplemented
392#534C22×C1314yes—
393#533C22×C1318yescomplemented
394C2×C4⋊Q8C22×C1314yescomplemented
395#529C22×C1318yes—
396#529C22×C1318yescomplemented
397#529C22×C1318yescomplemented
398C2×#126C22×C1314yescomplemented
399C2×#125C22×C1314yescomplemented
400C2×#125C22×C1314yescomplemented
401#525C22×C1318yes—
402C2×#123C22×C1314yes—
403C2×#123C22×C1314yescomplemented
404C2×C22⋊Q8C22×C1312yes—
405C2×C22⋊Q8C22×C1314yes—
406C2×C22⋊Q8C22×C1314yescomplemented
407C2×C22⋊Q8C22×C1318yescomplemented
408C2×#121C22×C1312yes—
409#518C22×C1318yes—
410C2×C4×D4C22×C1314yes—
411C2×#117C22×C1312yes—
412C22×C4⋊C4C22×C1311yescharacteristic
413C22×C13—21no—
414C22×C13—22no—
415C22×C13—21no—
416C22×C13—22no—
417C22×C13—28no—
418C22×C13—28no—
419C22×C13—28no—
420C22×C13—44no—
421C22×C13—88no—
422C22×C13C2×2−1+414yes—
423C22×C13C2×2−1+412yes—
424C22×C13C2611yescharacteristic
425C4×C13—24no—
426C4×C13—28no—
427C4×C13—24no—
428C4×C13—24no—
429C4×C13—28no—
430C4×C13—28no—
431C4×C13—28no—
432C4×C13—28no—
433C2×#41C23×C1318yes—
434C22×Q8C23×C1312yes—
435C22×Q8C23×C1314yes—
436C22×Q8C23×C1318yes—
437C22×D4C23×C1314yes—
438C22×D4C23×C1312yes—
439C23×C4C23×C1311yescharacteristic
440C23×C4C23×C1312yes—
441C23×C4C23×C1314yes—
442C4⋊Q8C23×C13116yes—
443C4⋊Q8C23×C1318yes—
444C4⋊Q8C23×C1318yes—
445C4⋊Q8C23×C1318yes—
446C4⋊Q8C23×C1318yes—
447C4⋊Q8C23×C13116yes—
448C4⋊Q8C23×C13116yes—
449#126C23×C13116yes—
450#126C23×C13116yes—
451#126C23×C13116yes—
452#126C23×C13116yes—
453#126C23×C13116yes—
454#126C23×C13116yes—
455#126C23×C13116yes—
456#126C23×C13116yes—
457#126C23×C13116yes—
458#125C23×C13116yes—
459#125C23×C13116yes—
460#125C23×C13116yes—
461#125C23×C1318yes—
462#125C23×C1318yes—
463#125C23×C1318yes—
464#125C23×C1318yes—
465#125C23×C1318yes—
466#125C23×C13116yes—
467#125C23×C13116yes—
468#125C23×C13116yes—
469#125C23×C13116yes—
470#125C23×C13116yes—
471#125C23×C13116yes—
472#124C23×C1318yes—
473#124C23×C1318yes—
474#124C23×C1318yes—
475#124C23×C13116yes—
476#123C23×C13116yes—
477#123C23×C13116yes—
478#123C23×C13116yes—
479#123C23×C13116yes—
480#123C23×C13116yes—
481#123C23×C13116yes—
482#123C23×C13116yes—
483#123C23×C13116yes—
484#123C23×C13116yes—
485#123C23×C13116yes—
486C22⋊Q8C23×C1318yes—
487C22⋊Q8C23×C1318yes—
488C22⋊Q8C23×C1318yes—
489C22⋊Q8C23×C1318yes—
490C22⋊Q8C23×C1318yes—
491C22⋊Q8C23×C1318yes—
492C22⋊Q8C23×C13116yes—
493C22⋊Q8C23×C13116yes—
494C22⋊Q8C23×C13116yes—
495C22⋊Q8C23×C1318yes—
496C22⋊Q8C23×C1318yes—
497C22⋊Q8C23×C13116yes—
498C22⋊Q8C23×C1318yes—
499C22⋊Q8C23×C1318yes—
500C22⋊Q8C23×C1318yes—
501C22⋊Q8C23×C13116yes—
502C22⋊Q8C23×C13116yes—
503C22⋊Q8C23×C13116yes—
504C22⋊Q8C23×C13116yes—
505C22⋊Q8C23×C13116yes—
506C22⋊Q8C23×C13116yes—
507C22⋊Q8C23×C13116yes—
508C22⋊Q8C23×C13116yes—
509#121C23×C1318yes—
510#121C23×C1318yes—
511#121C23×C1318yes—
512#121C23×C1318yes—
513#121C23×C1318yes—
514#121C23×C13116yes—
515#120C23×C13116yes—
516C4×Q8C23×C1318yes—
517C4×Q8C23×C1318yes—
518C4×Q8C23×C1318yes—
519C4×Q8C23×C1318yes—
520C4×Q8C23×C1318yes—
521C4×Q8C23×C13116yes—
522C4×D4C23×C1318yes—
523C4×D4C23×C1318yes—
524C4×D4C23×C1318yes—
525C4×D4C23×C1318yes—
526C4×D4C23×C13116yes—
527C4×D4C23×C13116yes—
528C4×D4C23×C13116yes—
529C4×D4C23×C13116yes—
530C4×D4C23×C13116yes—
531C4×D4C23×C1318yes—
532C4×D4C23×C1318yes—
533C4×D4C23×C1318yes—
534#117C23×C13116yes—
535#117C23×C13116yes—
536#117C23×C1318yes—
537#117C23×C13116yes—
538#117C23×C13116yes—
539#117C23×C13116yes—
540C2×C4⋊C4C23×C1314yes—
541C2×C4⋊C4C23×C1314yes—
542C2×C4⋊C4C23×C1314yes—
543C2×C4⋊C4C23×C1312yes—
544C2×C4⋊C4C23×C1312yes—
545C2×C4⋊C4C23×C1314yes—
546C2×C4⋊C4C23×C1312yes—
547C2×C4⋊C4C23×C1314yes—
548C2×C4⋊C4C23×C1314yes—
549C2×C4⋊C4C23×C1318yes—
550C2×C4⋊C4C23×C1312yes—
551C2×C4⋊C4C23×C1314yes—
552C2×C4⋊C4C23×C1318yes—
553C2×C4⋊C4C23×C13116yes—
554C2×C4⋊C4C23×C1314yes—
555C2×C22⋊C4C23×C1314yes—
556C2×C22⋊C4C23×C1314yes—
557C2×C22⋊C4C23×C1314yes—
558C2×C22⋊C4C23×C13116yes—
559C2×C22⋊C4C23×C1314yes—
560C2×C22⋊C4C23×C1314yes—
561C2×C22⋊C4C23×C1314yes—
562C2×C42C23×C1314yes—
563C2×C42C23×C1314yes—
564C2×C13—24no—
565C2×C13—22no—
566C2×C13—48no—
567C2×C13C22×2−1+411yescharacteristic
568C2×C13H(7,𝔽2)11yescharacteristic
569C2×C132−1+611yescharacteristic
570C24C24×C1314yes—
571C24C24×C1311yescharacteristic
572#41—88no—
573C2×Q8—82no—
574C2×Q8—84no—
575C2×Q8—88no—
576C2×Q8C24×C1318yes—
577C2×Q8C24×C1318yes—
578C2×Q8C24×C1318yes—
579C2×Q8C24×C1318yes—
580C2×Q8C24×C1318yes—
581C2×D4—216no—
582C2×D4—82no—
583C2×D4C24×C1318yes—
584C2×D4C24×C1318yes—
585C2×D4C24×C1318yes—
586C2×D4C24×C1318yes—
587C2×D4C24×C1318yes—
588C22×C4—24no—
589C22×C4—82no—
590C22×C4—84no—
591C22×C4C24×C1312yes—
592C22×C4C24×C1314yes—
593C22×C4C24×C1314yes—
594C22×C4C24×C1314yes—
595C22×C4C24×C1314yes—
596C22×C4C24×C1314yes—
597C22×C4C24×C1314yes—
598C22×C4C24×C1314yes—
599C22×C4C24×C1312yes—
600C22×C4C24×C13116yes—
601C22×C4C24×C13116yes—
602C22×C4C24×C1314yes—
603C22×C4C24×C1312yes—
604C22×C4C24×C1318yes—
605C22×C4C24×C1318yes—
606C4⋊C4C24×C1314yes—
607C4⋊C4C24×C1318yes—
608C4⋊C4C24×C1314yes—
609C4⋊C4C24×C1318yes—
610C4⋊C4C24×C13116yes—
611C4⋊C4C24×C13116yes—
612C4⋊C4C24×C1318yes—
613C4⋊C4C24×C1318yes—
614C4⋊C4C24×C1318yes—
615C4⋊C4C24×C1318yes—
616C4⋊C4C24×C1318yes—
617C4⋊C4C24×C13116yes—
618C4⋊C4C24×C1318yes—
619C4⋊C4C24×C13116yes—
620C4⋊C4C24×C13116yes—
621C4⋊C4C24×C13116yes—
622C4⋊C4C24×C13116yes—
623C4⋊C4C24×C1318yes—
624C4⋊C4C24×C1318yes—
625C4⋊C4C24×C1318yes—
626C4⋊C4C24×C13116yes—
627C4⋊C4C24×C13116yes—
628C4⋊C4C24×C1318yes—
629C4⋊C4C24×C1318yes—
630C22⋊C4C24×C1318yes—
631C22⋊C4C24×C13116yes—
632C22⋊C4C24×C13116yes—
633C22⋊C4C24×C13116yes—
634C22⋊C4C24×C13116yes—
635C22⋊C4C24×C1318yes—
636C22⋊C4C24×C1318yes—
637C22⋊C4C24×C13116yes—
638C22⋊C4C24×C13116yes—
639C22⋊C4C24×C1318yes—
640C22⋊C4C24×C13116yes—
641C22⋊C4C24×C13116yes—
642C42C24×C1318yes—
643C42C24×C1318yes—
644C42C24×C1318yes—
645C42C24×C1318yes—
646C42C24×C13116yes—
647C42C24×C13116yes—
648C13#6286511yescharacteristic, direct product factor, Sylow
649C23—28no—
650C23—41no—
651C23—41no—
652C23—44no—
653C23—44no—
654C23C13×2−1+414yes—
655C23C25×C1318yes—
656C23C25×C1312yes—
657C23C25×C1311yescharacteristic
658Q8—48no—
659Q8—48no—
660Q8—48no—
661Q8—48no—
662Q8—48no—
663D4—216no—
664D4—216no—
665D4—48no—
666D4—48no—
667D4—48no—
668C2×C4—28no—
669C2×C4—24no—
670C2×C4—28no—
671C2×C4—44no—
672C2×C4—42no—
673C2×C4—44no—
674C2×C4—42no—
675C2×C4—44no—
676C2×C4—48no—
677C2×C4—48no—
678C2×C4—44no—
679C2×C4—416no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—416no—
683C2×C4C25×C1318yes—
684C2×C4C25×C1314yes—
685C2×C4C25×C1318yes—
686C2×C4C25×C1318yes—
687C2×C4C25×C1318yes—
688C2×C4C25×C1314yes—
689C2×C4C25×C1318yes—
690C2×C4C25×C1314yes—
691C22—21no—
692C22—22no—
693C22—21no—
694C22—22no—
695C22—28no—
696C22—28no—
697C22—28no—
698C22—44no—
699C22—88no—
700C22C2×C13×2−1+414yes—
701C22C2×C13×2−1+412yes—
702C22C26×C1311yescharacteristic
703C4—24no—
704C4—28no—
705C4—24no—
706C4—24no—
707C4—28no—
708C4—28no—
709C4—28no—
710C4—28no—
711C2—24no—
712C2—22no—
713C2—48no—
714C2C22×C13×2−1+411yescharacteristic
715C2C13×H(7,𝔽2)11yescharacteristic
716C2C13×2−1+611yescharacteristic
subgroupG/H
center, socleC22×C13C26
commutator, Frattini, cosocleC22C26×C13
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3564C2semidirect
2. C13×#3563C2semidirect
3. C13×#3553C2semidirect
4. C13×#3552C2semidirect
5. C13×#3538C2semidirect
6. C13×#3535C2semidirect
7. C13×#3505C2semidirect
8. C13×#3501C2semidirect
9. C13×#3491C2semidirect
10. C2×C13×#544C2semidirect
11. C2×C13×#539C2semidirect
12. C13×#564C22semidirect
13. C13×#563C22semidirect
14. C13×#563C22semidirect
15. C13×#563C22semidirect
16. C13×#563C22semidirect
17. C13×#562C22semidirect
18. C13×#557C22semidirect
19. C13×#556C22semidirect
20. C13×#554C22semidirect
21. C13×#554C22semidirect
22. C13×#554C22semidirect
23. C13×#554C22semidirect
24. C13×#553C22semidirect
25. C13×#553C22semidirect
26. C13×#552C22semidirect
27. C13×#552C22semidirect
28. C13×#552C22semidirect
29. C13×#552C22semidirect
30. C13×#552C22semidirect
31. C13×#551C22semidirect
32. C13×#551C22semidirect
33. C13×#551C22semidirect
34. D4×Q8×C13C22semidirect
35. D4×Q8×C13C22semidirect
36. D4×Q8×C13C22semidirect
37. C13×#548C22semidirect
38. C13×#547C22semidirect
39. C13×#546C22semidirect
40. C13×#544C22semidirect
41. C13×#544C22semidirect
42. C13×#544C22semidirect
43. C13×#544C22semidirect
45. C13×#543C22semidirect
46. C13×#542C22semidirect
47. C13×#541C22semidirect
48. C13×#541C22semidirect
49. C13×#541C22semidirect
53. C13×#539C22semidirect
54. C13×#539C22semidirect
55. C13×#539C22semidirect
56. C13×#539C22semidirect
57. C13×#539C22semidirect
59. C13×#536C22semidirect
61. C13×#533C22semidirect
62. C2×C13×C4⋊Q8C22semidirect
64. C13×#529C22semidirect
65. C13×#529C22semidirect
66. C2×C13×#126C22semidirect
67. C2×C13×#125C22semidirect
68. C2×C13×#125C22semidirect
71. C2×C13×#123C22semidirect
74. C2×C13×C22⋊Q8C22semidirect
75. C2×C13×C22⋊Q8C22semidirect
212. #62865C13direct (N × H)
291. #3564C2×C13semidirect
292. #3563C2×C13semidirect
293. #3553C2×C13semidirect
294. #3552C2×C13semidirect
295. #3538C2×C13semidirect
296. #3535C2×C13semidirect
297. #3505C2×C13semidirect
298. #3501C2×C13semidirect
299. #3491C2×C13semidirect
300. C2×#544C2×C13semidirect
301. C2×#539C2×C13semidirect
344. #564C22×C13semidirect
345. #563C22×C13semidirect
346. #563C22×C13semidirect
347. #563C22×C13semidirect
348. #563C22×C13semidirect
349. #562C22×C13semidirect
350. #557C22×C13semidirect
351. #556C22×C13semidirect
352. #554C22×C13semidirect
353. #554C22×C13semidirect
354. #554C22×C13semidirect
355. #554C22×C13semidirect
356. #553C22×C13semidirect
357. #553C22×C13semidirect
358. #552C22×C13semidirect
359. #552C22×C13semidirect
360. #552C22×C13semidirect
361. #552C22×C13semidirect
362. #552C22×C13semidirect
363. #551C22×C13semidirect
364. #551C22×C13semidirect
365. #551C22×C13semidirect
366. D4×Q8C22×C13semidirect
367. D4×Q8C22×C13semidirect
368. D4×Q8C22×C13semidirect
369. #548C22×C13semidirect
370. #547C22×C13semidirect
371. #546C22×C13semidirect
372. #544C22×C13semidirect
373. #544C22×C13semidirect
374. #544C22×C13semidirect
375. #544C22×C13semidirect
377. #543C22×C13semidirect
378. #542C22×C13semidirect
379. #541C22×C13semidirect
380. #541C22×C13semidirect
381. #541C22×C13semidirect
385. #539C22×C13semidirect
386. #539C22×C13semidirect
387. #539C22×C13semidirect
388. #539C22×C13semidirect
389. #539C22×C13semidirect
391. #536C22×C13semidirect
393. #533C22×C13semidirect
394. C2×C4⋊Q8C22×C13semidirect
396. #529C22×C13semidirect
397. #529C22×C13semidirect
398. C2×#126C22×C13semidirect
399. C2×#125C22×C13semidirect
400. C2×#125C22×C13semidirect
403. C2×#123C22×C13semidirect
406. C2×C22⋊Q8C22×C13semidirect
407. C2×C22⋊Q8C22×C13semidirect
648. C13#62865direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35642
C13×#35632
C13×#35532
C13×#35522
C13×#35382
C13×#35352
C13×#35052
C13×#35012
C13×#34912
C2×C13×#5442
C2×C13×#5392
#6286513