Finite Group Databasebeta

← C13×#62863 #15749202

Subgroups — C13×#62863 #15749202

Order 3328.

7466 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3560C218yesmaximal, complemented
2C13×#3558C218yesmaximal, complemented
3C13×#3537C218yesmaximal, complemented
4C13×#3534C218yesmaximal, complemented
5C13×#3533C218yesmaximal, complemented
6C13×#3532C218yesmaximal, complemented
7C13×#3505C214yesmaximal, complemented
8C13×#3496C214yesmaximal, complemented
9C13×#3484C214yesmaximal, complemented
10C2×C13×#538C212yesmaximal, complemented
11C2×C13×#534C211yesmaximal, characteristic, complemented
12C2×C13×H(5,𝔽2)C2214yescomplemented
13C23×D4×C13C2212yescomplemented
14C13×#563C2218yescomplemented
15C13×#562C22116yescomplemented
16C13×H(3,𝔽4)C2218yescomplemented
17C13×#560C22116yescomplemented
18C13×#560C2218yescomplemented
19C13×#560C2218yescomplemented
20C13×#559C2218yescomplemented
21C13×#553C22116yescomplemented
22C13×#553C2218yescomplemented
23C13×#553C22116yescomplemented
24C13×#552C2218yescomplemented
25C13×#551C22116yescomplemented
26C13×#551C2218yescomplemented
27C13×#551C2218yescomplemented
28C13×#548C2218yescomplemented
29C13×#547C2218yescomplemented
30C13×#547C2218yescomplemented
31C13×#546C2218yescomplemented
32C13×#546C22116yescomplemented
33C13×#546C22116yescomplemented
34C13×#546C22116yescomplemented
35C13×#546C22116yescomplemented
36C13×#546C22116yescomplemented
37D42×C13C2218yescomplemented
38D42×C13C22116yescomplemented
39D42×C13C22116yescomplemented
40D42×C13C2218yescomplemented
41D42×C13C2218yescomplemented
42C13×#542C22116yescomplemented
43C13×#540C22116yescomplemented
44C13×#539C22116yescomplemented
45C13×#539C2218yescomplemented
46C13×#538C22116yescomplemented
47C13×#538C2218yescomplemented
48C13×#538C2218yescomplemented
49C13×#538C22116yescomplemented
50C13×#538C22116yescomplemented
51C13×#538C22116yescomplemented
52C13×#538C2218yescomplemented
53C13×#537C2218yescomplemented
54C13×#535C2218yescomplemented
55C13×#535C22116yescomplemented
56C13×#534C2218yescomplemented
57C13×#534C2218yescomplemented
58C13×#534C2218yescomplemented
59C13×#534C2218yescomplemented
60C13×#534C22116yescomplemented
61C13×#534C2218yescomplemented
62C13×#532C2218yescomplemented
63C13×#529C2218yescomplemented
64C2×C13×#126C2214yescomplemented
65C2×C13×#124C2214yescomplemented
66C13×#525C2218yescomplemented
67C13×#525C2218yescomplemented
68C2×C13×#123C2214yescomplemented
69C2×C13×#123C2214yescomplemented
70C2×C13×C22⋊Q8C2212yescomplemented
71C2×C13×#121C2214yescomplemented
72C2×C13×#121C2214yescomplemented
73C2×C13×#121C2212yescomplemented
74C2×C13×#121C2218yescomplemented
75C2×C13×#120C2214yescomplemented
76C2×C13×#120C2214yescomplemented
77C2×C13×#120C2218yescomplemented
78C13×#518C2214yescomplemented
79C2×C4×D4×C13C2214yescomplemented
80C22×C13×C22⋊C4C2211yescharacteristic, complemented
81C25×C13C2311yescharacteristic
82C25×C13C2312yes—
83C13×H(5,𝔽2)—416no—
84C2×C13×#41C2318yes—
85C2×C13×#41C23116yescomplemented
86C2×C13×#41C2318yescomplemented
87C22×Q8×C13C2312yescomplemented
88C22×D4×C13—48no—
89C22×D4×C13C2314yes—
90C22×D4×C13C2314yes—
91C22×D4×C13C2314yes—
92C22×D4×C13C2318yes—
93C22×D4×C13C23116yes—
94C22×D4×C13C2314yes—
95C22×D4×C13C2314yes—
96C22×D4×C13C2314yes—
97C22×D4×C13C23116yescomplemented
98C22×D4×C13C23116yescomplemented
99C22×D4×C13C2312yescomplemented
100C22×D4×C13C2318yescomplemented
101C23×C4×C13C2312yes—
102C23×C4×C13C2312yes—
103C23×C4×C13C2314yescomplemented
104C13×C4⋊Q8C2318yescomplemented
105C13×#127C2318yes—
106C13×#127C2318yes—
107C13×#127C2318yescomplemented
108C13×#126C23116yescomplemented
109C13×#126C23116yescomplemented
110C13×#126C23116yescomplemented
111C13×#126C23116yescomplemented
112C13×#126C23116yescomplemented
113C13×#125C2318yescomplemented
114C13×#125C23116yescomplemented
115C13×#124C2318yes—
116C13×#124C2318yes—
117C13×#124C23116yescomplemented
118C13×#124C23116yescomplemented
119C13×#124C2318yescomplemented
120C13×#124C23116yescomplemented
121C13×#124C23116yescomplemented
122C13×#123C23116yes—
123C13×#123C2318yes—
124C13×#123C2318yes—
125C13×#123C23116yes—
126C13×#123C2318yes—
127C13×#123C2318yes—
128C13×#123C23116yescomplemented
129C13×#123C23116yescomplemented
130C13×#123C23116yescomplemented
131C13×#123C23116yescomplemented
132C13×#123C23116yescomplemented
133C13×#123C23116yescomplemented
134C13×#123C23116yescomplemented
135C13×#123C23116yescomplemented
136C13×C22⋊Q8C2318yes—
137C13×C22⋊Q8C2318yescomplemented
138C13×C22⋊Q8C2318yescomplemented
139C13×C22⋊Q8C23116yescomplemented
140C13×C22⋊Q8C23116yescomplemented
141C13×C22⋊Q8C23116yescomplemented
142C13×C22⋊Q8C23116yescomplemented
143C13×#121C2318yes—
144C13×#121C2318yes—
145C13×#121C2318yes—
146C13×#121C2318yes—
147C13×#121C2318yes—
148C13×#121C23116yes—
149C13×#121C23116yes—
150C13×#121C23116yes—
151C13×#121C23116yes—
152C13×#121C2318yescomplemented
153C13×#121C23116yescomplemented
154C13×#121C23116yescomplemented
155C13×#121C23116yescomplemented
156C13×#121C2318yescomplemented
157C13×#121C23116yescomplemented
158C13×#121C2318yescomplemented
159C13×#121C2318yescomplemented
160C13×#121C23116yescomplemented
161C13×#121C23116yescomplemented
162C13×#121C23116yescomplemented
163C13×#121C23116yescomplemented
164C13×#121C23116yescomplemented
165C13×#120C23116yes—
166C13×#120C23116yes—
167C13×#120C2318yes—
168C13×#120C2318yes—
169C13×#120C23116yes—
170C13×#120C23116yes—
171C13×#120C2318yes—
172C13×#120C2318yes—
173C13×#120C23116yescomplemented
174C13×#120C23116yescomplemented
175C13×#120C23116yescomplemented
176C13×#120C23116yescomplemented
177C13×#120C23116yescomplemented
178C4×Q8×C13C2318yescomplemented
179C4×D4×C13C2318yes—
180C4×D4×C13C2318yes—
181C4×D4×C13C2318yescomplemented
182C4×D4×C13C2318yescomplemented
183C4×D4×C13C23116yescomplemented
184C4×D4×C13C23116yescomplemented
185C4×D4×C13C23116yescomplemented
186C4×D4×C13C23116yescomplemented
187C4×D4×C13C23116yescomplemented
188C4×D4×C13C2318yescomplemented
189C4×D4×C13C2318yescomplemented
190C4×D4×C13C2318yescomplemented
191C4×D4×C13C23116yescomplemented
192C13×#117C2318yes—
193C13×#117C2318yescomplemented
194C13×#117C23116yescomplemented
195C2×C13×C4⋊C4C2314yes—
196C2×C13×C4⋊C4C2314yescomplemented
197C2×C13×C4⋊C4C2314yescomplemented
198C2×C13×C4⋊C4C2312yescomplemented
199C2×C13×C4⋊C4C2318yescomplemented
200C2×C13×C4⋊C4C2312yescomplemented
201C2×C13×C22⋊C4C2314yes—
202C2×C13×C22⋊C4C2314yes—
203C2×C13×C22⋊C4C2314yes—
204C2×C13×C22⋊C4C2314yes—
205C2×C13×C22⋊C4C2318yes—
206C2×C13×C22⋊C4C2318yes—
207C2×C13×C22⋊C4C2314yes—
208C2×C13×C22⋊C4C2314yes—
209C2×C13×C22⋊C4C2314yescomplemented
210C2×C13×C22⋊C4C23116yescomplemented
211C2×C13×C22⋊C4C2314yescomplemented
212C2×C13×C22⋊C4C23116yescomplemented
213C2×C42×C13C2314yescomplemented
214#62863C1311yesmaximal, characteristic, direct product factor, Sylow
215C24×C13—24no—
216C24×C13—44no—
217C24×C13—82no—
218C24×C13—84no—
219C24×C13C2414yes—
220C24×C13C2414yes—
221C24×C13C2412yes—
222C24×C13C2414yes—
223C24×C13C2418yes—
224C24×C13C2418yes—
225C24×C13C2411yescharacteristic
226C13×#41—416no—
227C13×#41—432no—
228C13×#41—88no—
229C2×Q8×C13—82no—
230C2×Q8×C13C2418yes—
231C2×Q8×C13C2418yes—
232C2×D4×C13—216no—
233C2×D4×C13—216no—
234C2×D4×C13—48no—
235C2×D4×C13—432no—
236C2×D4×C13—416no—
237C2×D4×C13—432no—
238C2×D4×C13—84no—
239C2×D4×C13—84no—
240C2×D4×C13—84no—
241C2×D4×C13—82no—
242C2×D4×C13—88no—
243C2×D4×C13—816no—
244C2×D4×C13C2418yes—
245C2×D4×C13C2418yes—
246C2×D4×C13C24116yes—
247C2×D4×C13C2418yes—
248C2×D4×C13C2418yes—
249C2×D4×C13C24116yes—
250C2×D4×C13C24116yes—
251C2×D4×C13C24116yes—
252C2×D4×C13C24116yes—
253C2×D4×C13C2418yes—
254C2×D4×C13C2418yes—
255C2×D4×C13C2418yes—
256C2×D4×C13C24116yes—
257C2×D4×C13C2418yes—
258C22×C4×C13—44no—
259C22×C4×C13—82no—
260C22×C4×C13—84no—
261C22×C4×C13C2414yes—
262C22×C4×C13C2414yes—
263C22×C4×C13C2414yes—
264C22×C4×C13C2414yes—
265C22×C4×C13C2414yes—
266C22×C4×C13C2412yes—
267C22×C4×C13C2412yes—
268C22×C4×C13C2414yes—
269C22×C4×C13C24116yes—
270C22×C4×C13C2418yes—
271C22×C4×C13C2418yes—
272C22×C4×C13C24116yes—
273C22×C4×C13C2418yes—
274C22×C4×C13C2418yes—
275C13×C4⋊C4C2418yes—
276C13×C4⋊C4C2418yes—
277C13×C4⋊C4C2418yes—
278C13×C4⋊C4C24116yes—
279C13×C4⋊C4C24116yes—
280C13×C4⋊C4C2418yes—
281C13×C4⋊C4C2418yes—
282C13×C4⋊C4C2418yes—
283C13×C4⋊C4C24116yes—
284C13×C4⋊C4C24116yes—
285C13×C22⋊C4C2418yes—
286C13×C22⋊C4C2414yes—
287C13×C22⋊C4C2418yes—
288C13×C22⋊C4C2414yes—
289C13×C22⋊C4C24116yes—
290C13×C22⋊C4C24116yes—
291C13×C22⋊C4C24116yes—
292C13×C22⋊C4C24116yes—
293C13×C22⋊C4C2418yes—
294C13×C22⋊C4C2418yes—
295C13×C22⋊C4C2418yes—
296C13×C22⋊C4C24116yes—
297C13×C22⋊C4C24116yes—
298C13×C22⋊C4C24116yes—
299C13×C22⋊C4C24116yes—
300C13×C22⋊C4C2418yes—
301C13×C22⋊C4C2418yes—
302C13×C22⋊C4C24116yes—
303C42×C13C2418yes—
304C42×C13C2418yes—
305C42×C13C2418yes—
306C42×C13C2418yes—
307#3560C2×C1318yescomplemented
308#3558C2×C1318yescomplemented
309#3537C2×C1318yescomplemented
310#3534C2×C1318yescomplemented
311#3533C2×C1318yescomplemented
312#3532C2×C1318yescomplemented
313#3505C2×C1314yescomplemented
314#3496C2×C1314yescomplemented
315#3484C2×C1314yescomplemented
316C2×#538C2×C1312yescomplemented
317C2×#534C2×C1311yescharacteristic, complemented
318C23×C13—24no—
319C23×C13—28no—
320C23×C13—28no—
321C23×C13—28no—
322C23×C13—42no—
323C23×C13—44no—
324C23×C13—44no—
325C23×C13—48no—
326C23×C13—44no—
327C23×C13—44no—
328C23×C13—44no—
329C23×C13—48no—
330C23×C13—416no—
331C23×C13—48no—
332C23×C13—416no—
333C23×C13—88no—
334C23×C13—816no—
335C23×C13H(5,𝔽2)14yes—
336C23×C13C2514yes—
337C23×C13C2518yes—
338C23×C13C2518yes—
339C23×C13C2511yescharacteristic
340C23×C13C2512yes—
341Q8×C13—48no—
342Q8×C13—48no—
343D4×C13—232no—
344D4×C13—216no—
345D4×C13—216no—
346D4×C13—48no—
347D4×C13—48no—
348D4×C13—48no—
349D4×C13—416no—
350D4×C13—416no—
351D4×C13—48no—
352D4×C13—416no—
353D4×C13—48no—
354D4×C13—416no—
355D4×C13—48no—
356D4×C13—416no—
357C2×C4×C13—28no—
358C2×C4×C13—28no—
359C2×C4×C13—48no—
360C2×C4×C13—44no—
361C2×C4×C13—42no—
362C2×C4×C13—44no—
363C2×C4×C13—48no—
364C2×C4×C13—44no—
365C2×C4×C13—42no—
366C2×C4×C13—48no—
367C2×C4×C13—416no—
368C2×C4×C13—48no—
369C2×C4×C13—44no—
370C2×C4×C13—416no—
371C2×C4×C13C2518yes—
372C2×C4×C13C2514yes—
373C2×C4×C13C2514yes—
374C2×C4×C13C2518yes—
375C2×C4×C13C2518yes—
376C2×C4×C13C2518yes—
377C2×H(5,𝔽2)C22×C1314yescomplemented
378C23×D4C22×C1312yescomplemented
379#563C22×C1318yescomplemented
380#562C22×C13116yescomplemented
381H(3,𝔽4)C22×C1318yescomplemented
382#560C22×C13116yescomplemented
383#560C22×C1318yescomplemented
384#560C22×C1318yescomplemented
385#559C22×C1318yescomplemented
386#553C22×C13116yescomplemented
387#553C22×C1318yescomplemented
388#553C22×C13116yescomplemented
389#552C22×C1318yescomplemented
390#551C22×C13116yescomplemented
391#551C22×C1318yescomplemented
392#551C22×C1318yescomplemented
393#548C22×C1318yescomplemented
394#547C22×C1318yescomplemented
395#547C22×C1318yescomplemented
396#546C22×C1318yescomplemented
397#546C22×C13116yescomplemented
398#546C22×C13116yescomplemented
399#546C22×C13116yescomplemented
400#546C22×C13116yescomplemented
401#546C22×C13116yescomplemented
402D42C22×C1318yescomplemented
403D42C22×C13116yescomplemented
404D42C22×C13116yescomplemented
405D42C22×C1318yescomplemented
406D42C22×C1318yescomplemented
407#542C22×C13116yescomplemented
408#540C22×C13116yescomplemented
409#539C22×C13116yescomplemented
410#539C22×C1318yescomplemented
411#538C22×C13116yescomplemented
412#538C22×C1318yescomplemented
413#538C22×C1318yescomplemented
414#538C22×C13116yescomplemented
415#538C22×C13116yescomplemented
416#538C22×C13116yescomplemented
417#538C22×C1318yescomplemented
418#537C22×C1318yescomplemented
419#535C22×C1318yescomplemented
420#535C22×C13116yescomplemented
421#534C22×C1318yescomplemented
422#534C22×C1318yescomplemented
423#534C22×C1318yescomplemented
424#534C22×C1318yescomplemented
425#534C22×C13116yescomplemented
426#534C22×C1318yescomplemented
427#532C22×C1318yescomplemented
428#529C22×C1318yescomplemented
429C2×#126C22×C1314yescomplemented
430C2×#124C22×C1314yescomplemented
431#525C22×C1318yescomplemented
432#525C22×C1318yescomplemented
433C2×#123C22×C1314yescomplemented
434C2×#123C22×C1314yescomplemented
435C2×C22⋊Q8C22×C1312yescomplemented
436C2×#121C22×C1314yescomplemented
437C2×#121C22×C1314yescomplemented
438C2×#121C22×C1312yescomplemented
439C2×#121C22×C1318yescomplemented
440C2×#120C22×C1314yescomplemented
441C2×#120C22×C1314yescomplemented
442C2×#120C22×C1318yescomplemented
443#518C22×C1314yescomplemented
444C2×C4×D4C22×C1314yescomplemented
445C22×C22⋊C4C22×C1311yescharacteristic, complemented
446C22×C13—22no—
447C22×C13—22no—
448C22×C13—22no—
449C22×C13—28no—
450C22×C13—24no—
451C22×C13—28no—
452C22×C13—28no—
453C22×C13—216no—
454C22×C13—28no—
455C22×C13—28no—
456C22×C13—44no—
457C22×C13—48no—
458C22×C13—88no—
459C22×C13—88no—
460C22×C13—88no—
461C22×C13—816no—
462C22×C13—168no—
463C22×C13C2×H(5,𝔽2)12yes—
464C22×C13C2×H(5,𝔽2)14yes—
465C22×C13C2611yescharacteristic
466C4×C13—28no—
467C4×C13—28no—
468C4×C13—24no—
469C4×C13—28no—
470C4×C13—24no—
471C4×C13—28no—
472C25C23×C1311yescharacteristic
473C25C23×C1312yes—
474H(5,𝔽2)—416no—
475C2×#41C23×C1318yes—
476C2×#41C23×C13116yescomplemented
477C2×#41C23×C1318yescomplemented
478C22×Q8C23×C1312yescomplemented
479C22×D4—48no—
480C22×D4C23×C1314yes—
481C22×D4C23×C1314yes—
482C22×D4C23×C1314yes—
483C22×D4C23×C1318yes—
484C22×D4C23×C13116yes—
485C22×D4C23×C1314yes—
486C22×D4C23×C1314yes—
487C22×D4C23×C1314yes—
488C22×D4C23×C13116yescomplemented
489C22×D4C23×C13116yescomplemented
490C22×D4C23×C1312yescomplemented
491C22×D4C23×C1318yescomplemented
492C23×C4C23×C1312yes—
493C23×C4C23×C1312yes—
494C23×C4C23×C1314yescomplemented
495C4⋊Q8C23×C1318yescomplemented
496#127C23×C1318yes—
497#127C23×C1318yes—
498#127C23×C1318yescomplemented
499#126C23×C13116yescomplemented
500#126C23×C13116yescomplemented
501#126C23×C13116yescomplemented
502#126C23×C13116yescomplemented
503#126C23×C13116yescomplemented
504#125C23×C1318yescomplemented
505#125C23×C13116yescomplemented
506#124C23×C1318yes—
507#124C23×C1318yes—
508#124C23×C13116yescomplemented
509#124C23×C13116yescomplemented
510#124C23×C1318yescomplemented
511#124C23×C13116yescomplemented
512#124C23×C13116yescomplemented
513#123C23×C13116yes—
514#123C23×C1318yes—
515#123C23×C1318yes—
516#123C23×C13116yes—
517#123C23×C1318yes—
518#123C23×C1318yes—
519#123C23×C13116yescomplemented
520#123C23×C13116yescomplemented
521#123C23×C13116yescomplemented
522#123C23×C13116yescomplemented
523#123C23×C13116yescomplemented
524#123C23×C13116yescomplemented
525#123C23×C13116yescomplemented
526#123C23×C13116yescomplemented
527C22⋊Q8C23×C1318yes—
528C22⋊Q8C23×C1318yescomplemented
529C22⋊Q8C23×C1318yescomplemented
530C22⋊Q8C23×C13116yescomplemented
531C22⋊Q8C23×C13116yescomplemented
532C22⋊Q8C23×C13116yescomplemented
533C22⋊Q8C23×C13116yescomplemented
534#121C23×C1318yes—
535#121C23×C1318yes—
536#121C23×C1318yes—
537#121C23×C1318yes—
538#121C23×C1318yes—
539#121C23×C13116yes—
540#121C23×C13116yes—
541#121C23×C13116yes—
542#121C23×C13116yes—
543#121C23×C1318yescomplemented
544#121C23×C13116yescomplemented
545#121C23×C13116yescomplemented
546#121C23×C13116yescomplemented
547#121C23×C1318yescomplemented
548#121C23×C13116yescomplemented
549#121C23×C1318yescomplemented
550#121C23×C1318yescomplemented
551#121C23×C13116yescomplemented
552#121C23×C13116yescomplemented
553#121C23×C13116yescomplemented
554#121C23×C13116yescomplemented
555#121C23×C13116yescomplemented
556#120C23×C13116yes—
557#120C23×C13116yes—
558#120C23×C1318yes—
559#120C23×C1318yes—
560#120C23×C13116yes—
561#120C23×C13116yes—
562#120C23×C1318yes—
563#120C23×C1318yes—
564#120C23×C13116yescomplemented
565#120C23×C13116yescomplemented
566#120C23×C13116yescomplemented
567#120C23×C13116yescomplemented
568#120C23×C13116yescomplemented
569C4×Q8C23×C1318yescomplemented
570C4×D4C23×C1318yes—
571C4×D4C23×C1318yes—
572C4×D4C23×C1318yescomplemented
573C4×D4C23×C1318yescomplemented
574C4×D4C23×C13116yescomplemented
575C4×D4C23×C13116yescomplemented
576C4×D4C23×C13116yescomplemented
577C4×D4C23×C13116yescomplemented
578C4×D4C23×C13116yescomplemented
579C4×D4C23×C1318yescomplemented
580C4×D4C23×C1318yescomplemented
581C4×D4C23×C1318yescomplemented
582C4×D4C23×C13116yescomplemented
583#117C23×C1318yes—
584#117C23×C1318yescomplemented
585#117C23×C13116yescomplemented
586C2×C4⋊C4C23×C1314yes—
587C2×C4⋊C4C23×C1314yescomplemented
588C2×C4⋊C4C23×C1314yescomplemented
589C2×C4⋊C4C23×C1312yescomplemented
590C2×C4⋊C4C23×C1318yescomplemented
591C2×C4⋊C4C23×C1312yescomplemented
592C2×C22⋊C4C23×C1314yes—
593C2×C22⋊C4C23×C1314yes—
594C2×C22⋊C4C23×C1314yes—
595C2×C22⋊C4C23×C1314yes—
596C2×C22⋊C4C23×C1318yes—
597C2×C22⋊C4C23×C1318yes—
598C2×C22⋊C4C23×C1314yes—
599C2×C22⋊C4C23×C1314yes—
600C2×C22⋊C4C23×C1314yescomplemented
601C2×C22⋊C4C23×C13116yescomplemented
602C2×C22⋊C4C23×C1314yescomplemented
603C2×C22⋊C4C23×C13116yescomplemented
604C2×C42C23×C1314yescomplemented
605C2×C13—22no—
606C2×C13—24no—
607C2×C13—44no—
608C2×C13—48no—
609C2×C13—48no—
610C2×C13C22×H(5,𝔽2)11yescharacteristic
611C2×C13H(7,𝔽2)12yes—
612C24—24no—
613C24—44no—
614C24—82no—
615C24—84no—
616C24C24×C1314yes—
617C24C24×C1314yes—
618C24C24×C1312yes—
619C24C24×C1314yes—
620C24C24×C1318yes—
621C24C24×C1318yes—
622C24C24×C1311yescharacteristic
623#41—416no—
624#41—432no—
625#41—88no—
626C2×Q8—82no—
627C2×Q8C24×C1318yes—
628C2×Q8C24×C1318yes—
629C2×D4—216no—
630C2×D4—216no—
631C2×D4—48no—
632C2×D4—432no—
633C2×D4—416no—
634C2×D4—432no—
635C2×D4—84no—
636C2×D4—84no—
637C2×D4—84no—
638C2×D4—82no—
639C2×D4—88no—
640C2×D4—816no—
641C2×D4C24×C1318yes—
642C2×D4C24×C1318yes—
643C2×D4C24×C13116yes—
644C2×D4C24×C1318yes—
645C2×D4C24×C1318yes—
646C2×D4C24×C13116yes—
647C2×D4C24×C13116yes—
648C2×D4C24×C13116yes—
649C2×D4C24×C13116yes—
650C2×D4C24×C1318yes—
651C2×D4C24×C1318yes—
652C2×D4C24×C1318yes—
653C2×D4C24×C13116yes—
654C2×D4C24×C1318yes—
655C22×C4—44no—
656C22×C4—82no—
657C22×C4—84no—
658C22×C4C24×C1314yes—
659C22×C4C24×C1314yes—
660C22×C4C24×C1314yes—
661C22×C4C24×C1314yes—
662C22×C4C24×C1314yes—
663C22×C4C24×C1312yes—
664C22×C4C24×C1312yes—
665C22×C4C24×C1314yes—
666C22×C4C24×C13116yes—
667C22×C4C24×C1318yes—
668C22×C4C24×C1318yes—
669C22×C4C24×C13116yes—
670C22×C4C24×C1318yes—
671C22×C4C24×C1318yes—
672C4⋊C4C24×C1318yes—
673C4⋊C4C24×C1318yes—
674C4⋊C4C24×C1318yes—
675C4⋊C4C24×C13116yes—
676C4⋊C4C24×C13116yes—
677C4⋊C4C24×C1318yes—
678C4⋊C4C24×C1318yes—
679C4⋊C4C24×C1318yes—
680C4⋊C4C24×C13116yes—
681C4⋊C4C24×C13116yes—
682C22⋊C4C24×C1318yes—
683C22⋊C4C24×C1314yes—
684C22⋊C4C24×C1318yes—
685C22⋊C4C24×C1314yes—
686C22⋊C4C24×C13116yes—
687C22⋊C4C24×C13116yes—
688C22⋊C4C24×C13116yes—
689C22⋊C4C24×C13116yes—
690C22⋊C4C24×C1318yes—
691C22⋊C4C24×C1318yes—
692C22⋊C4C24×C1318yes—
693C22⋊C4C24×C13116yes—
694C22⋊C4C24×C13116yes—
695C22⋊C4C24×C13116yes—
696C22⋊C4C24×C13116yes—
697C22⋊C4C24×C1318yes—
698C22⋊C4C24×C1318yes—
699C22⋊C4C24×C13116yes—
700C42C24×C1318yes—
701C42C24×C1318yes—
702C42C24×C1318yes—
703C42C24×C1318yes—
704C13#6286311yescharacteristic, direct product factor, Sylow
705C23—24no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—42no—
710C23—44no—
711C23—44no—
712C23—48no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—48no—
717C23—416no—
718C23—48no—
719C23—416no—
720C23—88no—
721C23—816no—
722C23C13×H(5,𝔽2)14yes—
723C23C25×C1314yes—
724C23C25×C1318yes—
725C23C25×C1318yes—
726C23C25×C1311yescharacteristic
727C23C25×C1312yes—
728Q8—48no—
729Q8—48no—
730D4—232no—
731D4—216no—
732D4—216no—
733D4—48no—
734D4—48no—
735D4—48no—
736D4—416no—
737D4—416no—
738D4—48no—
739D4—416no—
740D4—48no—
741D4—416no—
742D4—48no—
743D4—416no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—48no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—48no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—48no—
754C2×C4—416no—
755C2×C4—48no—
756C2×C4—44no—
757C2×C4—416no—
758C2×C4C25×C1318yes—
759C2×C4C25×C1314yes—
760C2×C4C25×C1314yes—
761C2×C4C25×C1318yes—
762C2×C4C25×C1318yes—
763C2×C4C25×C1318yes—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—28no—
768C22—24no—
769C22—28no—
770C22—28no—
771C22—216no—
772C22—28no—
773C22—28no—
774C22—44no—
775C22—48no—
776C22—88no—
777C22—88no—
778C22—88no—
779C22—816no—
780C22—168no—
781C22C2×C13×H(5,𝔽2)12yes—
782C22C2×C13×H(5,𝔽2)14yes—
783C22C26×C1311yescharacteristic
784C4—28no—
785C4—28no—
786C4—24no—
787C4—28no—
788C4—24no—
789C4—28no—
790C2—22no—
791C2—24no—
792C2—44no—
793C2—48no—
794C2—48no—
795C2C22×C13×H(5,𝔽2)11yescharacteristic
796C2C13×H(7,𝔽2)12yes—
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×#3560C2semidirect
2. C13×#3558C2semidirect
3. C13×#3537C2semidirect
4. C13×#3534C2semidirect
5. C13×#3533C2semidirect
6. C13×#3532C2semidirect
7. C13×#3505C2semidirect
8. C13×#3496C2semidirect
9. C13×#3484C2semidirect
10. C2×C13×#538C2semidirect
11. C2×C13×#534C2semidirect
12. C2×C13×H(5,𝔽2)C22semidirect
13. C23×D4×C13C22semidirect
14. C13×#563C22semidirect
15. C13×#562C22semidirect
16. C13×H(3,𝔽4)C22semidirect
17. C13×#560C22semidirect
18. C13×#560C22semidirect
19. C13×#560C22semidirect
20. C13×#559C22semidirect
21. C13×#553C22semidirect
22. C13×#553C22semidirect
23. C13×#553C22semidirect
24. C13×#552C22semidirect
25. C13×#551C22semidirect
26. C13×#551C22semidirect
27. C13×#551C22semidirect
28. C13×#548C22semidirect
29. C13×#547C22semidirect
30. C13×#547C22semidirect
31. C13×#546C22semidirect
32. C13×#546C22semidirect
33. C13×#546C22semidirect
34. C13×#546C22semidirect
35. C13×#546C22semidirect
36. C13×#546C22semidirect
37. D42×C13C22semidirect
38. D42×C13C22semidirect
39. D42×C13C22semidirect
40. D42×C13C22semidirect
41. D42×C13C22semidirect
42. C13×#542C22semidirect
43. C13×#540C22semidirect
44. C13×#539C22semidirect
45. C13×#539C22semidirect
46. C13×#538C22semidirect
47. C13×#538C22semidirect
48. C13×#538C22semidirect
49. C13×#538C22semidirect
50. C13×#538C22semidirect
51. C13×#538C22semidirect
52. C13×#538C22semidirect
53. C13×#537C22semidirect
54. C13×#535C22semidirect
55. C13×#535C22semidirect
56. C13×#534C22semidirect
57. C13×#534C22semidirect
58. C13×#534C22semidirect
59. C13×#534C22semidirect
60. C13×#534C22semidirect
61. C13×#534C22semidirect
62. C13×#532C22semidirect
63. C13×#529C22semidirect
64. C2×C13×#126C22semidirect
65. C2×C13×#124C22semidirect
66. C13×#525C22semidirect
67. C13×#525C22semidirect
68. C2×C13×#123C22semidirect
69. C2×C13×#123C22semidirect
70. C2×C13×C22⋊Q8C22semidirect
71. C2×C13×#121C22semidirect
72. C2×C13×#121C22semidirect
73. C2×C13×#121C22semidirect
74. C2×C13×#121C22semidirect
75. C2×C13×#120C22semidirect
76. C2×C13×#120C22semidirect
77. C2×C13×#120C22semidirect
78. C13×#518C22semidirect
79. C2×C4×D4×C13C22semidirect
80. C22×C13×C22⋊C4C22semidirect
85. C2×C13×#41C23semidirect
86. C2×C13×#41C23semidirect
87. C22×Q8×C13C23semidirect
97. C22×D4×C13C23semidirect
98. C22×D4×C13C23semidirect
99. C22×D4×C13C23semidirect
100. C22×D4×C13C23semidirect
103. C23×C4×C13C23semidirect
104. C13×C4⋊Q8C23semidirect
107. C13×#127C23semidirect
108. C13×#126C23semidirect
109. C13×#126C23semidirect
110. C13×#126C23semidirect
111. C13×#126C23semidirect
112. C13×#126C23semidirect
113. C13×#125C23semidirect
114. C13×#125C23semidirect
117. C13×#124C23semidirect
118. C13×#124C23semidirect
119. C13×#124C23semidirect
120. C13×#124C23semidirect
121. C13×#124C23semidirect
128. C13×#123C23semidirect
129. C13×#123C23semidirect
130. C13×#123C23semidirect
131. C13×#123C23semidirect
132. C13×#123C23semidirect
133. C13×#123C23semidirect
134. C13×#123C23semidirect
135. C13×#123C23semidirect
137. C13×C22⋊Q8C23semidirect
138. C13×C22⋊Q8C23semidirect
139. C13×C22⋊Q8C23semidirect
140. C13×C22⋊Q8C23semidirect
141. C13×C22⋊Q8C23semidirect
142. C13×C22⋊Q8C23semidirect
152. C13×#121C23semidirect
153. C13×#121C23semidirect
154. C13×#121C23semidirect
155. C13×#121C23semidirect
156. C13×#121C23semidirect
157. C13×#121C23semidirect
158. C13×#121C23semidirect
159. C13×#121C23semidirect
160. C13×#121C23semidirect
161. C13×#121C23semidirect
162. C13×#121C23semidirect
163. C13×#121C23semidirect
164. C13×#121C23semidirect
173. C13×#120C23semidirect
174. C13×#120C23semidirect
175. C13×#120C23semidirect
176. C13×#120C23semidirect
177. C13×#120C23semidirect
178. C4×Q8×C13C23semidirect
181. C4×D4×C13C23semidirect
182. C4×D4×C13C23semidirect
183. C4×D4×C13C23semidirect
184. C4×D4×C13C23semidirect
185. C4×D4×C13C23semidirect
186. C4×D4×C13C23semidirect
187. C4×D4×C13C23semidirect
188. C4×D4×C13C23semidirect
189. C4×D4×C13C23semidirect
190. C4×D4×C13C23semidirect
191. C4×D4×C13C23semidirect
193. C13×#117C23semidirect
194. C13×#117C23semidirect
196. C2×C13×C4⋊C4C23semidirect
197. C2×C13×C4⋊C4C23semidirect
198. C2×C13×C4⋊C4C23semidirect
199. C2×C13×C4⋊C4C23semidirect
200. C2×C13×C4⋊C4C23semidirect
209. C2×C13×C22⋊C4C23semidirect
210. C2×C13×C22⋊C4C23semidirect
211. C2×C13×C22⋊C4C23semidirect
212. C2×C13×C22⋊C4C23semidirect
213. C2×C42×C13C23semidirect
214. #62863C13direct (N × H)
307. #3560C2×C13semidirect
308. #3558C2×C13semidirect
309. #3537C2×C13semidirect
310. #3534C2×C13semidirect
311. #3533C2×C13semidirect
312. #3532C2×C13semidirect
313. #3505C2×C13semidirect
314. #3496C2×C13semidirect
315. #3484C2×C13semidirect
316. C2×#538C2×C13semidirect
317. C2×#534C2×C13semidirect
377. C2×H(5,𝔽2)C22×C13semidirect
378. C23×D4C22×C13semidirect
379. #563C22×C13semidirect
380. #562C22×C13semidirect
381. H(3,𝔽4)C22×C13semidirect
382. #560C22×C13semidirect
383. #560C22×C13semidirect
384. #560C22×C13semidirect
385. #559C22×C13semidirect
386. #553C22×C13semidirect
387. #553C22×C13semidirect
388. #553C22×C13semidirect
389. #552C22×C13semidirect
390. #551C22×C13semidirect
391. #551C22×C13semidirect
392. #551C22×C13semidirect
393. #548C22×C13semidirect
394. #547C22×C13semidirect
395. #547C22×C13semidirect
396. #546C22×C13semidirect
397. #546C22×C13semidirect
398. #546C22×C13semidirect
399. #546C22×C13semidirect
400. #546C22×C13semidirect
401. #546C22×C13semidirect
402. D42C22×C13semidirect
403. D42C22×C13semidirect
404. D42C22×C13semidirect
405. D42C22×C13semidirect
406. D42C22×C13semidirect
407. #542C22×C13semidirect
408. #540C22×C13semidirect
409. #539C22×C13semidirect
410. #539C22×C13semidirect
411. #538C22×C13semidirect
412. #538C22×C13semidirect
413. #538C22×C13semidirect
414. #538C22×C13semidirect
415. #538C22×C13semidirect
416. #538C22×C13semidirect
417. #538C22×C13semidirect
418. #537C22×C13semidirect
419. #535C22×C13semidirect
420. #535C22×C13semidirect
421. #534C22×C13semidirect
422. #534C22×C13semidirect
423. #534C22×C13semidirect
424. #534C22×C13semidirect
425. #534C22×C13semidirect
426. #534C22×C13semidirect
427. #532C22×C13semidirect
428. #529C22×C13semidirect
429. C2×#126C22×C13semidirect
430. C2×#124C22×C13semidirect
431. #525C22×C13semidirect
432. #525C22×C13semidirect
433. C2×#123C22×C13semidirect
434. C2×#123C22×C13semidirect
435. C2×C22⋊Q8C22×C13semidirect
436. C2×#121C22×C13semidirect
437. C2×#121C22×C13semidirect
438. C2×#121C22×C13semidirect
439. C2×#121C22×C13semidirect
440. C2×#120C22×C13semidirect
441. C2×#120C22×C13semidirect
442. C2×#120C22×C13semidirect
443. #518C22×C13semidirect
444. C2×C4×D4C22×C13semidirect
445. C22×C22⋊C4C22×C13semidirect
476. C2×#41C23×C13semidirect
477. C2×#41C23×C13semidirect
478. C22×Q8C23×C13semidirect
488. C22×D4C23×C13semidirect
489. C22×D4C23×C13semidirect
490. C22×D4C23×C13semidirect
491. C22×D4C23×C13semidirect
494. C23×C4C23×C13semidirect
495. C4⋊Q8C23×C13semidirect
498. #127C23×C13semidirect
499. #126C23×C13semidirect
500. #126C23×C13semidirect
501. #126C23×C13semidirect
502. #126C23×C13semidirect
503. #126C23×C13semidirect
504. #125C23×C13semidirect
505. #125C23×C13semidirect
508. #124C23×C13semidirect
509. #124C23×C13semidirect
510. #124C23×C13semidirect
511. #124C23×C13semidirect
512. #124C23×C13semidirect
519. #123C23×C13semidirect
520. #123C23×C13semidirect
521. #123C23×C13semidirect
522. #123C23×C13semidirect
523. #123C23×C13semidirect
524. #123C23×C13semidirect
525. #123C23×C13semidirect
526. #123C23×C13semidirect
528. C22⋊Q8C23×C13semidirect
529. C22⋊Q8C23×C13semidirect
530. C22⋊Q8C23×C13semidirect
531. C22⋊Q8C23×C13semidirect
532. C22⋊Q8C23×C13semidirect
533. C22⋊Q8C23×C13semidirect
543. #121C23×C13semidirect
544. #121C23×C13semidirect
545. #121C23×C13semidirect
546. #121C23×C13semidirect
547. #121C23×C13semidirect
548. #121C23×C13semidirect
549. #121C23×C13semidirect
550. #121C23×C13semidirect
551. #121C23×C13semidirect
552. #121C23×C13semidirect
553. #121C23×C13semidirect
554. #121C23×C13semidirect
555. #121C23×C13semidirect
564. #120C23×C13semidirect
565. #120C23×C13semidirect
566. #120C23×C13semidirect
567. #120C23×C13semidirect
568. #120C23×C13semidirect
569. C4×Q8C23×C13semidirect
572. C4×D4C23×C13semidirect
573. C4×D4C23×C13semidirect
574. C4×D4C23×C13semidirect
575. C4×D4C23×C13semidirect
576. C4×D4C23×C13semidirect
577. C4×D4C23×C13semidirect
578. C4×D4C23×C13semidirect
579. C4×D4C23×C13semidirect
580. C4×D4C23×C13semidirect
581. C4×D4C23×C13semidirect
582. C4×D4C23×C13semidirect
584. #117C23×C13semidirect
585. #117C23×C13semidirect
587. C2×C4⋊C4C23×C13semidirect
588. C2×C4⋊C4C23×C13semidirect
589. C2×C4⋊C4C23×C13semidirect
590. C2×C4⋊C4C23×C13semidirect
591. C2×C4⋊C4C23×C13semidirect
600. C2×C22⋊C4C23×C13semidirect
601. C2×C22⋊C4C23×C13semidirect
602. C2×C22⋊C4C23×C13semidirect
603. C2×C22⋊C4C23×C13semidirect
604. C2×C42C23×C13semidirect
704. C13#62863direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35602
C13×#35582
C13×#35372
C13×#35342
C13×#35332
C13×#35322
C13×#35052
C13×#34962
C13×#34842
C2×C13×#5382
C2×C13×#5342
#6286313