Finite Group Databasebeta

← C13×#62862 #15749201

Subgroups — C13×#62862 #15749201

Order 3328.

7498 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3545C214yesmaximal, complemented
2C13×#3543C214yesmaximal, complemented
3C13×#3542C2116yesmaximal, complemented
4C13×#3534C218yesmaximal, complemented
5C13×#3533C218yesmaximal, complemented
6C13×#3532C218yesmaximal, complemented
7C13×#3491C212yesmaximal, complemented
8C13×#3490C214yesmaximal, complemented
9C13×#3485C212yesmaximal, complemented
10C13×#3484C214yesmaximal, complemented
11C2×C13×#535C211yesmaximal, characteristic, complemented
12C2×C13×#534C212yesmaximal, complemented
13C2×C13×H(5,𝔽2)C2212yescomplemented
14C22×C13×#41C2211yescharacteristic, complemented
15C23×D4×C13C2211yescharacteristic, complemented
16C23×D4×C13C2212yescomplemented
17C13×#563C2214yescomplemented
18C13×#562C22116yescomplemented
19C13×#562C2218yescomplemented
20C13×H(3,𝔽4)C2214yescomplemented
21C13×#560C2218yescomplemented
22C13×#560C22116yescomplemented
23C13×#560C2218yescomplemented
24C13×#559C2214yescomplemented
25C13×#555C2218yescomplemented
26C13×#553C22116yescomplemented
27C13×#552C22116yescomplemented
28C13×#551C22116yescomplemented
29C13×#551C22116yescomplemented
30C13×#551C2218yescomplemented
31C13×#551C22116yescomplemented
32C13×#550C2218yescomplemented
33C13×#547C22116yescomplemented
34C13×#546C22116yescomplemented
35C13×#546C22116yescomplemented
36C13×#546C22116yescomplemented
37C13×#546C22116yescomplemented
38C13×#546C22116yescomplemented
39C13×#546C22116yescomplemented
40D42×C13C22116yescomplemented
41D42×C13C2214yescomplemented
42D42×C13C22116yescomplemented
43C13×#543C2212yescomplemented
44C13×#542C22116yescomplemented
45C13×#540C22116yescomplemented
46C13×#540C22116yescomplemented
47C13×#539C2218yescomplemented
48C13×#539C2218yescomplemented
49C13×#538C22116yescomplemented
50C13×#538C22116yescomplemented
51C13×#538C22116yescomplemented
52C13×#538C2218yescomplemented
53C13×#537C2218yescomplemented
54C13×#536C2214yescomplemented
55C13×#535C2218yescomplemented
56C13×#535C2218yescomplemented
57C13×#535C2218yescomplemented
58C13×#535C22116yescomplemented
59C13×#534C2212yes—
60C13×#534C2218yescomplemented
61C13×#534C2218yescomplemented
62C13×#534C2214yescomplemented
63C13×#534C2218yescomplemented
64C13×#534C2218yescomplemented
65C13×#534C2218yescomplemented
66C13×#534C2218yescomplemented
67C13×#534C2214yescomplemented
68C2×C13×#127C2212yescomplemented
69C13×#529C2218yescomplemented
70C2×C13×#124C2212yescomplemented
71C13×#525C22116yescomplemented
72C13×#525C2218yescomplemented
73C13×#525C2214yescomplemented
74C2×C13×#123C2214yescomplemented
75C2×C13×#123C2214yescomplemented
76C2×C13×#123C2214yescomplemented
77C2×C13×#121C2218yescomplemented
78C2×C13×#121C2214yescomplemented
79C2×C13×#120C2214yescomplemented
80C2×C13×#120C2214yescomplemented
81C2×C13×#120C2214yescomplemented
82C2×C13×#120C2218yescomplemented
83C13×#518C2214yescomplemented
84C13×#518C2212yescomplemented
85C2×C13×#117C2211yescharacteristic, complemented
86C22×C13×C22⋊C4C2212yescomplemented
87C25×C13C2312yes—
88C25×C13C2312yescomplemented
89C13×H(5,𝔽2)—48no—
90C2×C13×#41—44no—
91C2×C13×#41C2318yes—
92C2×C13×#41C2314yes—
93C2×C13×#41C2318yescomplemented
94C2×C13×#41C23116yescomplemented
95C22×Q8×C13C2311yescharacteristic, complemented
96C22×D4×C13—44no—
97C22×D4×C13—48no—
98C22×D4×C13C2312yes—
99C22×D4×C13C2314yes—
100C22×D4×C13C2314yes—
101C22×D4×C13C2318yes—
102C22×D4×C13C2312yes—
103C22×D4×C13C2314yes—
104C22×D4×C13C2314yes—
105C22×D4×C13C2312yes—
106C22×D4×C13C2318yes—
107C22×D4×C13C2318yes—
108C22×D4×C13C2314yescomplemented
109C22×D4×C13C2311yescharacteristic, complemented
110C22×D4×C13C2318yescomplemented
111C22×D4×C13C2318yescomplemented
112C22×D4×C13C23116yescomplemented
113C23×C4×C13C2311yescharacteristic
114C23×C4×C13C2312yescomplemented
115C23×C4×C13C2312yescomplemented
116C23×C4×C13C2314yescomplemented
117C13×C4⋊Q8C2318yescomplemented
118C13×#127C2314yes—
119C13×#127C2318yescomplemented
120C13×#127C2314yescomplemented
121C13×#127C23116yescomplemented
122C13×#126C23116yescomplemented
123C13×#126C23116yescomplemented
124C13×#126C23116yescomplemented
125C13×#126C23116yescomplemented
126C13×#125C2318yescomplemented
127C13×#125C23116yescomplemented
128C13×#124C2314yes—
129C13×#124C2318yescomplemented
130C13×#124C2314yescomplemented
131C13×#124C2318yescomplemented
132C13×#124C23116yescomplemented
133C13×#124C23116yescomplemented
134C13×#124C2318yescomplemented
135C13×#124C23116yescomplemented
136C13×#123C2318yes—
137C13×#123C23116yes—
138C13×#123C2318yes—
139C13×#123C2318yes—
140C13×#123C2318yescomplemented
141C13×#123C2318yescomplemented
142C13×#123C2318yescomplemented
143C13×#123C2318yescomplemented
144C13×#123C2318yescomplemented
145C13×#123C23116yescomplemented
146C13×#123C2318yescomplemented
147C13×#123C23116yescomplemented
148C13×#123C23116yescomplemented
149C13×#123C23116yescomplemented
150C13×#123C23116yescomplemented
151C13×#123C2318yescomplemented
152C13×#123C23116yescomplemented
153C13×#123C23116yescomplemented
154C13×C22⋊Q8C23116yescomplemented
155C13×C22⋊Q8C2318yescomplemented
156C13×C22⋊Q8C23116yescomplemented
157C13×C22⋊Q8C23116yescomplemented
158C13×C22⋊Q8C2318yescomplemented
159C13×C22⋊Q8C23116yescomplemented
160C13×C22⋊Q8C23116yescomplemented
161C13×#121C23116yes—
162C13×#121C23116yes—
163C13×#121C2318yes—
164C13×#121C23116yes—
165C13×#121C2318yes—
166C13×#121C23116yescomplemented
167C13×#121C23116yescomplemented
168C13×#121C2318yescomplemented
169C13×#121C23116yescomplemented
170C13×#121C2318yescomplemented
171C13×#121C23116yescomplemented
172C13×#121C23116yescomplemented
173C13×#121C23116yescomplemented
174C13×#121C23116yescomplemented
175C13×#121C23116yescomplemented
176C13×#121C23116yescomplemented
177C13×#121C23116yescomplemented
178C13×#121C23116yescomplemented
179C13×#121C23116yescomplemented
180C13×#120C2318yes—
181C13×#120C2318yes—
182C13×#120C2318yes—
183C13×#120C2318yes—
184C13×#120C23116yes—
185C13×#120C2318yes—
186C13×#120C23116yes—
187C13×#120C2318yescomplemented
188C13×#120C2318yescomplemented
189C13×#120C2318yescomplemented
190C13×#120C2318yescomplemented
191C13×#120C2318yescomplemented
192C13×#120C23116yescomplemented
193C13×#120C23116yescomplemented
194C13×#120C2318yescomplemented
195C13×#120C2318yescomplemented
196C13×#120C23116yescomplemented
197C4×Q8×C13C2318yescomplemented
198C4×D4×C13C23116yes—
199C4×D4×C13C23116yescomplemented
200C4×D4×C13C23116yescomplemented
201C4×D4×C13C23116yescomplemented
202C4×D4×C13C23116yescomplemented
203C4×D4×C13C23116yescomplemented
204C4×D4×C13C23116yescomplemented
205C4×D4×C13C23116yescomplemented
206C4×D4×C13C2318yescomplemented
207C13×#117C2318yescomplemented
208C13×#117C2318yescomplemented
209C13×#117C2314yescomplemented
210C13×#117C23116yescomplemented
211C13×#117C23116yescomplemented
212C2×C13×C4⋊C4C2312yescomplemented
213C2×C13×C4⋊C4C2318yescomplemented
214C2×C13×C4⋊C4C2318yescomplemented
215C2×C13×C22⋊C4C2314yes—
216C2×C13×C22⋊C4C2318yes—
217C2×C13×C22⋊C4C2312yes—
218C2×C13×C22⋊C4C2318yes—
219C2×C13×C22⋊C4C2314yescomplemented
220C2×C13×C22⋊C4C2318yescomplemented
221C2×C13×C22⋊C4C2318yescomplemented
222C2×C13×C22⋊C4C2314yescomplemented
223C2×C13×C22⋊C4C2318yescomplemented
224C2×C13×C22⋊C4C2318yescomplemented
225C2×C13×C22⋊C4C23116yescomplemented
226C2×C13×C22⋊C4C2318yescomplemented
227C2×C42×C13C2312yescomplemented
228#62862C1311yesmaximal, characteristic, direct product factor, Sylow
229C24×C13—28no—
230C24×C13—44no—
231C24×C13—84no—
232C24×C13—84no—
233C24×C13C2414yes—
234C24×C13C2414yes—
235C24×C13C2414yes—
236C24×C13C2412yes—
237C24×C13C2412yes—
238C24×C13C2412yes—
239C24×C13C2418yes—
240C24×C13C2414yes—
241C24×C13C2411yescharacteristic
242C13×#41—416no—
243C13×#41—416no—
244C13×#41—48no—
245C13×#41—816no—
246C2×Q8×C13—42no—
247C2×Q8×C13C2418yes—
248C2×Q8×C13C2414yes—
249C2×Q8×C13C2414yes—
250C2×D4×C13—216no—
251C2×D4×C13—28no—
252C2×D4×C13—44no—
253C2×D4×C13—44no—
254C2×D4×C13—48no—
255C2×D4×C13—48no—
256C2×D4×C13—48no—
257C2×D4×C13—42no—
258C2×D4×C13—416no—
259C2×D4×C13—416no—
260C2×D4×C13—48no—
261C2×D4×C13—416no—
262C2×D4×C13—88no—
263C2×D4×C13—88no—
264C2×D4×C13—816no—
265C2×D4×C13C2418yes—
266C2×D4×C13C2418yes—
267C2×D4×C13C2418yes—
268C2×D4×C13C24116yes—
269C2×D4×C13C24116yes—
270C2×D4×C13C2418yes—
271C2×D4×C13C24116yes—
272C2×D4×C13C24116yes—
273C2×D4×C13C24116yes—
274C2×D4×C13C2412yes—
275C2×D4×C13C2412yes—
276C2×D4×C13C2414yes—
277C2×D4×C13C2414yes—
278C2×D4×C13C2414yes—
279C2×D4×C13C2418yes—
280C2×D4×C13C2414yes—
281C2×D4×C13C24116yes—
282C2×D4×C13C2412yes—
283C2×D4×C13C2412yes—
284C22×C4×C13—24no—
285C22×C4×C13—44no—
286C22×C4×C13—44no—
287C22×C4×C13—84no—
288C22×C4×C13C2411yescharacteristic
289C22×C4×C13C2414yes—
290C22×C4×C13C2412yes—
291C22×C4×C13C2414yes—
292C22×C4×C13C2411yescharacteristic
293C22×C4×C13C2414yes—
294C22×C4×C13C2418yes—
295C22×C4×C13C24116yes—
296C22×C4×C13C2418yes—
297C22×C4×C13C24116yes—
298C22×C4×C13C2418yes—
299C22×C4×C13C2418yes—
300C22×C4×C13C2414yes—
301C22×C4×C13C2418yes—
302C13×C4⋊C4C24116yes—
303C13×C4⋊C4C2418yes—
304C13×C4⋊C4C24116yes—
305C13×C4⋊C4C24116yes—
306C13×C4⋊C4C24116yes—
307C13×C4⋊C4C24116yes—
308C13×C4⋊C4C2418yes—
309C13×C4⋊C4C2418yes—
310C13×C4⋊C4C2418yes—
311C13×C22⋊C4C2418yes—
312C13×C22⋊C4C2418yes—
313C13×C22⋊C4C2418yes—
314C13×C22⋊C4C2418yes—
315C13×C22⋊C4C2418yes—
316C13×C22⋊C4C24116yes—
317C13×C22⋊C4C24116yes—
318C13×C22⋊C4C24116yes—
319C13×C22⋊C4C24116yes—
320C13×C22⋊C4C24116yes—
321C13×C22⋊C4C24116yes—
322C13×C22⋊C4C24116yes—
323C13×C22⋊C4C24116yes—
324C13×C22⋊C4C24116yes—
325C13×C22⋊C4C2418yes—
326C13×C22⋊C4C24116yes—
327C42×C13C2414yes—
328C42×C13C2414yes—
329C42×C13C24116yes—
330C42×C13C2418yes—
331#3545C2×C1314yescomplemented
332#3543C2×C1314yescomplemented
333#3542C2×C13116yescomplemented
334#3534C2×C1318yescomplemented
335#3533C2×C1318yescomplemented
336#3532C2×C1318yescomplemented
337#3491C2×C1312yescomplemented
338#3490C2×C1314yescomplemented
339#3485C2×C1312yescomplemented
340#3484C2×C1314yescomplemented
341C2×#535C2×C1311yescharacteristic, complemented
342C2×#534C2×C1312yescomplemented
343C23×C13—24no—
344C23×C13—24no—
345C23×C13—24no—
346C23×C13—28no—
347C23×C13—28no—
348C23×C13—28no—
349C23×C13—44no—
350C23×C13—42no—
351C23×C13—44no—
352C23×C13—48no—
353C23×C13—44no—
354C23×C13—48no—
355C23×C13—48no—
356C23×C13—48no—
357C23×C13—416no—
358C23×C13—44no—
359C23×C13—48no—
360C23×C13—816no—
361C23×C13—816no—
362C23×C13H(5,𝔽2)14yes—
363C23×C13C2514yes—
364C23×C13C2518yes—
365C23×C13C2514yes—
366C23×C13C2514yes—
367C23×C13C2512yes—
368C23×C13C2511yescharacteristic
369Q8×C13—44no—
370Q8×C13—44no—
371Q8×C13—48no—
372D4×C13—216no—
373D4×C13—216no—
374D4×C13—216no—
375D4×C13—42no—
376D4×C13—44no—
377D4×C13—42no—
378D4×C13—42no—
379D4×C13—44no—
380D4×C13—42no—
381D4×C13—416no—
382D4×C13—48no—
383D4×C13—44no—
384D4×C13—44no—
385D4×C13—416no—
386D4×C13—416no—
387D4×C13—48no—
388D4×C13—416no—
389D4×C13—416no—
390D4×C13—416no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—28no—
394C2×C4×C13—28no—
395C2×C4×C13—24no—
396C2×C4×C13—48no—
397C2×C4×C13—48no—
398C2×C4×C13—48no—
399C2×C4×C13—416no—
400C2×C4×C13—44no—
401C2×C4×C13—48no—
402C2×C4×C13—44no—
403C2×C4×C13—416no—
404C2×C4×C13—48no—
405C2×C4×C13C2518yes—
406C2×C4×C13C2512yes—
407C2×C4×C13C25116yes—
408C2×C4×C13C2514yes—
409C2×C4×C13C2518yes—
410C2×C4×C13C2512yes—
411C2×H(5,𝔽2)C22×C1312yescomplemented
412C22×#41C22×C1311yescharacteristic, complemented
413C23×D4C22×C1311yescharacteristic, complemented
414C23×D4C22×C1312yescomplemented
415#563C22×C1314yescomplemented
416#562C22×C13116yescomplemented
417#562C22×C1318yescomplemented
418H(3,𝔽4)C22×C1314yescomplemented
419#560C22×C1318yescomplemented
420#560C22×C13116yescomplemented
421#560C22×C1318yescomplemented
422#559C22×C1314yescomplemented
423#555C22×C1318yescomplemented
424#553C22×C13116yescomplemented
425#552C22×C13116yescomplemented
426#551C22×C13116yescomplemented
427#551C22×C13116yescomplemented
428#551C22×C1318yescomplemented
429#551C22×C13116yescomplemented
430#550C22×C1318yescomplemented
431#547C22×C13116yescomplemented
432#546C22×C13116yescomplemented
433#546C22×C13116yescomplemented
434#546C22×C13116yescomplemented
435#546C22×C13116yescomplemented
436#546C22×C13116yescomplemented
437#546C22×C13116yescomplemented
438D42C22×C13116yescomplemented
439D42C22×C1314yescomplemented
440D42C22×C13116yescomplemented
441#543C22×C1312yescomplemented
442#542C22×C13116yescomplemented
443#540C22×C13116yescomplemented
444#540C22×C13116yescomplemented
445#539C22×C1318yescomplemented
446#539C22×C1318yescomplemented
447#538C22×C13116yescomplemented
448#538C22×C13116yescomplemented
449#538C22×C13116yescomplemented
450#538C22×C1318yescomplemented
451#537C22×C1318yescomplemented
452#536C22×C1314yescomplemented
453#535C22×C1318yescomplemented
454#535C22×C1318yescomplemented
455#535C22×C1318yescomplemented
456#535C22×C13116yescomplemented
457#534C22×C1312yes—
458#534C22×C1318yescomplemented
459#534C22×C1318yescomplemented
460#534C22×C1314yescomplemented
461#534C22×C1318yescomplemented
462#534C22×C1318yescomplemented
463#534C22×C1318yescomplemented
464#534C22×C1318yescomplemented
465#534C22×C1314yescomplemented
466C2×#127C22×C1312yescomplemented
467#529C22×C1318yescomplemented
468C2×#124C22×C1312yescomplemented
469#525C22×C13116yescomplemented
470#525C22×C1318yescomplemented
471#525C22×C1314yescomplemented
472C2×#123C22×C1314yescomplemented
473C2×#123C22×C1314yescomplemented
474C2×#123C22×C1314yescomplemented
475C2×#121C22×C1318yescomplemented
476C2×#121C22×C1314yescomplemented
477C2×#120C22×C1314yescomplemented
478C2×#120C22×C1314yescomplemented
479C2×#120C22×C1314yescomplemented
480C2×#120C22×C1318yescomplemented
481#518C22×C1314yescomplemented
482#518C22×C1312yescomplemented
483C2×#117C22×C1311yescharacteristic, complemented
484C22×C22⋊C4C22×C1312yescomplemented
485C22×C13—24no—
486C22×C13—22no—
487C22×C13—24no—
488C22×C13—24no—
489C22×C13—28no—
490C22×C13—24no—
491C22×C13—28no—
492C22×C13—28no—
493C22×C13—216no—
494C22×C13—28no—
495C22×C13—44no—
496C22×C13—48no—
497C22×C13—48no—
498C22×C13—84no—
499C22×C13—88no—
500C22×C13—88no—
501C22×C13—88no—
502C22×C13—816no—
503C22×C13—164no—
504C22×C13C2×H(5,𝔽2)14yes—
505C22×C13C2×H(5,𝔽2)12yes—
506C22×C13C2611yescharacteristic
507C4×C13—22no—
508C4×C13—22no—
509C4×C13—28no—
510C4×C13—24no—
511C4×C13—216no—
512C4×C13—28no—
513C25C23×C1312yes—
514C25C23×C1312yescomplemented
515H(5,𝔽2)—48no—
516C2×#41—44no—
517C2×#41C23×C1318yes—
518C2×#41C23×C1314yes—
519C2×#41C23×C1318yescomplemented
520C2×#41C23×C13116yescomplemented
521C22×Q8C23×C1311yescharacteristic, complemented
522C22×D4—44no—
523C22×D4—48no—
524C22×D4C23×C1312yes—
525C22×D4C23×C1314yes—
526C22×D4C23×C1314yes—
527C22×D4C23×C1318yes—
528C22×D4C23×C1312yes—
529C22×D4C23×C1314yes—
530C22×D4C23×C1314yes—
531C22×D4C23×C1312yes—
532C22×D4C23×C1318yes—
533C22×D4C23×C1318yes—
534C22×D4C23×C1314yescomplemented
535C22×D4C23×C1311yescharacteristic, complemented
536C22×D4C23×C1318yescomplemented
537C22×D4C23×C1318yescomplemented
538C22×D4C23×C13116yescomplemented
539C23×C4C23×C1311yescharacteristic
540C23×C4C23×C1312yescomplemented
541C23×C4C23×C1312yescomplemented
542C23×C4C23×C1314yescomplemented
543C4⋊Q8C23×C1318yescomplemented
544#127C23×C1314yes—
545#127C23×C1318yescomplemented
546#127C23×C1314yescomplemented
547#127C23×C13116yescomplemented
548#126C23×C13116yescomplemented
549#126C23×C13116yescomplemented
550#126C23×C13116yescomplemented
551#126C23×C13116yescomplemented
552#125C23×C1318yescomplemented
553#125C23×C13116yescomplemented
554#124C23×C1314yes—
555#124C23×C1318yescomplemented
556#124C23×C1314yescomplemented
557#124C23×C1318yescomplemented
558#124C23×C13116yescomplemented
559#124C23×C13116yescomplemented
560#124C23×C1318yescomplemented
561#124C23×C13116yescomplemented
562#123C23×C1318yes—
563#123C23×C13116yes—
564#123C23×C1318yes—
565#123C23×C1318yes—
566#123C23×C1318yescomplemented
567#123C23×C1318yescomplemented
568#123C23×C1318yescomplemented
569#123C23×C1318yescomplemented
570#123C23×C1318yescomplemented
571#123C23×C13116yescomplemented
572#123C23×C1318yescomplemented
573#123C23×C13116yescomplemented
574#123C23×C13116yescomplemented
575#123C23×C13116yescomplemented
576#123C23×C13116yescomplemented
577#123C23×C1318yescomplemented
578#123C23×C13116yescomplemented
579#123C23×C13116yescomplemented
580C22⋊Q8C23×C13116yescomplemented
581C22⋊Q8C23×C1318yescomplemented
582C22⋊Q8C23×C13116yescomplemented
583C22⋊Q8C23×C13116yescomplemented
584C22⋊Q8C23×C1318yescomplemented
585C22⋊Q8C23×C13116yescomplemented
586C22⋊Q8C23×C13116yescomplemented
587#121C23×C13116yes—
588#121C23×C13116yes—
589#121C23×C1318yes—
590#121C23×C13116yes—
591#121C23×C1318yes—
592#121C23×C13116yescomplemented
593#121C23×C13116yescomplemented
594#121C23×C1318yescomplemented
595#121C23×C13116yescomplemented
596#121C23×C1318yescomplemented
597#121C23×C13116yescomplemented
598#121C23×C13116yescomplemented
599#121C23×C13116yescomplemented
600#121C23×C13116yescomplemented
601#121C23×C13116yescomplemented
602#121C23×C13116yescomplemented
603#121C23×C13116yescomplemented
604#121C23×C13116yescomplemented
605#121C23×C13116yescomplemented
606#120C23×C1318yes—
607#120C23×C1318yes—
608#120C23×C1318yes—
609#120C23×C1318yes—
610#120C23×C13116yes—
611#120C23×C1318yes—
612#120C23×C13116yes—
613#120C23×C1318yescomplemented
614#120C23×C1318yescomplemented
615#120C23×C1318yescomplemented
616#120C23×C1318yescomplemented
617#120C23×C1318yescomplemented
618#120C23×C13116yescomplemented
619#120C23×C13116yescomplemented
620#120C23×C1318yescomplemented
621#120C23×C1318yescomplemented
622#120C23×C13116yescomplemented
623C4×Q8C23×C1318yescomplemented
624C4×D4C23×C13116yes—
625C4×D4C23×C13116yescomplemented
626C4×D4C23×C13116yescomplemented
627C4×D4C23×C13116yescomplemented
628C4×D4C23×C13116yescomplemented
629C4×D4C23×C13116yescomplemented
630C4×D4C23×C13116yescomplemented
631C4×D4C23×C13116yescomplemented
632C4×D4C23×C1318yescomplemented
633#117C23×C1318yescomplemented
634#117C23×C1318yescomplemented
635#117C23×C1314yescomplemented
636#117C23×C13116yescomplemented
637#117C23×C13116yescomplemented
638C2×C4⋊C4C23×C1312yescomplemented
639C2×C4⋊C4C23×C1318yescomplemented
640C2×C4⋊C4C23×C1318yescomplemented
641C2×C22⋊C4C23×C1314yes—
642C2×C22⋊C4C23×C1318yes—
643C2×C22⋊C4C23×C1312yes—
644C2×C22⋊C4C23×C1318yes—
645C2×C22⋊C4C23×C1314yescomplemented
646C2×C22⋊C4C23×C1318yescomplemented
647C2×C22⋊C4C23×C1318yescomplemented
648C2×C22⋊C4C23×C1314yescomplemented
649C2×C22⋊C4C23×C1318yescomplemented
650C2×C22⋊C4C23×C1318yescomplemented
651C2×C22⋊C4C23×C13116yescomplemented
652C2×C22⋊C4C23×C1318yescomplemented
653C2×C42C23×C1312yescomplemented
654C2×C13—24no—
655C2×C13—22no—
656C2×C13—44no—
657C2×C13—44no—
658C2×C13—48no—
659C2×C13—44no—
660C2×C13C22×H(5,𝔽2)11yescharacteristic
661C2×C13H(7,𝔽2)12yes—
662C24—28no—
663C24—44no—
664C24—84no—
665C24—84no—
666C24C24×C1314yes—
667C24C24×C1314yes—
668C24C24×C1314yes—
669C24C24×C1312yes—
670C24C24×C1312yes—
671C24C24×C1312yes—
672C24C24×C1318yes—
673C24C24×C1314yes—
674C24C24×C1311yescharacteristic
675#41—416no—
676#41—416no—
677#41—48no—
678#41—816no—
679C2×Q8—42no—
680C2×Q8C24×C1318yes—
681C2×Q8C24×C1314yes—
682C2×Q8C24×C1314yes—
683C2×D4—216no—
684C2×D4—28no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—48no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—42no—
691C2×D4—416no—
692C2×D4—416no—
693C2×D4—48no—
694C2×D4—416no—
695C2×D4—88no—
696C2×D4—88no—
697C2×D4—816no—
698C2×D4C24×C1318yes—
699C2×D4C24×C1318yes—
700C2×D4C24×C1318yes—
701C2×D4C24×C13116yes—
702C2×D4C24×C13116yes—
703C2×D4C24×C1318yes—
704C2×D4C24×C13116yes—
705C2×D4C24×C13116yes—
706C2×D4C24×C13116yes—
707C2×D4C24×C1312yes—
708C2×D4C24×C1312yes—
709C2×D4C24×C1314yes—
710C2×D4C24×C1314yes—
711C2×D4C24×C1314yes—
712C2×D4C24×C1318yes—
713C2×D4C24×C1314yes—
714C2×D4C24×C13116yes—
715C2×D4C24×C1312yes—
716C2×D4C24×C1312yes—
717C22×C4—24no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—84no—
721C22×C4C24×C1311yescharacteristic
722C22×C4C24×C1314yes—
723C22×C4C24×C1312yes—
724C22×C4C24×C1314yes—
725C22×C4C24×C1311yescharacteristic
726C22×C4C24×C1314yes—
727C22×C4C24×C1318yes—
728C22×C4C24×C13116yes—
729C22×C4C24×C1318yes—
730C22×C4C24×C13116yes—
731C22×C4C24×C1318yes—
732C22×C4C24×C1318yes—
733C22×C4C24×C1314yes—
734C22×C4C24×C1318yes—
735C4⋊C4C24×C13116yes—
736C4⋊C4C24×C1318yes—
737C4⋊C4C24×C13116yes—
738C4⋊C4C24×C13116yes—
739C4⋊C4C24×C13116yes—
740C4⋊C4C24×C13116yes—
741C4⋊C4C24×C1318yes—
742C4⋊C4C24×C1318yes—
743C4⋊C4C24×C1318yes—
744C22⋊C4C24×C1318yes—
745C22⋊C4C24×C1318yes—
746C22⋊C4C24×C1318yes—
747C22⋊C4C24×C1318yes—
748C22⋊C4C24×C1318yes—
749C22⋊C4C24×C13116yes—
750C22⋊C4C24×C13116yes—
751C22⋊C4C24×C13116yes—
752C22⋊C4C24×C13116yes—
753C22⋊C4C24×C13116yes—
754C22⋊C4C24×C13116yes—
755C22⋊C4C24×C13116yes—
756C22⋊C4C24×C13116yes—
757C22⋊C4C24×C13116yes—
758C22⋊C4C24×C1318yes—
759C22⋊C4C24×C13116yes—
760C42C24×C1314yes—
761C42C24×C1314yes—
762C42C24×C13116yes—
763C42C24×C1318yes—
764C13#6286211yescharacteristic, direct product factor, Sylow
765C23—24no—
766C23—24no—
767C23—24no—
768C23—28no—
769C23—28no—
770C23—28no—
771C23—44no—
772C23—42no—
773C23—44no—
774C23—48no—
775C23—44no—
776C23—48no—
777C23—48no—
778C23—48no—
779C23—416no—
780C23—44no—
781C23—48no—
782C23—816no—
783C23—816no—
784C23C13×H(5,𝔽2)14yes—
785C23C25×C1314yes—
786C23C25×C1318yes—
787C23C25×C1314yes—
788C23C25×C1314yes—
789C23C25×C1312yes—
790C23C25×C1311yescharacteristic
791Q8—44no—
792Q8—44no—
793Q8—48no—
794D4—216no—
795D4—216no—
796D4—216no—
797D4—42no—
798D4—44no—
799D4—42no—
800D4—42no—
801D4—44no—
802D4—42no—
803D4—416no—
804D4—48no—
805D4—44no—
806D4—44no—
807D4—416no—
808D4—416no—
809D4—48no—
810D4—416no—
811D4—416no—
812D4—416no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—28no—
816C2×C4—28no—
817C2×C4—24no—
818C2×C4—48no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—416no—
822C2×C4—44no—
823C2×C4—48no—
824C2×C4—44no—
825C2×C4—416no—
826C2×C4—48no—
827C2×C4C25×C1318yes—
828C2×C4C25×C1312yes—
829C2×C4C25×C13116yes—
830C2×C4C25×C1314yes—
831C2×C4C25×C1318yes—
832C2×C4C25×C1312yes—
833C22—24no—
834C22—22no—
835C22—24no—
836C22—24no—
837C22—28no—
838C22—24no—
839C22—28no—
840C22—28no—
841C22—216no—
842C22—28no—
843C22—44no—
844C22—48no—
845C22—48no—
846C22—84no—
847C22—88no—
848C22—88no—
849C22—88no—
850C22—816no—
851C22—164no—
852C22C2×C13×H(5,𝔽2)14yes—
853C22C2×C13×H(5,𝔽2)12yes—
854C22C26×C1311yescharacteristic
855C4—22no—
856C4—22no—
857C4—28no—
858C4—24no—
859C4—216no—
860C4—28no—
861C2—24no—
862C2—22no—
863C2—44no—
864C2—44no—
865C2—48no—
866C2—44no—
867C2C22×C13×H(5,𝔽2)11yescharacteristic
868C2C13×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×#3545C2semidirect
2. C13×#3543C2semidirect
3. C13×#3542C2semidirect
4. C13×#3534C2semidirect
5. C13×#3533C2semidirect
6. C13×#3532C2semidirect
7. C13×#3491C2semidirect
8. C13×#3490C2semidirect
9. C13×#3485C2semidirect
10. C13×#3484C2semidirect
11. C2×C13×#535C2semidirect
12. C2×C13×#534C2semidirect
13. C2×C13×H(5,𝔽2)C22semidirect
14. C22×C13×#41C22semidirect
15. C23×D4×C13C22semidirect
16. C23×D4×C13C22semidirect
17. C13×#563C22semidirect
18. C13×#562C22semidirect
19. C13×#562C22semidirect
20. C13×H(3,𝔽4)C22semidirect
21. C13×#560C22semidirect
22. C13×#560C22semidirect
23. C13×#560C22semidirect
24. C13×#559C22semidirect
25. C13×#555C22semidirect
26. C13×#553C22semidirect
27. C13×#552C22semidirect
28. C13×#551C22semidirect
29. C13×#551C22semidirect
30. C13×#551C22semidirect
31. C13×#551C22semidirect
32. C13×#550C22semidirect
33. C13×#547C22semidirect
34. C13×#546C22semidirect
35. C13×#546C22semidirect
36. C13×#546C22semidirect
37. C13×#546C22semidirect
38. C13×#546C22semidirect
39. C13×#546C22semidirect
40. D42×C13C22semidirect
41. D42×C13C22semidirect
42. D42×C13C22semidirect
43. C13×#543C22semidirect
44. C13×#542C22semidirect
45. C13×#540C22semidirect
46. C13×#540C22semidirect
47. C13×#539C22semidirect
48. C13×#539C22semidirect
49. C13×#538C22semidirect
50. C13×#538C22semidirect
51. C13×#538C22semidirect
52. C13×#538C22semidirect
53. C13×#537C22semidirect
54. C13×#536C22semidirect
55. C13×#535C22semidirect
56. C13×#535C22semidirect
57. C13×#535C22semidirect
58. C13×#535C22semidirect
60. C13×#534C22semidirect
61. C13×#534C22semidirect
62. C13×#534C22semidirect
63. C13×#534C22semidirect
64. C13×#534C22semidirect
65. C13×#534C22semidirect
66. C13×#534C22semidirect
67. C13×#534C22semidirect
68. C2×C13×#127C22semidirect
69. C13×#529C22semidirect
70. C2×C13×#124C22semidirect
71. C13×#525C22semidirect
72. C13×#525C22semidirect
73. C13×#525C22semidirect
74. C2×C13×#123C22semidirect
75. C2×C13×#123C22semidirect
76. C2×C13×#123C22semidirect
77. C2×C13×#121C22semidirect
78. C2×C13×#121C22semidirect
79. C2×C13×#120C22semidirect
80. C2×C13×#120C22semidirect
81. C2×C13×#120C22semidirect
82. C2×C13×#120C22semidirect
83. C13×#518C22semidirect
84. C13×#518C22semidirect
85. C2×C13×#117C22semidirect
86. C22×C13×C22⋊C4C22semidirect
88. C25×C13C23semidirect
93. C2×C13×#41C23semidirect
94. C2×C13×#41C23semidirect
95. C22×Q8×C13C23semidirect
108. C22×D4×C13C23semidirect
109. C22×D4×C13C23semidirect
110. C22×D4×C13C23semidirect
111. C22×D4×C13C23semidirect
112. C22×D4×C13C23semidirect
114. C23×C4×C13C23semidirect
115. C23×C4×C13C23semidirect
116. C23×C4×C13C23semidirect
117. C13×C4⋊Q8C23semidirect
119. C13×#127C23semidirect
120. C13×#127C23semidirect
121. C13×#127C23semidirect
122. C13×#126C23semidirect
123. C13×#126C23semidirect
124. C13×#126C23semidirect
125. C13×#126C23semidirect
126. C13×#125C23semidirect
127. C13×#125C23semidirect
129. C13×#124C23semidirect
130. C13×#124C23semidirect
131. C13×#124C23semidirect
132. C13×#124C23semidirect
133. C13×#124C23semidirect
134. C13×#124C23semidirect
135. C13×#124C23semidirect
140. C13×#123C23semidirect
141. C13×#123C23semidirect
142. C13×#123C23semidirect
143. C13×#123C23semidirect
144. C13×#123C23semidirect
145. C13×#123C23semidirect
146. C13×#123C23semidirect
147. C13×#123C23semidirect
148. C13×#123C23semidirect
149. C13×#123C23semidirect
150. C13×#123C23semidirect
151. C13×#123C23semidirect
152. C13×#123C23semidirect
153. C13×#123C23semidirect
154. C13×C22⋊Q8C23semidirect
155. C13×C22⋊Q8C23semidirect
156. C13×C22⋊Q8C23semidirect
157. C13×C22⋊Q8C23semidirect
158. C13×C22⋊Q8C23semidirect
159. C13×C22⋊Q8C23semidirect
160. C13×C22⋊Q8C23semidirect
166. C13×#121C23semidirect
167. C13×#121C23semidirect
168. C13×#121C23semidirect
169. C13×#121C23semidirect
170. C13×#121C23semidirect
171. C13×#121C23semidirect
172. C13×#121C23semidirect
173. C13×#121C23semidirect
174. C13×#121C23semidirect
175. C13×#121C23semidirect
176. C13×#121C23semidirect
177. C13×#121C23semidirect
178. C13×#121C23semidirect
179. C13×#121C23semidirect
187. C13×#120C23semidirect
188. C13×#120C23semidirect
189. C13×#120C23semidirect
190. C13×#120C23semidirect
191. C13×#120C23semidirect
192. C13×#120C23semidirect
193. C13×#120C23semidirect
194. C13×#120C23semidirect
195. C13×#120C23semidirect
196. C13×#120C23semidirect
197. C4×Q8×C13C23semidirect
199. C4×D4×C13C23semidirect
200. C4×D4×C13C23semidirect
201. C4×D4×C13C23semidirect
202. C4×D4×C13C23semidirect
203. C4×D4×C13C23semidirect
204. C4×D4×C13C23semidirect
205. C4×D4×C13C23semidirect
206. C4×D4×C13C23semidirect
207. C13×#117C23semidirect
208. C13×#117C23semidirect
209. C13×#117C23semidirect
210. C13×#117C23semidirect
211. C13×#117C23semidirect
212. C2×C13×C4⋊C4C23semidirect
213. C2×C13×C4⋊C4C23semidirect
214. C2×C13×C4⋊C4C23semidirect
219. C2×C13×C22⋊C4C23semidirect
220. C2×C13×C22⋊C4C23semidirect
221. C2×C13×C22⋊C4C23semidirect
222. C2×C13×C22⋊C4C23semidirect
223. C2×C13×C22⋊C4C23semidirect
224. C2×C13×C22⋊C4C23semidirect
225. C2×C13×C22⋊C4C23semidirect
226. C2×C13×C22⋊C4C23semidirect
227. C2×C42×C13C23semidirect
228. #62862C13direct (N × H)
331. #3545C2×C13semidirect
332. #3543C2×C13semidirect
333. #3542C2×C13semidirect
334. #3534C2×C13semidirect
335. #3533C2×C13semidirect
336. #3532C2×C13semidirect
337. #3491C2×C13semidirect
338. #3490C2×C13semidirect
339. #3485C2×C13semidirect
340. #3484C2×C13semidirect
341. C2×#535C2×C13semidirect
342. C2×#534C2×C13semidirect
411. C2×H(5,𝔽2)C22×C13semidirect
412. C22×#41C22×C13semidirect
413. C23×D4C22×C13semidirect
414. C23×D4C22×C13semidirect
415. #563C22×C13semidirect
416. #562C22×C13semidirect
417. #562C22×C13semidirect
418. H(3,𝔽4)C22×C13semidirect
419. #560C22×C13semidirect
420. #560C22×C13semidirect
421. #560C22×C13semidirect
422. #559C22×C13semidirect
423. #555C22×C13semidirect
424. #553C22×C13semidirect
425. #552C22×C13semidirect
426. #551C22×C13semidirect
427. #551C22×C13semidirect
428. #551C22×C13semidirect
429. #551C22×C13semidirect
430. #550C22×C13semidirect
431. #547C22×C13semidirect
432. #546C22×C13semidirect
433. #546C22×C13semidirect
434. #546C22×C13semidirect
435. #546C22×C13semidirect
436. #546C22×C13semidirect
437. #546C22×C13semidirect
438. D42C22×C13semidirect
439. D42C22×C13semidirect
440. D42C22×C13semidirect
441. #543C22×C13semidirect
442. #542C22×C13semidirect
443. #540C22×C13semidirect
444. #540C22×C13semidirect
445. #539C22×C13semidirect
446. #539C22×C13semidirect
447. #538C22×C13semidirect
448. #538C22×C13semidirect
449. #538C22×C13semidirect
450. #538C22×C13semidirect
451. #537C22×C13semidirect
452. #536C22×C13semidirect
453. #535C22×C13semidirect
454. #535C22×C13semidirect
455. #535C22×C13semidirect
456. #535C22×C13semidirect
458. #534C22×C13semidirect
459. #534C22×C13semidirect
460. #534C22×C13semidirect
461. #534C22×C13semidirect
462. #534C22×C13semidirect
463. #534C22×C13semidirect
464. #534C22×C13semidirect
465. #534C22×C13semidirect
466. C2×#127C22×C13semidirect
467. #529C22×C13semidirect
468. C2×#124C22×C13semidirect
469. #525C22×C13semidirect
470. #525C22×C13semidirect
471. #525C22×C13semidirect
472. C2×#123C22×C13semidirect
473. C2×#123C22×C13semidirect
474. C2×#123C22×C13semidirect
475. C2×#121C22×C13semidirect
476. C2×#121C22×C13semidirect
477. C2×#120C22×C13semidirect
478. C2×#120C22×C13semidirect
479. C2×#120C22×C13semidirect
480. C2×#120C22×C13semidirect
481. #518C22×C13semidirect
482. #518C22×C13semidirect
483. C2×#117C22×C13semidirect
484. C22×C22⋊C4C22×C13semidirect
514. C25C23×C13semidirect
519. C2×#41C23×C13semidirect
520. C2×#41C23×C13semidirect
521. C22×Q8C23×C13semidirect
534. C22×D4C23×C13semidirect
535. C22×D4C23×C13semidirect
536. C22×D4C23×C13semidirect
537. C22×D4C23×C13semidirect
538. C22×D4C23×C13semidirect
540. C23×C4C23×C13semidirect
541. C23×C4C23×C13semidirect
542. C23×C4C23×C13semidirect
543. C4⋊Q8C23×C13semidirect
545. #127C23×C13semidirect
546. #127C23×C13semidirect
547. #127C23×C13semidirect
548. #126C23×C13semidirect
549. #126C23×C13semidirect
550. #126C23×C13semidirect
551. #126C23×C13semidirect
552. #125C23×C13semidirect
553. #125C23×C13semidirect
555. #124C23×C13semidirect
556. #124C23×C13semidirect
557. #124C23×C13semidirect
558. #124C23×C13semidirect
559. #124C23×C13semidirect
560. #124C23×C13semidirect
561. #124C23×C13semidirect
566. #123C23×C13semidirect
567. #123C23×C13semidirect
568. #123C23×C13semidirect
569. #123C23×C13semidirect
570. #123C23×C13semidirect
571. #123C23×C13semidirect
572. #123C23×C13semidirect
573. #123C23×C13semidirect
574. #123C23×C13semidirect
575. #123C23×C13semidirect
576. #123C23×C13semidirect
577. #123C23×C13semidirect
578. #123C23×C13semidirect
579. #123C23×C13semidirect
580. C22⋊Q8C23×C13semidirect
581. C22⋊Q8C23×C13semidirect
582. C22⋊Q8C23×C13semidirect
583. C22⋊Q8C23×C13semidirect
584. C22⋊Q8C23×C13semidirect
585. C22⋊Q8C23×C13semidirect
586. C22⋊Q8C23×C13semidirect
592. #121C23×C13semidirect
593. #121C23×C13semidirect
594. #121C23×C13semidirect
595. #121C23×C13semidirect
596. #121C23×C13semidirect
597. #121C23×C13semidirect
598. #121C23×C13semidirect
599. #121C23×C13semidirect
600. #121C23×C13semidirect
601. #121C23×C13semidirect
602. #121C23×C13semidirect
603. #121C23×C13semidirect
604. #121C23×C13semidirect
605. #121C23×C13semidirect
613. #120C23×C13semidirect
614. #120C23×C13semidirect
615. #120C23×C13semidirect
616. #120C23×C13semidirect
617. #120C23×C13semidirect
618. #120C23×C13semidirect
619. #120C23×C13semidirect
620. #120C23×C13semidirect
621. #120C23×C13semidirect
622. #120C23×C13semidirect
623. C4×Q8C23×C13semidirect
625. C4×D4C23×C13semidirect
626. C4×D4C23×C13semidirect
627. C4×D4C23×C13semidirect
628. C4×D4C23×C13semidirect
629. C4×D4C23×C13semidirect
630. C4×D4C23×C13semidirect
631. C4×D4C23×C13semidirect
632. C4×D4C23×C13semidirect
633. #117C23×C13semidirect
634. #117C23×C13semidirect
635. #117C23×C13semidirect
636. #117C23×C13semidirect
637. #117C23×C13semidirect
638. C2×C4⋊C4C23×C13semidirect
639. C2×C4⋊C4C23×C13semidirect
640. C2×C4⋊C4C23×C13semidirect
645. C2×C22⋊C4C23×C13semidirect
646. C2×C22⋊C4C23×C13semidirect
647. C2×C22⋊C4C23×C13semidirect
648. C2×C22⋊C4C23×C13semidirect
649. C2×C22⋊C4C23×C13semidirect
650. C2×C22⋊C4C23×C13semidirect
651. C2×C22⋊C4C23×C13semidirect
652. C2×C22⋊C4C23×C13semidirect
653. C2×C42C23×C13semidirect
764. C13#62862direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35452
C13×#35432
C13×#35422
C13×#35342
C13×#35332
C13×#35322
C13×#34912
C13×#34902
C13×#34852
C13×#34842
C2×C13×#5352
C2×C13×#5342
#6286213