Finite Group Databasebeta

← C13×#62837 #15749176

Subgroups — C13×#62837 #15749176

Order 3328.

6428 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3563C218yesmaximal, complemented
2C13×#3556C212yesmaximal, complemented
3C13×#3555C218yesmaximal, complemented
4C13×#3550C212yesmaximal, complemented
5C13×#3538C214yesmaximal, complemented
6C13×#3523C218yesmaximal, complemented
7C13×#3509C214yesmaximal, complemented
8C13×#3509C214yesmaximal, complemented
9C13×#3507C214yesmaximal, complemented
10C13×#3503C214yesmaximal, complemented
11C13×#3502C214yesmaximal, complemented
12C13×#3495C218yesmaximal, complemented
13C13×#3444C211yesmaximal, characteristic
14C2×C13×#533C212yesmaximal, complemented
15C13×#564C2218yescomplemented
16C13×#563C22116yes—
17C13×#563C2218yescomplemented
18C13×#559C2214yescomplemented
19Q82×C13C2214yescomplemented
20Q82×C13C2218yescomplemented
21C13×#557C22116yescomplemented
22C13×#557C2218yescomplemented
23C13×#557C2218yescomplemented
24C13×#557C2218yescomplemented
25C13×#557C2218yescomplemented
26C13×#557C22116yescomplemented
27C13×#556C22116yes—
28C13×#556C2218yescomplemented
29C13×#556C22116yescomplemented
30C13×#556C2218yescomplemented
31C13×#554C22116yes—
32C13×#554C2218yescomplemented
33C13×#552C22116yes—
34C13×#552C22132yes—
35C13×#552C22116yes—
36C13×#552C22116yes—
37C13×#552C22116yescomplemented
38C13×#551C22116yes—
39D4×Q8×C13C22116yes—
40D4×Q8×C13C2218yescomplemented
41C13×#544C22116yes—
42C13×#544C2218yes—
43C13×#544C22116yescomplemented
44C13×#542C22116yes—
45C13×#541C2218yes—
46C13×#541C22116yes—
47C13×#541C2218yescomplemented
48C13×#541C22132yescomplemented
49C13×#541C22116yescomplemented
50C13×#539C22116yes—
51C13×#536C2218yes—
52C13×#536C2218yes—
53C13×#533C2214yes—
54C13×#533C22116yes—
55C13×#533C2214yes—
56C13×#533C2214yes—
57C13×#533C2214yes—
58C13×#533C2211yescharacteristic
59C13×#533C2214yes—
60C13×#533C2214yes—
61C13×#533C2214yes—
62C13×#533C2214yes—
63C13×#533C2212yes—
64C13×#533C2218yescomplemented
65C13×#533C2214yescomplemented
66C13×#532C2211yescharacteristic
67C13×#532C2212yes—
68C2×C13×C4⋊Q8C2212yes—
69C2×C13×C4⋊Q8C2212yes—
70C2×C13×C4⋊Q8C2214yescomplemented
71C13×#529C2214yes—
72C13×#529C22116yes—
73C13×#529C2214yes—
74C13×#529C2214yes—
75C2×C13×#125C2214yes—
76C13×#525C2212yes—
77C13×#525C2214yes—
78C2×C13×C22⋊Q8C2214yes—
79C2×C13×C22⋊Q8C2214yes—
80C13×#520C2218yes—
81C13×#519C2218yes—
82C13×#519C2218yescomplemented
83C4×C13×#41C2214yes—
84C4×C13×#41C2212yes—
85C2×C4×Q8×C13C2214yes—
86C2×C4×Q8×C13C2214yes—
87C2×C13×#117C2214yes—
88C22×C42×C13C2211yescharacteristic
89C2×C13×#41C2314yes—
90C2×C13×#41C2312yes—
91C22×Q8×C13C2314yes—
92C22×Q8×C13C2314yes—
93C22×Q8×C13C2318yes—
94C23×C4×C13C2312yes—
95C23×C4×C13C2311yescharacteristic
96C13×C4⋊Q8C2314yes—
97C13×C4⋊Q8C2314yes—
98C13×C4⋊Q8C2314yes—
99C13×C4⋊Q8C2314yes—
100C13×C4⋊Q8C2314yes—
101C13×C4⋊Q8C2314yes—
102C13×C4⋊Q8C2314yes—
103C13×C4⋊Q8C2314yes—
104C13×C4⋊Q8C2318yes—
105C13×C4⋊Q8C23116yes—
106C13×C4⋊Q8C2312yes—
107C13×C4⋊Q8C2311yescharacteristic
108C13×C4⋊Q8C23116yes—
109C13×C4⋊Q8C23116yes—
110C13×C4⋊Q8C23116yes—
111C13×C4⋊Q8C23132yes—
112C13×#127C2311yescharacteristic
113C13×#126C2318yes—
114C13×#126C23132yes—
115C13×#126C23132yes—
116C13×#126C23132yes—
117C13×#126C23132yes—
118C13×#125C2318yes—
119C13×#125C2318yes—
120C13×#125C2318yes—
121C13×#125C2318yes—
122C13×#125C2314yes—
123C13×#125C2312yes—
124C13×#125C23116yes—
125C13×#125C23132yes—
126C13×#125C2318yes—
127C13×#125C23116yes—
128C13×#125C23132yes—
129C13×#125C23132yes—
130C13×#125C23132yes—
131C13×#125C23132yes—
132C13×#124C2314yes—
133C13×#124C2312yes—
134C13×#124C23116yes—
135C13×#124C23116yes—
136C13×#123C2318yes—
137C13×#123C2314yes—
138C13×#123C23132yes—
139C13×#123C23116yes—
140C13×#123C23116yes—
141C13×C22⋊Q8C2318yes—
142C13×C22⋊Q8C2318yes—
143C13×C22⋊Q8C2318yes—
144C13×C22⋊Q8C2318yes—
145C13×C22⋊Q8C2318yes—
146C13×C22⋊Q8C2318yes—
147C13×C22⋊Q8C2318yes—
148C13×C22⋊Q8C2318yes—
149C13×C22⋊Q8C2314yes—
150C13×C22⋊Q8C2314yes—
151C13×C22⋊Q8C2314yes—
152C13×C22⋊Q8C23132yes—
153C13×C22⋊Q8C23116yes—
154C13×C22⋊Q8C23116yes—
155C13×C22⋊Q8C23116yes—
156C13×C22⋊Q8C23132yes—
157C13×C22⋊Q8C23132yes—
158C13×#121C2314yes—
159C13×#121C2314yes—
160C13×#121C2314yes—
161C13×#120C2314yes—
162C4×Q8×C13C2318yes—
163C4×Q8×C13C2318yes—
164C4×Q8×C13C2318yes—
165C4×Q8×C13C2318yes—
166C4×Q8×C13C2318yes—
167C4×Q8×C13C2318yes—
168C4×Q8×C13C2318yes—
169C4×Q8×C13C2318yes—
170C4×Q8×C13C2314yes—
171C4×Q8×C13C2314yes—
172C4×Q8×C13C2314yes—
173C4×Q8×C13C23116yes—
174C4×Q8×C13C23116yes—
175C4×Q8×C13C23116yes—
176C4×Q8×C13C23116yes—
177C4×Q8×C13C23132yes—
178C4×Q8×C13C23116yes—
179C4×Q8×C13C23116yes—
180C4×D4×C13C2318yes—
181C4×D4×C13C2318yes—
182C4×D4×C13C2318yes—
183C4×D4×C13C2314yes—
184C4×D4×C13C2314yes—
185C4×D4×C13C2314yes—
186C4×D4×C13C23132yes—
187C4×D4×C13C23116yes—
188C13×#117C2318yes—
189C13×#117C2318yes—
190C13×#117C2318yes—
191C13×#117C2318yes—
192C13×#117C2314yes—
193C13×#117C2314yes—
194C13×#117C2312yes—
195C13×#117C2318yes—
196C13×#117C23132yes—
197C13×#117C23132yes—
198C13×#117C2318yes—
199C13×#117C23116yes—
200C2×C13×C4⋊C4C2314yes—
201C2×C13×C4⋊C4C2314yes—
202C2×C13×C4⋊C4C2314yes—
203C2×C13×C4⋊C4C2318yes—
204C2×C13×C4⋊C4C2318yes—
205C2×C13×C4⋊C4C2314yes—
206C2×C13×C4⋊C4C23116yes—
207C2×C13×C22⋊C4C2318yes—
208C2×C42×C13C2312yes—
209C2×C42×C13C2312yes—
210C2×C42×C13C2312yes—
211C2×C42×C13C2311yescharacteristic
212C2×C42×C13C2312yes—
213C2×C42×C13C2312yes—
214C2×C42×C13C2311yescharacteristic
215C2×C42×C13C2318yes—
216C2×C42×C13C2314yes—
217#62837C1311yesmaximal, characteristic, direct product factor, Sylow
218C24×C13C2411yescharacteristic
219C13×#41—216no—
220C13×#41—44no—
221C2×Q8×C13—216no—
222C2×Q8×C13—48no—
223C2×Q8×C13—416no—
224C2×Q8×C13C2418yes—
225C2×Q8×C13C2418yes—
226C2×Q8×C13C2414yes—
227C2×Q8×C13C2418yes—
228C2×Q8×C13C2418yes—
229C2×Q8×C13C24116yes—
230C2×Q8×C13C2412yes—
231C2×D4×C13C2418yes—
232C2×D4×C13C2414yes—
233C2×D4×C13C2414yes—
234C2×D4×C13C2412yes—
235C22×C4×C13—28no—
236C22×C4×C13—42no—
237C22×C4×C13C2412yes—
238C22×C4×C13C2412yes—
239C22×C4×C13C2412yes—
240C22×C4×C13C2412yes—
241C22×C4×C13C2412yes—
242C22×C4×C13C2412yes—
243C22×C4×C13C2411yescharacteristic
244C22×C4×C13C2418yes—
245C22×C4×C13C2418yes—
246C22×C4×C13C2414yes—
247C22×C4×C13C2412yes—
248C22×C4×C13C2411yescharacteristic
249C22×C4×C13C2418yes—
250C22×C4×C13C24116yes—
251C22×C4×C13C2412yes—
252C13×C4⋊C4C2418yes—
253C13×C4⋊C4C2418yes—
254C13×C4⋊C4C2418yes—
255C13×C4⋊C4C2418yes—
256C13×C4⋊C4C24116yes—
257C13×C4⋊C4C2418yes—
258C13×C4⋊C4C2418yes—
259C13×C4⋊C4C2418yes—
260C13×C4⋊C4C24132yes—
261C13×C4⋊C4C24116yes—
262C13×C4⋊C4C24116yes—
263C13×C4⋊C4C24116yes—
264C13×C4⋊C4C2418yes—
265C13×C4⋊C4C2414yes—
266C13×C4⋊C4C2414yes—
267C13×C4⋊C4C2418yes—
268C13×C4⋊C4C2414yes—
269C13×C4⋊C4C2418yes—
270C13×C4⋊C4C2418yes—
271C13×C4⋊C4C24132yes—
272C13×C4⋊C4C24132yes—
273C13×C4⋊C4C24132yes—
274C13×C22⋊C4C24116yes—
275C13×C22⋊C4C24116yes—
276C13×C22⋊C4C2418yes—
277C13×C22⋊C4C2418yes—
278C13×C22⋊C4C24116yes—
279C13×C22⋊C4C2414yes—
280C13×C22⋊C4C2418yes—
281C13×C22⋊C4C2418yes—
282C13×C22⋊C4C24132yes—
283C42×C13C2411yescharacteristic
284C42×C13C2411yescharacteristic
285C42×C13C2412yes—
286C42×C13C2412yes—
287C42×C13C2412yes—
288C42×C13C2412yes—
289C42×C13C2412yes—
290C42×C13C2411yescharacteristic
291C42×C13C2412yes—
292C42×C13C2411yescharacteristic
293C42×C13C24116yes—
294C42×C13C2414yes—
295C42×C13C2418yes—
296C42×C13C24116yes—
297C42×C13C24132yes—
298C42×C13C24116yes—
299#3563C2×C1318yescomplemented
300#3556C2×C1312yescomplemented
301#3555C2×C1318yescomplemented
302#3550C2×C1312yescomplemented
303#3538C2×C1314yescomplemented
304#3523C2×C1318yescomplemented
305#3509C2×C1314yescomplemented
306#3509C2×C1314yescomplemented
307#3507C2×C1314yescomplemented
308#3503C2×C1314yescomplemented
309#3502C2×C1314yescomplemented
310#3495C2×C1318yescomplemented
311#3444C2×C1311yescharacteristic
312C2×#533C2×C1312yescomplemented
313C23×C13—24no—
314C23×C13—41no—
315C23×C13C2511yescharacteristic
316C23×C13C2514yes—
317C23×C13C2512yes—
318Q8×C13—216no—
319Q8×C13—216no—
320Q8×C13—28no—
321Q8×C13—216no—
322Q8×C13—48no—
323Q8×C13—416no—
324Q8×C13—42no—
325D4×C13—216no—
326D4×C13—28no—
327D4×C13—42no—
328D4×C13—44no—
329C2×C4×C13—24no—
330C2×C4×C13—216no—
331C2×C4×C13—24no—
332C2×C4×C13—24no—
333C2×C4×C13—24no—
334C2×C4×C13—24no—
335C2×C4×C13—216no—
336C2×C4×C13—24no—
337C2×C4×C13—22no—
338C2×C4×C13—28no—
339C2×C4×C13—42no—
340C2×C4×C13—41no—
341C2×C4×C13—48no—
342C2×C4×C13—416no—
343C2×C4×C132−1+418yes—
344C2×C4×C13C2512yes—
345C2×C4×C13C25116yes—
346C2×C4×C13C2518yes—
347C2×C4×C13C2514yes—
348C2×C4×C13C2512yes—
349C2×C4×C13C2512yes—
350C2×C4×C13C25116yes—
351C2×C4×C13C2511yescharacteristic
352C2×C4×C13C2512yes—
353C2×C4×C13C2512yes—
354C2×C4×C13C2511yescharacteristic
355#564C22×C1318yescomplemented
356#563C22×C13116yes—
357#563C22×C1318yescomplemented
358#559C22×C1314yescomplemented
359Q82C22×C1314yescomplemented
360Q82C22×C1318yescomplemented
361#557C22×C1318yescomplemented
362#557C22×C1318yescomplemented
363#557C22×C13116yescomplemented
364#557C22×C13116yescomplemented
365#557C22×C1318yescomplemented
366#557C22×C1318yescomplemented
367#556C22×C13116yes—
368#556C22×C1318yescomplemented
369#556C22×C13116yescomplemented
370#556C22×C1318yescomplemented
371#554C22×C13116yes—
372#554C22×C1318yescomplemented
373#552C22×C13116yes—
374#552C22×C13116yes—
375#552C22×C13132yes—
376#552C22×C13116yes—
377#552C22×C13116yescomplemented
378#551C22×C13116yes—
379D4×Q8C22×C13116yes—
380D4×Q8C22×C1318yescomplemented
381#544C22×C1318yes—
382#544C22×C13116yes—
383#544C22×C13116yescomplemented
384#542C22×C13116yes—
385#541C22×C13116yes—
386#541C22×C1318yes—
387#541C22×C1318yescomplemented
388#541C22×C13116yescomplemented
389#541C22×C13132yescomplemented
390#539C22×C13116yes—
391#536C22×C1318yes—
392#536C22×C1318yes—
393#533C22×C1314yes—
394#533C22×C1314yes—
395#533C22×C1314yes—
396#533C22×C1314yes—
397#533C22×C1314yes—
398#533C22×C1314yes—
399#533C22×C1314yes—
400#533C22×C1314yes—
401#533C22×C1312yes—
402#533C22×C1311yescharacteristic
403#533C22×C13116yes—
404#533C22×C1318yescomplemented
405#533C22×C1314yescomplemented
406#532C22×C1312yes—
407#532C22×C1311yescharacteristic
408C2×C4⋊Q8C22×C1312yes—
409C2×C4⋊Q8C22×C1312yes—
410C2×C4⋊Q8C22×C1314yescomplemented
411#529C22×C1314yes—
412#529C22×C1314yes—
413#529C22×C1314yes—
414#529C22×C13116yes—
415C2×#125C22×C1314yes—
416#525C22×C1314yes—
417#525C22×C1312yes—
418C2×C22⋊Q8C22×C1314yes—
419C2×C22⋊Q8C22×C1314yes—
420#520C22×C1318yes—
421#519C22×C1318yes—
422#519C22×C1318yescomplemented
423C4×#41C22×C1314yes—
424C4×#41C22×C1312yes—
425C2×C4×Q8C22×C1314yes—
426C2×C4×Q8C22×C1314yes—
427C2×#117C22×C1314yes—
428C22×C42C22×C1311yescharacteristic
429C22×C13—22no—
430C22×C13—22no—
431C22×C13—22no—
432C22×C13—28no—
433C22×C13—24no—
434C22×C13—21no—
435C22×C13—44no—
436C22×C13C2×2−1+414yes—
437C22×C13C2611yescharacteristic
438C4×C13—22no—
439C4×C13—22no—
440C4×C13—28no—
441C4×C13—216no—
442C4×C13—21no—
443C4×C13—22no—
444C4×C13—24no—
445C4×C13—216no—
446C4×C13C2×2−1+414yes—
447C4×C13C2×2−1+414yes—
448C4×C13#58512yes—
449C2×#41C23×C1314yes—
450C2×#41C23×C1312yes—
451C22×Q8C23×C1314yes—
452C22×Q8C23×C1314yes—
453C22×Q8C23×C1318yes—
454C23×C4C23×C1312yes—
455C23×C4C23×C1311yescharacteristic
456C4⋊Q8C23×C1314yes—
457C4⋊Q8C23×C1314yes—
458C4⋊Q8C23×C1314yes—
459C4⋊Q8C23×C1314yes—
460C4⋊Q8C23×C1314yes—
461C4⋊Q8C23×C1314yes—
462C4⋊Q8C23×C1314yes—
463C4⋊Q8C23×C1314yes—
464C4⋊Q8C23×C1318yes—
465C4⋊Q8C23×C13116yes—
466C4⋊Q8C23×C1312yes—
467C4⋊Q8C23×C1311yescharacteristic
468C4⋊Q8C23×C13116yes—
469C4⋊Q8C23×C13116yes—
470C4⋊Q8C23×C13116yes—
471C4⋊Q8C23×C13132yes—
472#127C23×C1311yescharacteristic
473#126C23×C1318yes—
474#126C23×C13132yes—
475#126C23×C13132yes—
476#126C23×C13132yes—
477#126C23×C13132yes—
478#125C23×C1318yes—
479#125C23×C1318yes—
480#125C23×C1318yes—
481#125C23×C1318yes—
482#125C23×C1314yes—
483#125C23×C1312yes—
484#125C23×C13116yes—
485#125C23×C13132yes—
486#125C23×C1318yes—
487#125C23×C13116yes—
488#125C23×C13132yes—
489#125C23×C13132yes—
490#125C23×C13132yes—
491#125C23×C13132yes—
492#124C23×C1314yes—
493#124C23×C1312yes—
494#124C23×C13116yes—
495#124C23×C13116yes—
496#123C23×C1318yes—
497#123C23×C1314yes—
498#123C23×C13132yes—
499#123C23×C13116yes—
500#123C23×C13116yes—
501C22⋊Q8C23×C1318yes—
502C22⋊Q8C23×C1318yes—
503C22⋊Q8C23×C1318yes—
504C22⋊Q8C23×C1318yes—
505C22⋊Q8C23×C1318yes—
506C22⋊Q8C23×C1318yes—
507C22⋊Q8C23×C1318yes—
508C22⋊Q8C23×C1318yes—
509C22⋊Q8C23×C1314yes—
510C22⋊Q8C23×C1314yes—
511C22⋊Q8C23×C1314yes—
512C22⋊Q8C23×C13132yes—
513C22⋊Q8C23×C13116yes—
514C22⋊Q8C23×C13116yes—
515C22⋊Q8C23×C13116yes—
516C22⋊Q8C23×C13132yes—
517C22⋊Q8C23×C13132yes—
518#121C23×C1314yes—
519#121C23×C1314yes—
520#121C23×C1314yes—
521#120C23×C1314yes—
522C4×Q8C23×C1318yes—
523C4×Q8C23×C1318yes—
524C4×Q8C23×C1318yes—
525C4×Q8C23×C1318yes—
526C4×Q8C23×C1318yes—
527C4×Q8C23×C1318yes—
528C4×Q8C23×C1318yes—
529C4×Q8C23×C1318yes—
530C4×Q8C23×C1314yes—
531C4×Q8C23×C1314yes—
532C4×Q8C23×C1314yes—
533C4×Q8C23×C13116yes—
534C4×Q8C23×C13116yes—
535C4×Q8C23×C13116yes—
536C4×Q8C23×C13116yes—
537C4×Q8C23×C13132yes—
538C4×Q8C23×C13116yes—
539C4×Q8C23×C13116yes—
540C4×D4C23×C1318yes—
541C4×D4C23×C1318yes—
542C4×D4C23×C1318yes—
543C4×D4C23×C1314yes—
544C4×D4C23×C1314yes—
545C4×D4C23×C1314yes—
546C4×D4C23×C13132yes—
547C4×D4C23×C13116yes—
548#117C23×C1318yes—
549#117C23×C1318yes—
550#117C23×C1318yes—
551#117C23×C1318yes—
552#117C23×C1314yes—
553#117C23×C1314yes—
554#117C23×C1312yes—
555#117C23×C1318yes—
556#117C23×C13132yes—
557#117C23×C13132yes—
558#117C23×C1318yes—
559#117C23×C13116yes—
560C2×C4⋊C4C23×C1314yes—
561C2×C4⋊C4C23×C1314yes—
562C2×C4⋊C4C23×C1314yes—
563C2×C4⋊C4C23×C1318yes—
564C2×C4⋊C4C23×C1318yes—
565C2×C4⋊C4C23×C1314yes—
566C2×C4⋊C4C23×C13116yes—
567C2×C22⋊C4C23×C1318yes—
568C2×C42C23×C1318yes—
569C2×C42C23×C1312yes—
570C2×C42C23×C1312yes—
571C2×C42C23×C1314yes—
572C2×C42C23×C1312yes—
573C2×C42C23×C1311yescharacteristic
574C2×C42C23×C1312yes—
575C2×C42C23×C1312yes—
576C2×C42C23×C1311yescharacteristic
577C2×C13—24no—
578C2×C13—44no—
579C2×C13—41no—
580C2×C13C22×2−1+412yes—
581C2×C13C2×#58511yescharacteristic
582C24C24×C1311yescharacteristic
583#41—216no—
584#41—44no—
585C2×Q8—216no—
586C2×Q8—48no—
587C2×Q8—416no—
588C2×Q8C24×C1318yes—
589C2×Q8C24×C1318yes—
590C2×Q8C24×C1314yes—
591C2×Q8C24×C1318yes—
592C2×Q8C24×C1318yes—
593C2×Q8C24×C13116yes—
594C2×Q8C24×C1312yes—
595C2×D4C24×C1318yes—
596C2×D4C24×C1314yes—
597C2×D4C24×C1314yes—
598C2×D4C24×C1312yes—
599C22×C4—28no—
600C22×C4—42no—
601C22×C4C24×C1312yes—
602C22×C4C24×C1312yes—
603C22×C4C24×C1312yes—
604C22×C4C24×C1312yes—
605C22×C4C24×C1312yes—
606C22×C4C24×C1312yes—
607C22×C4C24×C1311yescharacteristic
608C22×C4C24×C1318yes—
609C22×C4C24×C1318yes—
610C22×C4C24×C1314yes—
611C22×C4C24×C1312yes—
612C22×C4C24×C1311yescharacteristic
613C22×C4C24×C1318yes—
614C22×C4C24×C13116yes—
615C22×C4C24×C1312yes—
616C4⋊C4C24×C1318yes—
617C4⋊C4C24×C1318yes—
618C4⋊C4C24×C1318yes—
619C4⋊C4C24×C1318yes—
620C4⋊C4C24×C13116yes—
621C4⋊C4C24×C1318yes—
622C4⋊C4C24×C1318yes—
623C4⋊C4C24×C1318yes—
624C4⋊C4C24×C13132yes—
625C4⋊C4C24×C13116yes—
626C4⋊C4C24×C13116yes—
627C4⋊C4C24×C13116yes—
628C4⋊C4C24×C1318yes—
629C4⋊C4C24×C1314yes—
630C4⋊C4C24×C1314yes—
631C4⋊C4C24×C1318yes—
632C4⋊C4C24×C1314yes—
633C4⋊C4C24×C1318yes—
634C4⋊C4C24×C1318yes—
635C4⋊C4C24×C13132yes—
636C4⋊C4C24×C13132yes—
637C4⋊C4C24×C13132yes—
638C22⋊C4C24×C13116yes—
639C22⋊C4C24×C13116yes—
640C22⋊C4C24×C1318yes—
641C22⋊C4C24×C1318yes—
642C22⋊C4C24×C13116yes—
643C22⋊C4C24×C1314yes—
644C22⋊C4C24×C1318yes—
645C22⋊C4C24×C1318yes—
646C22⋊C4C24×C13132yes—
647C42C24×C1311yescharacteristic
648C42C24×C1311yescharacteristic
649C42C24×C1312yes—
650C42C24×C1312yes—
651C42C24×C1312yes—
652C42C24×C1312yes—
653C42C24×C1312yes—
654C42C24×C1311yescharacteristic
655C42C24×C1312yes—
656C42C24×C1311yescharacteristic
657C42C24×C13116yes—
658C42C24×C1314yes—
659C42C24×C1318yes—
660C42C24×C13116yes—
661C42C24×C13132yes—
662C42C24×C13116yes—
663C13#6283711yescharacteristic, direct product factor, Sylow
664C23—24no—
665C23—41no—
666C23C25×C1311yescharacteristic
667C23C25×C1314yes—
668C23C25×C1312yes—
669Q8—216no—
670Q8—216no—
671Q8—28no—
672Q8—216no—
673Q8—48no—
674Q8—416no—
675Q8—42no—
676D4—216no—
677D4—28no—
678D4—42no—
679D4—44no—
680C2×C4—24no—
681C2×C4—216no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—216no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—28no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—48no—
693C2×C4—416no—
694C2×C4C13×2−1+418yes—
695C2×C4C25×C1312yes—
696C2×C4C25×C13116yes—
697C2×C4C25×C1318yes—
698C2×C4C25×C1314yes—
699C2×C4C25×C1312yes—
700C2×C4C25×C1312yes—
701C2×C4C25×C13116yes—
702C2×C4C25×C1311yescharacteristic
703C2×C4C25×C1312yes—
704C2×C4C25×C1312yes—
705C2×C4C25×C1311yescharacteristic
706C22—22no—
707C22—22no—
708C22—22no—
709C22—28no—
710C22—24no—
711C22—21no—
712C22—44no—
713C22C2×C13×2−1+414yes—
714C22C26×C1311yescharacteristic
715C4—22no—
716C4—22no—
717C4—28no—
718C4—216no—
719C4—21no—
720C4—22no—
721C4—24no—
722C4—216no—
723C4C2×C13×2−1+414yes—
724C4C2×C13×2−1+414yes—
725C4C13×#58512yes—
726C2—24no—
727C2—41no—
728C2—44no—
729C2C22×C13×2−1+412yes—
730C2C2×C13×#58511yescharacteristic
subgroupG/H
center, socleC22×C13C26
commutator, Frattini, cosocleC22C26×C13
prime radicalC13×#3444C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3563C2semidirect
2. C13×#3556C2semidirect
3. C13×#3555C2semidirect
4. C13×#3550C2semidirect
5. C13×#3538C2semidirect
6. C13×#3523C2semidirect
7. C13×#3509C2semidirect
8. C13×#3509C2semidirect
9. C13×#3507C2semidirect
10. C13×#3503C2semidirect
11. C13×#3502C2semidirect
12. C13×#3495C2semidirect
14. C2×C13×#533C2semidirect
15. C13×#564C22semidirect
17. C13×#563C22semidirect
18. C13×#559C22semidirect
19. Q82×C13C22semidirect
20. Q82×C13C22semidirect
21. C13×#557C22semidirect
22. C13×#557C22semidirect
23. C13×#557C22semidirect
24. C13×#557C22semidirect
25. C13×#557C22semidirect
26. C13×#557C22semidirect
28. C13×#556C22semidirect
29. C13×#556C22semidirect
30. C13×#556C22semidirect
32. C13×#554C22semidirect
37. C13×#552C22semidirect
40. D4×Q8×C13C22semidirect
43. C13×#544C22semidirect
47. C13×#541C22semidirect
48. C13×#541C22semidirect
49. C13×#541C22semidirect
64. C13×#533C22semidirect
65. C13×#533C22semidirect
70. C2×C13×C4⋊Q8C22semidirect
82. C13×#519C22semidirect
217. #62837C13direct (N × H)
299. #3563C2×C13semidirect
300. #3556C2×C13semidirect
301. #3555C2×C13semidirect
302. #3550C2×C13semidirect
303. #3538C2×C13semidirect
304. #3523C2×C13semidirect
305. #3509C2×C13semidirect
306. #3509C2×C13semidirect
307. #3507C2×C13semidirect
308. #3503C2×C13semidirect
309. #3502C2×C13semidirect
310. #3495C2×C13semidirect
312. C2×#533C2×C13semidirect
355. #564C22×C13semidirect
357. #563C22×C13semidirect
358. #559C22×C13semidirect
359. Q82C22×C13semidirect
360. Q82C22×C13semidirect
361. #557C22×C13semidirect
362. #557C22×C13semidirect
363. #557C22×C13semidirect
364. #557C22×C13semidirect
365. #557C22×C13semidirect
366. #557C22×C13semidirect
368. #556C22×C13semidirect
369. #556C22×C13semidirect
370. #556C22×C13semidirect
372. #554C22×C13semidirect
377. #552C22×C13semidirect
380. D4×Q8C22×C13semidirect
383. #544C22×C13semidirect
387. #541C22×C13semidirect
388. #541C22×C13semidirect
389. #541C22×C13semidirect
404. #533C22×C13semidirect
405. #533C22×C13semidirect
410. C2×C4⋊Q8C22×C13semidirect
422. #519C22×C13semidirect
663. C13#62837direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35632
C13×#35562
C13×#35552
C13×#35502
C13×#35382
C13×#35232
C13×#35092
C13×#35072
C13×#35032
C13×#35022
C13×#34952
C13×#34442
C2×C13×#5332
#6283713