Finite Group Databasebeta

← C13×#63069 #15749408

Subgroups — C13×#63069 #15749408

Order 3328.

6496 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3568C2110yesmaximal, complemented
2C13×#3561C2110yesmaximal, complemented
3C13×#3561C215yesmaximal, complemented
4C13×#3558C215yesmaximal, complemented
5C13×#3550C215yesmaximal, complemented
6C13×#3545C2110yesmaximal, complemented
7C13×#3531C211yesmaximal, characteristic, complemented
8C13×#3531C212yesmaximal, complemented
9C13×#3518C215yesmaximal, complemented
10C13×#3514C215yesmaximal, complemented
11C13×#3510C215yesmaximal, complemented
12C13×#564C2211yescharacteristic, complemented
13C13×#563C22110yescomplemented
14C13×#563C2215yescomplemented
15C13×#563C22110yescomplemented
16C13×#563C2215yescomplemented
17C13×#563C22110yescomplemented
18C13×#562C2215yescomplemented
19C13×#562C22110yescomplemented
20C13×#562C22110yescomplemented
21C13×H(3,𝔽4)C22110yescomplemented
22C13×#559C22110yescomplemented
23C13×#559C2215yescomplemented
24Q82×C13C2215yescomplemented
25C13×#556C2215yescomplemented
26C13×#556C22120yescomplemented
27C13×#556C22110yescomplemented
28C13×#556C2215yescomplemented
29C13×#556C22110yescomplemented
30C13×#556C22110yescomplemented
31C13×#555C22110yescomplemented
32C13×#555C2215yescomplemented
33C13×#551C22120yescomplemented
34C13×#551C22120yescomplemented
35C13×#551C22120yescomplemented
36C13×#551C22120yescomplemented
37D4×Q8×C13C2215yescomplemented
38D4×Q8×C13C2215yescomplemented
39D4×Q8×C13C22110yescomplemented
40C13×#548C22110yescomplemented
41C13×#548C22110yescomplemented
42C13×#546C22110yescomplemented
43C13×#546C22120yescomplemented
44C13×#546C22110yescomplemented
45D42×C13C2215yescomplemented
46C13×#543C22110yescomplemented
47C13×#542C22120yescomplemented
48C13×#542C22110yescomplemented
49C13×#542C22120yescomplemented
50C13×#542C22110yescomplemented
51C13×#542C22120yescomplemented
52C13×#542C22110yescomplemented
53C13×#542C22110yescomplemented
54C13×#538C22110yescomplemented
55C13×#538C22120yescomplemented
56C13×#538C22120yescomplemented
57C13×#538C22110yescomplemented
58C13×#536C22120yescomplemented
59C13×#536C2215yescomplemented
60C13×#535C2215yes—
61C13×#534C22110yescomplemented
62C13×#533C22110yescomplemented
63C13×#533C2215yescomplemented
64C13×#533C2215yescomplemented
65C13×#532C2215yes—
66C13×#529C2215yescomplemented
67C13×#529C22110yescomplemented
68C13×#529C22110yescomplemented
69C13×#529C2215yescomplemented
70C13×#529C22110yescomplemented
71C13×#529C22110yescomplemented
72C2×C13×#124C22110yescomplemented
73C2×C13×#124C2215yescomplemented
74C13×#519C2215yescomplemented
75C13×#518C2215yescomplemented
76C4×C13×#41C2215yescomplemented
77C2×C13×#41C2315yes—
78C2×C13×#41C23110yes—
79C22×Q8×C13C2315yes—
80C22×Q8×C13C23110yes—
81C22×D4×C13C2315yes—
82C22×D4×C13C23110yes—
83C13×C4⋊Q8C2315yes—
84C13×C4⋊Q8C2315yes—
85C13×C4⋊Q8C23110yes—
86C13×C4⋊Q8C2315yes—
87C13×C4⋊Q8C2315yes—
88C13×C4⋊Q8C23110yes—
89C13×C4⋊Q8C2315yes—
90C13×C4⋊Q8C23120yes—
91C13×#127C2315yes—
92C13×#126C23110yes—
93C13×#126C23120yes—
94C13×#126C23120yes—
95C13×#126C23120yes—
96C13×#126C23120yes—
97C13×#126C23110yes—
98C13×#126C23120yes—
99C13×#126C23120yes—
100C13×#125C2315yes—
101C13×#125C2315yes—
102C13×#125C2315yes—
103C13×#125C2315yes—
104C13×#125C23110yes—
105C13×#124C2315yes—
106C13×#124C23110yes—
107C13×#124C23110yes—
108C13×#124C23110yes—
109C13×#124C23120yes—
110C13×#124C23110yes—
111C13×#124C23110yes—
112C13×#124C23120yes—
113C13×#124C23110yes—
114C13×#124C23110yes—
115C13×#124C2315yes—
116C13×#124C23120yes—
117C13×#124C23120yes—
118C13×#124C23120yes—
119C13×#123C23120yes—
120C13×#123C23120yes—
121C13×#123C23110yes—
122C13×#123C23120yes—
123C13×#123C23120yes—
124C13×#123C23110yes—
125C13×#123C23120yes—
126C13×#123C23120yes—
127C13×#123C23120yes—
128C13×C22⋊Q8C23110yes—
129C13×C22⋊Q8C23110yes—
130C13×C22⋊Q8C2315yes—
131C13×C22⋊Q8C23110yes—
132C13×C22⋊Q8C23110yes—
133C13×C22⋊Q8C2315yes—
134C13×C22⋊Q8C23110yes—
135C13×C22⋊Q8C23110yes—
136C13×C22⋊Q8C23120yes—
137C13×C22⋊Q8C23110yes—
138C13×C22⋊Q8C23120yes—
139C13×C22⋊Q8C23110yes—
140C13×C22⋊Q8C23120yes—
141C13×C22⋊Q8C23120yes—
142C13×C22⋊Q8C23120yes—
143C13×C22⋊Q8C23120yes—
144C13×#121C2315yes—
145C13×#121C23110yes—
146C13×#121C23110yes—
147C13×#121C23110yes—
148C13×#121C23110yes—
149C13×#121C2315yes—
150C13×#121C23110yes—
151C13×#121C23110yes—
152C13×#121C23120yes—
153C13×#121C23120yes—
154C13×#120C23120yes—
155C13×#120C23120yes—
156C13×#120C23120yes—
157C4×Q8×C13C2315yes—
158C4×Q8×C13C2315yes—
159C4×Q8×C13C23110yes—
160C4×Q8×C13C23110yes—
161C4×Q8×C13C23110yes—
162C4×Q8×C13C23110yes—
163C4×Q8×C13C2315yes—
164C4×Q8×C13C2315yes—
165C4×Q8×C13C23110yes—
166C4×Q8×C13C23110yes—
167C4×D4×C13C2315yes—
168C4×D4×C13C23110yes—
169C4×D4×C13C2315yes—
170C4×D4×C13C23110yes—
171C4×D4×C13C23110yes—
172C4×D4×C13C23110yes—
173C4×D4×C13C23110yes—
174C4×D4×C13C2315yes—
175C4×D4×C13C2315yes—
176C4×D4×C13C23110yes—
177C4×D4×C13C23110yes—
178C4×D4×C13C23120yes—
179C4×D4×C13C23120yes—
180C4×D4×C13C23110yes—
181C13×#117C2315yes—
182C13×#117C23110yes—
183C13×#117C2315yes—
184C13×#117C2315yes—
185C13×#117C23120yes—
186C13×#117C23110yes—
187C13×#117C23110yes—
188C13×#117C23120yes—
189C13×#117C23110yes—
190C2×C13×C22⋊C4C23120yes—
191C2×C13×C22⋊C4C23110yes—
192C2×C13×C22⋊C4C23120yes—
193C2×C13×C22⋊C4C23110yes—
194C2×C42×C13C23110yes—
195C2×C42×C13C2315yes—
196#63069C1311yesmaximal, characteristic, direct product factor, Sylow
197C24×C13C24110yes—
198C13×#41—410no—
199C13×#41—810no—
200C2×Q8×C13—410no—
201C2×Q8×C13—810no—
202C2×Q8×C13C2415yes—
203C2×Q8×C13C2415yes—
204C2×Q8×C13C24110yes—
205C2×Q8×C13C2415yes—
206C2×Q8×C13C24110yes—
207C2×Q8×C13C24110yes—
208C2×D4×C13—410no—
209C2×D4×C13—810no—
210C2×D4×C13C2415yes—
211C2×D4×C13C2415yes—
212C2×D4×C13C24110yes—
213C2×D4×C13C24110yes—
214C2×D4×C13C24110yes—
215C2×D4×C13C24120yes—
216C2×D4×C13C24110yes—
217C2×D4×C13C2415yes—
218C22×C4×C13C2415yes—
219C22×C4×C13C24110yes—
220C22×C4×C13C2415yes—
221C22×C4×C13C24110yes—
222C22×C4×C13C2415yes—
223C22×C4×C13C24110yes—
224C22×C4×C13C24110yes—
225C22×C4×C13C24120yes—
226C13×C4⋊C4C2411yescharacteristic
227C13×C4⋊C4C24110yes—
228C13×C4⋊C4C24110yes—
229C13×C4⋊C4C2415yes—
230C13×C4⋊C4C24110yes—
231C13×C4⋊C4C2415yes—
232C13×C4⋊C4C24110yes—
233C13×C4⋊C4C24110yes—
234C13×C4⋊C4C2415yes—
235C13×C4⋊C4C2415yes—
236C13×C4⋊C4C2415yes—
237C13×C4⋊C4C24110yes—
238C13×C4⋊C4C2415yes—
239C13×C4⋊C4C2415yes—
240C13×C4⋊C4C24120yes—
241C13×C4⋊C4C2415yes—
242C13×C4⋊C4C24110yes—
243C13×C4⋊C4C2415yes—
244C13×C4⋊C4C24120yes—
245C13×C4⋊C4C24110yes—
246C13×C22⋊C4C24110yes—
247C13×C22⋊C4C24110yes—
248C13×C22⋊C4C24110yes—
249C13×C22⋊C4C24110yes—
250C13×C22⋊C4C24120yes—
251C13×C22⋊C4C24120yes—
252C13×C22⋊C4C24120yes—
253C13×C22⋊C4C24120yes—
254C13×C22⋊C4C24120yes—
255C13×C22⋊C4C24120yes—
256C13×C22⋊C4C24120yes—
257C13×C22⋊C4C24110yes—
258C13×C22⋊C4C24110yes—
259C13×C22⋊C4C24110yes—
260C42×C13C2415yes—
261C42×C13C24110yes—
262C42×C13C24110yes—
263C42×C13C2415yes—
264C42×C13C2415yes—
265C42×C13C2415yes—
266C42×C13C24110yes—
267C42×C13C24120yes—
268#3568C2×C13110yescomplemented
269#3561C2×C1315yescomplemented
270#3561C2×C13110yescomplemented
271#3558C2×C1315yescomplemented
272#3550C2×C1315yescomplemented
273#3545C2×C13110yescomplemented
274#3531C2×C1312yescomplemented
275#3531C2×C1311yescharacteristic, complemented
276#3518C2×C1315yescomplemented
277#3514C2×C1315yescomplemented
278#3510C2×C1315yescomplemented
279C23×C13—410no—
280C23×C13—410no—
281C23×C13—410no—
282C23×C13C2515yes—
283C23×C13C25110yes—
284Q8×C13—210no—
285Q8×C13—410no—
286Q8×C13—45no—
287Q8×C13—410no—
288Q8×C13—410no—
289Q8×C13—45no—
290D4×C13—210no—
291D4×C13—410no—
292D4×C13—45no—
293D4×C13—410no—
294D4×C13—420no—
295D4×C13—45no—
296D4×C13—410no—
297D4×C13—410no—
298C2×C4×C13—210no—
299C2×C4×C13—410no—
300C2×C4×C13—45no—
301C2×C4×C13—410no—
302C2×C4×C13—410no—
303C2×C4×C13—420no—
304C2×C4×C13—410no—
305C2×C4×C13—45no—
306C2×C4×C13C2512yes—
307C2×C4×C13C2515yes—
308C2×C4×C13C2515yes—
309C2×C4×C13C25110yes—
310C2×C4×C13C2515yes—
311C2×C4×C13C25110yes—
312C2×C4×C13C2515yes—
313C2×C4×C13C2515yes—
314C2×C4×C13C2511yescharacteristic
315#564C22×C1311yescharacteristic, complemented
316#563C22×C13110yescomplemented
317#563C22×C1315yescomplemented
318#563C22×C13110yescomplemented
319#563C22×C1315yescomplemented
320#563C22×C13110yescomplemented
321#562C22×C1315yescomplemented
322#562C22×C13110yescomplemented
323#562C22×C13110yescomplemented
324H(3,𝔽4)C22×C13110yescomplemented
325#559C22×C1315yescomplemented
326#559C22×C13110yescomplemented
327Q82C22×C1315yescomplemented
328#556C22×C1315yescomplemented
329#556C22×C13110yescomplemented
330#556C22×C1315yescomplemented
331#556C22×C13120yescomplemented
332#556C22×C13110yescomplemented
333#556C22×C13110yescomplemented
334#555C22×C1315yescomplemented
335#555C22×C13110yescomplemented
336#551C22×C13120yescomplemented
337#551C22×C13120yescomplemented
338#551C22×C13120yescomplemented
339#551C22×C13120yescomplemented
340D4×Q8C22×C1315yescomplemented
341D4×Q8C22×C1315yescomplemented
342D4×Q8C22×C13110yescomplemented
343#548C22×C13110yescomplemented
344#548C22×C13110yescomplemented
345#546C22×C13110yescomplemented
346#546C22×C13110yescomplemented
347#546C22×C13120yescomplemented
348D42C22×C1315yescomplemented
349#543C22×C13110yescomplemented
350#542C22×C13110yescomplemented
351#542C22×C13110yescomplemented
352#542C22×C13110yescomplemented
353#542C22×C13120yescomplemented
354#542C22×C13110yescomplemented
355#542C22×C13120yescomplemented
356#542C22×C13120yescomplemented
357#538C22×C13120yescomplemented
358#538C22×C13110yescomplemented
359#538C22×C13120yescomplemented
360#538C22×C13110yescomplemented
361#536C22×C1315yescomplemented
362#536C22×C13120yescomplemented
363#535C22×C1315yes—
364#534C22×C13110yescomplemented
365#533C22×C1315yescomplemented
366#533C22×C13110yescomplemented
367#533C22×C1315yescomplemented
368#532C22×C1315yes—
369#529C22×C13110yescomplemented
370#529C22×C13110yescomplemented
371#529C22×C1315yescomplemented
372#529C22×C13110yescomplemented
373#529C22×C1315yescomplemented
374#529C22×C13110yescomplemented
375C2×#124C22×C1315yescomplemented
376C2×#124C22×C13110yescomplemented
377#519C22×C1315yescomplemented
378#518C22×C1315yescomplemented
379C4×#41C22×C1315yescomplemented
380C22×C13—25no—
381C22×C13—210no—
382C22×C13—210no—
383C22×C13—25no—
384C22×C13—25no—
385C22×C13—210no—
386C22×C13—1610no—
387C22×C13C2611yescharacteristic
388C4×C13—25no—
389C4×C13—210no—
390C4×C13—25no—
391C4×C13—25no—
392C4×C13—210no—
393C4×C13—22no—
394C4×C13—25no—
395C4×C13—25no—
396C4×C13#58512yes—
397C2×#41C23×C1315yes—
398C2×#41C23×C13110yes—
399C22×Q8C23×C1315yes—
400C22×Q8C23×C13110yes—
401C22×D4C23×C1315yes—
402C22×D4C23×C13110yes—
403C4⋊Q8C23×C1315yes—
404C4⋊Q8C23×C1315yes—
405C4⋊Q8C23×C13110yes—
406C4⋊Q8C23×C1315yes—
407C4⋊Q8C23×C1315yes—
408C4⋊Q8C23×C13110yes—
409C4⋊Q8C23×C1315yes—
410C4⋊Q8C23×C13120yes—
411#127C23×C1315yes—
412#126C23×C13110yes—
413#126C23×C13120yes—
414#126C23×C13120yes—
415#126C23×C13120yes—
416#126C23×C13120yes—
417#126C23×C13110yes—
418#126C23×C13120yes—
419#126C23×C13120yes—
420#125C23×C1315yes—
421#125C23×C1315yes—
422#125C23×C1315yes—
423#125C23×C1315yes—
424#125C23×C13110yes—
425#124C23×C1315yes—
426#124C23×C13110yes—
427#124C23×C13110yes—
428#124C23×C13110yes—
429#124C23×C13120yes—
430#124C23×C13110yes—
431#124C23×C13110yes—
432#124C23×C13120yes—
433#124C23×C13110yes—
434#124C23×C13110yes—
435#124C23×C1315yes—
436#124C23×C13120yes—
437#124C23×C13120yes—
438#124C23×C13120yes—
439#123C23×C13120yes—
440#123C23×C13120yes—
441#123C23×C13110yes—
442#123C23×C13120yes—
443#123C23×C13120yes—
444#123C23×C13110yes—
445#123C23×C13120yes—
446#123C23×C13120yes—
447#123C23×C13120yes—
448C22⋊Q8C23×C13110yes—
449C22⋊Q8C23×C13110yes—
450C22⋊Q8C23×C1315yes—
451C22⋊Q8C23×C13110yes—
452C22⋊Q8C23×C13110yes—
453C22⋊Q8C23×C1315yes—
454C22⋊Q8C23×C13110yes—
455C22⋊Q8C23×C13110yes—
456C22⋊Q8C23×C13120yes—
457C22⋊Q8C23×C13110yes—
458C22⋊Q8C23×C13120yes—
459C22⋊Q8C23×C13110yes—
460C22⋊Q8C23×C13120yes—
461C22⋊Q8C23×C13120yes—
462C22⋊Q8C23×C13120yes—
463C22⋊Q8C23×C13120yes—
464#121C23×C1315yes—
465#121C23×C13110yes—
466#121C23×C13110yes—
467#121C23×C13110yes—
468#121C23×C13110yes—
469#121C23×C1315yes—
470#121C23×C13110yes—
471#121C23×C13110yes—
472#121C23×C13120yes—
473#121C23×C13120yes—
474#120C23×C13120yes—
475#120C23×C13120yes—
476#120C23×C13120yes—
477C4×Q8C23×C1315yes—
478C4×Q8C23×C1315yes—
479C4×Q8C23×C13110yes—
480C4×Q8C23×C13110yes—
481C4×Q8C23×C13110yes—
482C4×Q8C23×C13110yes—
483C4×Q8C23×C1315yes—
484C4×Q8C23×C1315yes—
485C4×Q8C23×C13110yes—
486C4×Q8C23×C13110yes—
487C4×D4C23×C1315yes—
488C4×D4C23×C13110yes—
489C4×D4C23×C1315yes—
490C4×D4C23×C13110yes—
491C4×D4C23×C13110yes—
492C4×D4C23×C13110yes—
493C4×D4C23×C13110yes—
494C4×D4C23×C1315yes—
495C4×D4C23×C1315yes—
496C4×D4C23×C13110yes—
497C4×D4C23×C13110yes—
498C4×D4C23×C13120yes—
499C4×D4C23×C13120yes—
500C4×D4C23×C13110yes—
501#117C23×C1315yes—
502#117C23×C13110yes—
503#117C23×C1315yes—
504#117C23×C1315yes—
505#117C23×C13120yes—
506#117C23×C13110yes—
507#117C23×C13110yes—
508#117C23×C13120yes—
509#117C23×C13110yes—
510C2×C22⋊C4C23×C13120yes—
511C2×C22⋊C4C23×C13110yes—
512C2×C22⋊C4C23×C13120yes—
513C2×C22⋊C4C23×C13110yes—
514C2×C42C23×C13110yes—
515C2×C42C23×C1315yes—
516C2×C13—45no—
517C2×C13—410no—
518C2×C13C2×#58511yescharacteristic
519C2×C13H(7,𝔽2)11yescharacteristic
520C2×C132−1+611yescharacteristic
521C24C24×C13110yes—
522#41—410no—
523#41—810no—
524C2×Q8—410no—
525C2×Q8—810no—
526C2×Q8C24×C1315yes—
527C2×Q8C24×C1315yes—
528C2×Q8C24×C13110yes—
529C2×Q8C24×C1315yes—
530C2×Q8C24×C13110yes—
531C2×Q8C24×C13110yes—
532C2×D4—410no—
533C2×D4—810no—
534C2×D4C24×C1315yes—
535C2×D4C24×C1315yes—
536C2×D4C24×C13110yes—
537C2×D4C24×C13110yes—
538C2×D4C24×C13110yes—
539C2×D4C24×C13120yes—
540C2×D4C24×C13110yes—
541C2×D4C24×C1315yes—
542C22×C4C24×C1315yes—
543C22×C4C24×C13110yes—
544C22×C4C24×C1315yes—
545C22×C4C24×C13110yes—
546C22×C4C24×C1315yes—
547C22×C4C24×C13110yes—
548C22×C4C24×C13110yes—
549C22×C4C24×C13120yes—
550C4⋊C4C24×C1311yescharacteristic
551C4⋊C4C24×C13110yes—
552C4⋊C4C24×C13110yes—
553C4⋊C4C24×C1315yes—
554C4⋊C4C24×C13110yes—
555C4⋊C4C24×C1315yes—
556C4⋊C4C24×C13110yes—
557C4⋊C4C24×C13110yes—
558C4⋊C4C24×C1315yes—
559C4⋊C4C24×C1315yes—
560C4⋊C4C24×C1315yes—
561C4⋊C4C24×C13110yes—
562C4⋊C4C24×C1315yes—
563C4⋊C4C24×C1315yes—
564C4⋊C4C24×C13120yes—
565C4⋊C4C24×C1315yes—
566C4⋊C4C24×C13110yes—
567C4⋊C4C24×C1315yes—
568C4⋊C4C24×C13120yes—
569C4⋊C4C24×C13110yes—
570C22⋊C4C24×C13110yes—
571C22⋊C4C24×C13110yes—
572C22⋊C4C24×C13110yes—
573C22⋊C4C24×C13110yes—
574C22⋊C4C24×C13120yes—
575C22⋊C4C24×C13120yes—
576C22⋊C4C24×C13120yes—
577C22⋊C4C24×C13120yes—
578C22⋊C4C24×C13120yes—
579C22⋊C4C24×C13120yes—
580C22⋊C4C24×C13120yes—
581C22⋊C4C24×C13110yes—
582C22⋊C4C24×C13110yes—
583C22⋊C4C24×C13110yes—
584C42C24×C1315yes—
585C42C24×C13110yes—
586C42C24×C13110yes—
587C42C24×C1315yes—
588C42C24×C1315yes—
589C42C24×C1315yes—
590C42C24×C13110yes—
591C42C24×C13120yes—
592C13#6306911yescharacteristic, direct product factor, Sylow
593C23—410no—
594C23—410no—
595C23—410no—
596C23C25×C1315yes—
597C23C25×C13110yes—
598Q8—210no—
599Q8—410no—
600Q8—45no—
601Q8—410no—
602Q8—410no—
603Q8—45no—
604D4—210no—
605D4—410no—
606D4—45no—
607D4—410no—
608D4—420no—
609D4—45no—
610D4—410no—
611D4—410no—
612C2×C4—210no—
613C2×C4—410no—
614C2×C4—410no—
615C2×C4—45no—
616C2×C4—410no—
617C2×C4—420no—
618C2×C4—410no—
619C2×C4—45no—
620C2×C4C25×C1312yes—
621C2×C4C25×C1315yes—
622C2×C4C25×C1315yes—
623C2×C4C25×C13110yes—
624C2×C4C25×C1315yes—
625C2×C4C25×C13110yes—
626C2×C4C25×C1315yes—
627C2×C4C25×C1315yes—
628C2×C4C25×C1311yescharacteristic
629C22—25no—
630C22—210no—
631C22—210no—
632C22—25no—
633C22—25no—
634C22—210no—
635C22—1610no—
636C22C26×C1311yescharacteristic
637C4—25no—
638C4—210no—
639C4—25no—
640C4—25no—
641C4—210no—
642C4—22no—
643C4—25no—
644C4—25no—
645C4C13×#58512yes—
646C2—45no—
647C2—410no—
648C2C2×C13×#58511yescharacteristic
649C2C13×H(7,𝔽2)11yescharacteristic
650C2C13×2−1+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×#3568C2semidirect
2. C13×#3561C2semidirect
3. C13×#3561C2semidirect
4. C13×#3558C2semidirect
5. C13×#3550C2semidirect
6. C13×#3545C2semidirect
7. C13×#3531C2semidirect
8. C13×#3531C2semidirect
9. C13×#3518C2semidirect
10. C13×#3514C2semidirect
11. C13×#3510C2semidirect
12. C13×#564C22semidirect
13. C13×#563C22semidirect
14. C13×#563C22semidirect
15. C13×#563C22semidirect
16. C13×#563C22semidirect
17. C13×#563C22semidirect
18. C13×#562C22semidirect
19. C13×#562C22semidirect
20. C13×#562C22semidirect
21. C13×H(3,𝔽4)C22semidirect
22. C13×#559C22semidirect
23. C13×#559C22semidirect
24. Q82×C13C22semidirect
25. C13×#556C22semidirect
26. C13×#556C22semidirect
27. C13×#556C22semidirect
28. C13×#556C22semidirect
29. C13×#556C22semidirect
30. C13×#556C22semidirect
31. C13×#555C22semidirect
32. C13×#555C22semidirect
33. C13×#551C22semidirect
34. C13×#551C22semidirect
35. C13×#551C22semidirect
36. C13×#551C22semidirect
37. D4×Q8×C13C22semidirect
38. D4×Q8×C13C22semidirect
39. D4×Q8×C13C22semidirect
40. C13×#548C22semidirect
41. C13×#548C22semidirect
42. C13×#546C22semidirect
43. C13×#546C22semidirect
44. C13×#546C22semidirect
45. D42×C13C22semidirect
46. C13×#543C22semidirect
47. C13×#542C22semidirect
48. C13×#542C22semidirect
49. C13×#542C22semidirect
50. C13×#542C22semidirect
51. C13×#542C22semidirect
52. C13×#542C22semidirect
53. C13×#542C22semidirect
54. C13×#538C22semidirect
55. C13×#538C22semidirect
56. C13×#538C22semidirect
57. C13×#538C22semidirect
58. C13×#536C22semidirect
59. C13×#536C22semidirect
61. C13×#534C22semidirect
62. C13×#533C22semidirect
63. C13×#533C22semidirect
64. C13×#533C22semidirect
66. C13×#529C22semidirect
67. C13×#529C22semidirect
68. C13×#529C22semidirect
69. C13×#529C22semidirect
70. C13×#529C22semidirect
71. C13×#529C22semidirect
72. C2×C13×#124C22semidirect
73. C2×C13×#124C22semidirect
74. C13×#519C22semidirect
75. C13×#518C22semidirect
76. C4×C13×#41C22semidirect
196. #63069C13direct (N × H)
268. #3568C2×C13semidirect
269. #3561C2×C13semidirect
270. #3561C2×C13semidirect
271. #3558C2×C13semidirect
272. #3550C2×C13semidirect
273. #3545C2×C13semidirect
274. #3531C2×C13semidirect
275. #3531C2×C13semidirect
276. #3518C2×C13semidirect
277. #3514C2×C13semidirect
278. #3510C2×C13semidirect
315. #564C22×C13semidirect
316. #563C22×C13semidirect
317. #563C22×C13semidirect
318. #563C22×C13semidirect
319. #563C22×C13semidirect
320. #563C22×C13semidirect
321. #562C22×C13semidirect
322. #562C22×C13semidirect
323. #562C22×C13semidirect
324. H(3,𝔽4)C22×C13semidirect
325. #559C22×C13semidirect
326. #559C22×C13semidirect
327. Q82C22×C13semidirect
328. #556C22×C13semidirect
329. #556C22×C13semidirect
330. #556C22×C13semidirect
331. #556C22×C13semidirect
332. #556C22×C13semidirect
333. #556C22×C13semidirect
334. #555C22×C13semidirect
335. #555C22×C13semidirect
336. #551C22×C13semidirect
337. #551C22×C13semidirect
338. #551C22×C13semidirect
339. #551C22×C13semidirect
340. D4×Q8C22×C13semidirect
341. D4×Q8C22×C13semidirect
342. D4×Q8C22×C13semidirect
343. #548C22×C13semidirect
344. #548C22×C13semidirect
345. #546C22×C13semidirect
346. #546C22×C13semidirect
347. #546C22×C13semidirect
348. D42C22×C13semidirect
349. #543C22×C13semidirect
350. #542C22×C13semidirect
351. #542C22×C13semidirect
352. #542C22×C13semidirect
353. #542C22×C13semidirect
354. #542C22×C13semidirect
355. #542C22×C13semidirect
356. #542C22×C13semidirect
357. #538C22×C13semidirect
358. #538C22×C13semidirect
359. #538C22×C13semidirect
360. #538C22×C13semidirect
361. #536C22×C13semidirect
362. #536C22×C13semidirect
364. #534C22×C13semidirect
365. #533C22×C13semidirect
366. #533C22×C13semidirect
367. #533C22×C13semidirect
369. #529C22×C13semidirect
370. #529C22×C13semidirect
371. #529C22×C13semidirect
372. #529C22×C13semidirect
373. #529C22×C13semidirect
374. #529C22×C13semidirect
375. C2×#124C22×C13semidirect
376. C2×#124C22×C13semidirect
377. #519C22×C13semidirect
378. #518C22×C13semidirect
379. C4×#41C22×C13semidirect
592. C13#63069direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35682
C13×#35612
C13×#35582
C13×#35502
C13×#35452
C13×#35312
C13×#35182
C13×#35142
C13×#35102
#6306913