Finite Group Databasebeta

← C13×#32735 #15719074

Subgroups — C13×#32735 #15719074

Order 3328.

766 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2624C211yesmaximal, characteristic, complemented
2C13×#2620C211yesmaximal, characteristic, complemented
3C13×#2100C211yesmaximal, characteristic, complemented
4C13×#2093C211yesmaximal, characteristic, complemented
5C13×#2068C211yesmaximal, characteristic, complemented
6C13×#2067C211yesmaximal, characteristic, complemented
7C13×#2055C211yesmaximal, characteristic, complemented
8C13×#2054C211yesmaximal, characteristic, complemented
9C13×#2042C211yesmaximal, characteristic, complemented
10C13×#2036C211yesmaximal, characteristic, complemented
11C13×#2033C211yesmaximal, characteristic, complemented
12C13×#2012C211yesmaximal, characteristic, complemented
13C13×#2000C211yesmaximal, characteristic, complemented
14C13×#1999C211yesmaximal, characteristic
15C13×#1798C211yesmaximal, characteristic, complemented
16C22×C13×SD16C2211yescharacteristic
17C22×C13×D8C2211yescharacteristic
18C2×C13×#124C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×#121C2211yescharacteristic
21C2×C13×#121C2211yescharacteristic
22C2×C13×#117C2211yescharacteristic
23C2×C13×#107C2211yescharacteristic
24C2×C13×#107C2211yescharacteristic
25C2×C13×C4⋊C8C2211yescharacteristic
26C2×C13×C4⋊C8C2211yescharacteristic
27C2×C13×#103C2211yescharacteristic
28C2×C13×#103C2211yescharacteristic
29C2×C13×#103C2211yescharacteristic
30C2×C13×#102C2211yescharacteristic
31C2×C13×#102C2211yescharacteristic
32C2×C13×#102C2211yescharacteristic
33C2×C13×#102C2211yescharacteristic
34C2×C13×#102C2211yescharacteristic
35C2×C13×C22⋊C8C2211yescharacteristic
36C2×C13×C22⋊C8C2211yescharacteristic
37C13×#399—21no—
38C13×#397—21no—
39C13×#396—21no—
40C13×#396—21no—
41C13×#394—21no—
42C13×#394—21no—
43C13×#394—21no—
44C13×#394—21no—
45C13×#391C2211yescharacteristic
46C13×#390C2211yescharacteristic
47C13×#390C2211yescharacteristic
48C13×#390C2211yescharacteristic
49C13×#389C2211yescharacteristic
50C13×#389C2211yescharacteristic
51C13×#384C2211yescharacteristic
52C13×#380C2211yescharacteristic
53C13×#340C2211yescharacteristic
54C13×#340C2211yescharacteristic
55C13×#340C2211yescharacteristic
56C13×#340C2211yescharacteristic
57C13×#336C2211yescharacteristic
58C13×#336C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C22×D4×C13—21no—
61C22×D4×C13—21no—
62C22×D4×C13C2311yescharacteristic
63C22×D4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C2×C13×SD16—41no—
66C2×C13×SD16—41no—
67C2×C13×SD16—41no—
68C2×C13×D8—41no—
69C2×C13×D8—41no—
70C2×C13×D8—41no—
71C22×C8×C13C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C22×C8×C13C2311yescharacteristic
75C13×#124—41no—
76C13×#124—41no—
77C13×C22⋊Q8—41no—
78C13×C22⋊Q8—41no—
79C13×#121—41no—
80C13×#121—41no—
81C13×#121—41no—
82C13×#121—41no—
83C13×#117—41no—
84C13×#117—41no—
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4D411yescharacteristic
91C2×C13×C4⋊C4D411yescharacteristic
92C2×C13×C4⋊C4C2311yescharacteristic
93C2×C13×C4⋊C4C2311yescharacteristic
94C2×C13×C4⋊C4C2311yescharacteristic
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C13×C22⋊C4—21no—
98C2×C13×C22⋊C4—21no—
99C2×C13×C22⋊C4—21no—
100C2×C13×C22⋊C4—21no—
101C2×C13×C22⋊C4—21no—
102C2×C13×C22⋊C4—21no—
103C2×C13×C22⋊C4—21no—
104C2×C13×C22⋊C4—21no—
105C2×C13×C22⋊C4—21no—
106C2×C13×C22⋊C4—21no—
107C2×C13×C22⋊C4—21no—
108C2×C13×C22⋊C4—21no—
109C2×C13×C22⋊C4D411yescharacteristic
110C2×C13×C22⋊C4D411yescharacteristic
111C2×C42×C13C2311yescharacteristic
112C2×C42×C13C2311yescharacteristic
113C13×#107—41no—
114C13×#107—41no—
115C13×C4⋊C8—41no—
116C13×C4⋊C8—41no—
117C13×#103—41no—
118C13×#103—41no—
119C13×#103—41no—
120C13×#102—41no—
121C13×#102—41no—
122C13×#102—41no—
123C13×#102—41no—
124C13×#102—41no—
125C13×C22⋊C8—41no—
126C13×C22⋊C8—41no—
127C13×#95—21no—
128C13×#95—21no—
129C13×#95—21no—
130C13×#95—21no—
131C13×#95—21no—
132#32735C1311yesmaximal, characteristic, direct product factor, Sylow
133C24×C13—21no—
134C24×C13—21no—
135C24×C13C2×D411yescharacteristic
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×D4×C13—21no—
143C2×D4×C13—21no—
144C2×D4×C13—21no—
145C2×D4×C13—21no—
146C2×D4×C13—21no—
147C2×D4×C13—21no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13—42no—
155C2×D4×C13—42no—
156C2×D4×C13—81no—
157C2×D4×C13—81no—
158C2×D4×C13—81no—
159C2×D4×C13—81no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2411yescharacteristic
178C13×SD16—44no—
179C13×D8—44no—
180C2×C8×C13—21no—
181C2×C8×C13—21no—
182C2×C8×C13—21no—
183C2×C8×C13—21no—
184C2×C8×C13—21no—
185C2×C8×C13—21no—
186C2×C8×C13—21no—
187C2×C8×C13—21no—
188C2×C8×C13—21no—
189C2×C8×C13—21no—
190C2×C8×C13—21no—
191C2×C8×C13—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4—21no—
197C13×C4⋊C4—21no—
198C13×C4⋊C4—21no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—41no—
203C13×C4⋊C4—41no—
204C13×C4⋊C4—42no—
205C13×C4⋊C4—81no—
206C13×C4⋊C4—81no—
207C13×C4⋊C4—81no—
208C13×C4⋊C4—81no—
209C13×C22⋊C4—41no—
210C13×C22⋊C4—41no—
211C13×C22⋊C4—42no—
212C13×C22⋊C4—42no—
213C13×C22⋊C4—42no—
214C13×C22⋊C4—42no—
215C13×C22⋊C4—42no—
216C13×C22⋊C4—81no—
217C13×C22⋊C4—81no—
218C13×C22⋊C4—81no—
219C13×C22⋊C4—81no—
220C13×C22⋊C4—81no—
221C13×C22⋊C4—81no—
222C13×C22⋊C4—81no—
223C42×C13—21no—
224C42×C13—21no—
225C42×C13—21no—
226C42×C13—21no—
227#2624C2×C1311yescharacteristic, complemented
228#2620C2×C1311yescharacteristic, complemented
229#2100C2×C1311yescharacteristic, complemented
230#2093C2×C1311yescharacteristic, complemented
231#2068C2×C1311yescharacteristic, complemented
232#2067C2×C1311yescharacteristic, complemented
233#2055C2×C1311yescharacteristic, complemented
234#2054C2×C1311yescharacteristic, complemented
235#2042C2×C1311yescharacteristic, complemented
236#2036C2×C1311yescharacteristic, complemented
237#2033C2×C1311yescharacteristic, complemented
238#2012C2×C1311yescharacteristic, complemented
239#2000C2×C1311yescharacteristic, complemented
240#1999C2×C1311yescharacteristic
241#1798C2×C1311yescharacteristic, complemented
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13—21no—
248C23×C13—21no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13—41no—
257C23×C13—41no—
258C23×C13—41no—
259C23×C13—41no—
260C23×C13—41no—
261C23×C13—41no—
262C23×C13—41no—
263C23×C13C22×D411yescharacteristic
264Q8×C13—41no—
265Q8×C13—41no—
266Q8×C13—41no—
267Q8×C13—41no—
268D4×C13—41no—
269D4×C13—41no—
270D4×C13—41no—
271D4×C13—41no—
272D4×C13—41no—
273D4×C13—41no—
274D4×C13—41no—
275D4×C13—41no—
276D4×C13—84no—
277D4×C13—84no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13H(5,𝔽2)11yescharacteristic
316C2×C4×C13H(5,𝔽2)11yescharacteristic
317C2×C4×C13H(5,𝔽2)11yescharacteristic
318C2×C4×C13H(5,𝔽2)11yescharacteristic
319C2×C4×C13H(5,𝔽2)11yescharacteristic
320C2×C4×C132−1+411yescharacteristic
321C8×C13—41no—
322C8×C13—41no—
323C8×C13—41no—
324C8×C13—41no—
325C22×SD16C22×C1311yescharacteristic
326C22×D8C22×C1311yescharacteristic
327C2×#124C22×C1311yescharacteristic
328C2×C22⋊Q8C22×C1311yescharacteristic
329C2×#121C22×C1311yescharacteristic
330C2×#121C22×C1311yescharacteristic
331C2×#117C22×C1311yescharacteristic
332C2×#107C22×C1311yescharacteristic
333C2×#107C22×C1311yescharacteristic
334C2×C4⋊C8C22×C1311yescharacteristic
335C2×C4⋊C8C22×C1311yescharacteristic
336C2×#103C22×C1311yescharacteristic
337C2×#103C22×C1311yescharacteristic
338C2×#103C22×C1311yescharacteristic
339C2×#102C22×C1311yescharacteristic
340C2×#102C22×C1311yescharacteristic
341C2×#102C22×C1311yescharacteristic
342C2×#102C22×C1311yescharacteristic
343C2×#102C22×C1311yescharacteristic
344C2×C22⋊C8C22×C1311yescharacteristic
345C2×C22⋊C8C22×C1311yescharacteristic
346#399—21no—
347#397—21no—
348#396—21no—
349#396—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#391C22×C1311yescharacteristic
355#390C22×C1311yescharacteristic
356#390C22×C1311yescharacteristic
357#390C22×C1311yescharacteristic
358#389C22×C1311yescharacteristic
359#389C22×C1311yescharacteristic
360#384C22×C1311yescharacteristic
361#380C22×C1311yescharacteristic
362#340C22×C1311yescharacteristic
363#340C22×C1311yescharacteristic
364#340C22×C1311yescharacteristic
365#340C22×C1311yescharacteristic
366#336C22×C1311yescharacteristic
367#336C22×C1311yescharacteristic
368C22×C13—41no—
369C22×C13—41no—
370C22×C13—41no—
371C22×C13—41no—
372C22×C13—41no—
373C22×C13—41no—
374C22×C13—41no—
375C22×C13—81no—
376C22×C13—81no—
377C22×C13—81no—
378C22×C13—81no—
379C22×C13—81no—
380C22×C13—81no—
381C22×C13—81no—
382C22×C13—81no—
383C22×C13—81no—
384C22×C13—81no—
385C22×C13—81no—
386C22×C13—81no—
387C22×C13—81no—
388C22×C13—81no—
389C22×C13#53411yescharacteristic
390C22×C13#53511yescharacteristic
391C22×C13#53711yescharacteristic
392C22×C13#57611yescharacteristic
393C22×C13#57611yescharacteristic
394C22×C13#57711yescharacteristic
395C22×C13#57811yescharacteristic
396C4×C13—41no—
397C4×C13—41no—
398C4×C13—41no—
399C4×C13—41no—
400C4×C13—41no—
401C4×C13—81no—
402C4×C13—81no—
403C4×C13—81no—
404C4×C13—81no—
405C4×C13—81no—
406C4×C13—81no—
407C4×C13#56011yescharacteristic
408C4×C13#56011yescharacteristic
409C4×C13#56211yescharacteristic
410C4×C13#56211yescharacteristic
411C22×Q8C23×C1311yescharacteristic
412C22×D4—21no—
413C22×D4—21no—
414C22×D4C23×C1311yescharacteristic
415C22×D4C23×C1311yescharacteristic
416C23×C4C23×C1311yescharacteristic
417C2×SD16—41no—
418C2×SD16—41no—
419C2×SD16—41no—
420C2×D8—41no—
421C2×D8—41no—
422C2×D8—41no—
423C22×C8C23×C1311yescharacteristic
424C22×C8C23×C1311yescharacteristic
425C22×C8C23×C1311yescharacteristic
426C22×C8C23×C1311yescharacteristic
427#124—41no—
428#124—41no—
429C22⋊Q8—41no—
430C22⋊Q8—41no—
431#121—41no—
432#121—41no—
433#121—41no—
434#121—41no—
435#117—41no—
436#117—41no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4D4×C1311yescharacteristic
443C2×C4⋊C4D4×C1311yescharacteristic
444C2×C4⋊C4C23×C1311yescharacteristic
445C2×C4⋊C4C23×C1311yescharacteristic
446C2×C4⋊C4C23×C1311yescharacteristic
447C2×C4⋊C4C23×C1311yescharacteristic
448C2×C4⋊C4C23×C1311yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4D4×C1311yescharacteristic
462C2×C22⋊C4D4×C1311yescharacteristic
463C2×C42C23×C1311yescharacteristic
464C2×C42C23×C1311yescharacteristic
465#107—41no—
466#107—41no—
467C4⋊C8—41no—
468C4⋊C8—41no—
469#103—41no—
470#103—41no—
471#103—41no—
472#102—41no—
473#102—41no—
474#102—41no—
475#102—41no—
476#102—41no—
477C22⋊C8—41no—
478C22⋊C8—41no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484C2×C13—81no—
485C2×C13—161no—
486C2×C13—161no—
487C2×C13#281311yescharacteristic
488C2×C13#319811yescharacteristic
489C2×C13#320311yescharacteristic
490C2×C13#322011yescharacteristic
491C2×C13#322511yescharacteristic
492C2×C13#325711yescharacteristic
493C2×C13#326211yescharacteristic
494C24—21no—
495C24—21no—
496C24C2×D4×C1311yescharacteristic
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—81no—
518C2×D4—81no—
519C2×D4—81no—
520C2×D4—81no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4C2×D4×C1311yescharacteristic
534C22×C4C2×D4×C1311yescharacteristic
535C22×C4C2×D4×C1311yescharacteristic
536C22×C4C2×D4×C1311yescharacteristic
537C22×C4C2×D4×C1311yescharacteristic
538C22×C4C24×C1311yescharacteristic
539SD16—44no—
540D8—44no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—42no—
566C4⋊C4—81no—
567C4⋊C4—81no—
568C4⋊C4—81no—
569C4⋊C4—81no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—81no—
578C22⋊C4—81no—
579C22⋊C4—81no—
580C22⋊C4—81no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C13#3273511yescharacteristic, direct product factor, Sylow
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C22×D4×C1311yescharacteristic
611Q8—41no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—84no—
624D4—84no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4C13×H(5,𝔽2)11yescharacteristic
663C2×C4C13×H(5,𝔽2)11yescharacteristic
664C2×C4C13×H(5,𝔽2)11yescharacteristic
665C2×C4C13×H(5,𝔽2)11yescharacteristic
666C2×C4C13×H(5,𝔽2)11yescharacteristic
667C2×C4C13×2−1+411yescharacteristic
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22C13×#53411yescharacteristic
694C22C13×#53511yescharacteristic
695C22C13×#53711yescharacteristic
696C22C13×#57611yescharacteristic
697C22C13×#57611yescharacteristic
698C22C13×#57711yescharacteristic
699C22C13×#57811yescharacteristic
700C4—41no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4C13×#56011yescharacteristic
712C4C13×#56011yescharacteristic
713C4C13×#56211yescharacteristic
714C4C13×#56211yescharacteristic
715C2—81no—
716C2—161no—
717C2—161no—
718C2C13×#281311yescharacteristic
719C2C13×#319811yescharacteristic
720C2C13×#320311yescharacteristic
721C2C13×#322011yescharacteristic
722C2C13×#322511yescharacteristic
723C2C13×#325711yescharacteristic
724C2C13×#326211yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C13×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2624C2semidirect
2. C13×#2620C2semidirect
3. C13×#2100C2semidirect
4. C13×#2093C2semidirect
5. C13×#2068C2semidirect
6. C13×#2067C2semidirect
7. C13×#2055C2semidirect
8. C13×#2054C2semidirect
9. C13×#2042C2semidirect
10. C13×#2036C2semidirect
11. C13×#2033C2semidirect
12. C13×#2012C2semidirect
13. C13×#2000C2semidirect
15. C13×#1798C2semidirect
132. #32735C13direct (N × H)
227. #2624C2×C13semidirect
228. #2620C2×C13semidirect
229. #2100C2×C13semidirect
230. #2093C2×C13semidirect
231. #2068C2×C13semidirect
232. #2067C2×C13semidirect
233. #2055C2×C13semidirect
234. #2054C2×C13semidirect
235. #2042C2×C13semidirect
236. #2036C2×C13semidirect
237. #2033C2×C13semidirect
238. #2012C2×C13semidirect
239. #2000C2×C13semidirect
241. #1798C2×C13semidirect
588. C13#32735direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26242
C13×#26202
C13×#21002
C13×#20932
C13×#20682
C13×#20672
C13×#20552
C13×#20542
C13×#20422
C13×#20362
C13×#20332
C13×#20122
C13×#20002
C13×#19992
C13×#17982
#3273513