Finite Group Databasebeta

← C13×#29418 #15715757

Subgroups — C13×#29418 #15715757

Order 3328.

836 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2324C211yesmaximal, characteristic, complemented
2C13×#2324C211yesmaximal, characteristic, complemented
3C13×#2077C211yesmaximal, characteristic, complemented
4C13×#2034C211yesmaximal, characteristic, complemented
5C13×#2033C211yesmaximal, characteristic, complemented
6C13×#1999C211yesmaximal, characteristic
7C13×#1926C211yesmaximal, characteristic, complemented
8C13×#1925C211yesmaximal, characteristic, complemented
9C13×#1919C211yesmaximal, characteristic, complemented
10C13×#1918C211yesmaximal, characteristic, complemented
11C13×#1879C211yesmaximal, characteristic, complemented
12C13×#1879C211yesmaximal, characteristic, complemented
13C13×#1864C211yesmaximal, characteristic, complemented
14C13×#1864C211yesmaximal, characteristic, complemented
15C13×#1818C211yesmaximal, characteristic, complemented
16C22×C13×D8C2211yescharacteristic
17C2×C13×#121C2211yescharacteristic
18C2×C13×#121C2211yescharacteristic
19C2×C4×D4×C13C2211yescharacteristic
20C2×C4×D4×C13C2211yescharacteristic
21C2×C13×#117C2211yescharacteristic
22C2×C13×#107C2211yescharacteristic
23C2×C13×#106C2211yescharacteristic
24C2×C13×#106C2211yescharacteristic
25C2×C13×#102C2211yescharacteristic
26C2×C13×#102C2211yescharacteristic
27C2×C13×#102C2211yescharacteristic
28C2×C13×#102C2211yescharacteristic
29C2×C13×#102C2211yescharacteristic
30C2×C13×#102C2211yescharacteristic
31C2×C13×C22⋊C8C2211yescharacteristic
32C2×C13×C22⋊C8C2211yescharacteristic
33C13×#390—21no—
34C13×#390—21no—
35C13×#390C2211yescharacteristic
36C13×#390C2211yescharacteristic
37C13×#389C2211yescharacteristic
38C13×#389C2211yescharacteristic
39C13×#388—21no—
40C13×#388—21no—
41C13×#386—21no—
42C13×#386—21no—
43C13×#385—21no—
44C13×#385—21no—
45C13×#380C2211yescharacteristic
46C13×#380C2211yescharacteristic
47C4×C13×C4⋊C4C2211yescharacteristic
48C4×C13×C4⋊C4C2211yescharacteristic
49C13×#340C2211yescharacteristic
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54C13×#340C2211yescharacteristic
55C13×#336C2211yescharacteristic
56C13×#336C2211yescharacteristic
57C13×#336C2211yescharacteristic
58C13×#336C2211yescharacteristic
59C22×D4×C13—21no—
60C22×D4×C13—21no—
61C22×D4×C13C2311yescharacteristic
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13—21no—
65C23×C4×C13C2311yescharacteristic
66C2×C13×D8—22no—
67C2×C13×D8—22no—
68C2×C13×D8—41no—
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C13×#121—22no—
74C13×#121—22no—
75C13×#121—22no—
76C13×#121—22no—
77C4×D4×C13—41no—
78C4×D4×C13—41no—
79C4×D4×C13—41no—
80C4×D4×C13—41no—
81C13×#117—41no—
82C13×#117—41no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—21no—
85C2×C13×C4⋊C4D411yescharacteristic
86C2×C13×C4⋊C4D411yescharacteristic
87C2×C13×C4⋊C4C2311yescharacteristic
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C4⋊C4C2311yescharacteristic
91C2×C13×C4⋊C4C2311yescharacteristic
92C2×C13×C4⋊C4C2311yescharacteristic
93C2×C13×C22⋊C4—21no—
94C2×C13×C22⋊C4—21no—
95C2×C13×C22⋊C4—21no—
96C2×C13×C22⋊C4—21no—
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⋊C4D411yescharacteristic
104C2×C13×C22⋊C4D411yescharacteristic
105C2×C42×C13—21no—
106C2×C42×C13—21no—
107C2×C42×C13C2311yescharacteristic
108C2×C42×C13C2311yescharacteristic
109C13×#107—22no—
110C13×#106—22no—
111C13×#106—41no—
112C13×#102—22no—
113C13×#102—22no—
114C13×#102—22no—
115C13×#102—22no—
116C13×#102—41no—
117C13×#102—41no—
118C13×C22⋊C8—41no—
119C13×C22⋊C8—41no—
120C13×#95—21no—
121C13×#95—21no—
122C13×#95—21no—
123C13×#95—21no—
124C13×#95—21no—
125C13×#95—21no—
126#29418C1311yesmaximal, characteristic, direct product factor, Sylow
127C24×C13—21no—
128C24×C13—21no—
129C24×C13C2×D411yescharacteristic
130C2×D4×C13—24no—
131C2×D4×C13—24no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13—21no—
141C2×D4×C13—21no—
142C2×D4×C13—81no—
143C2×D4×C13—81no—
144C2×D4×C13—81no—
145C2×D4×C13—81no—
146C2×D4×C13#4112yes—
147C2×D4×C13#4112yes—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—42no—
161C22×C4×C13—42no—
162C22×C4×C13—81no—
163C22×C4×C13—81no—
164C22×C4×C13—81no—
165C22×C4×C13—81no—
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2411yescharacteristic
172C13×D8—44no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—21no—
180C2×C8×C13—21no—
181C2×C8×C13—21no—
182C2×C8×C13—21no—
183C2×C8×C13—21no—
184C2×C8×C13—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—41no—
196C13×C4⋊C4—41no—
197C13×C4⋊C4—81no—
198C13×C4⋊C4—81no—
199C13×C4⋊C4#4112yes—
200C13×C4⋊C4#4112yes—
201C13×C22⋊C4—24no—
202C13×C22⋊C4—24no—
203C13×C22⋊C4—41no—
204C13×C22⋊C4—41no—
205C13×C22⋊C4—42no—
206C13×C22⋊C4—42no—
207C13×C22⋊C4—81no—
208C13×C22⋊C4—81no—
209C13×C22⋊C4—81no—
210C13×C22⋊C4—81no—
211C13×C22⋊C4—81no—
212C13×C22⋊C4—81no—
213C42×C13—21no—
214C42×C13—21no—
215C42×C13—21no—
216C42×C13—21no—
217C42×C13—81no—
218C42×C13—81no—
219#2324C2×C1311yescharacteristic, complemented
220#2324C2×C1311yescharacteristic, complemented
221#2077C2×C1311yescharacteristic, complemented
222#2034C2×C1311yescharacteristic, complemented
223#2033C2×C1311yescharacteristic, complemented
224#1999C2×C1311yescharacteristic
225#1926C2×C1311yescharacteristic, complemented
226#1925C2×C1311yescharacteristic, complemented
227#1919C2×C1311yescharacteristic, complemented
228#1918C2×C1311yescharacteristic, complemented
229#1879C2×C1311yescharacteristic, complemented
230#1879C2×C1311yescharacteristic, complemented
231#1864C2×C1311yescharacteristic, complemented
232#1864C2×C1311yescharacteristic, complemented
233#1818C2×C1311yescharacteristic, complemented
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13C22×D411yescharacteristic
256D4×C13—22no—
257D4×C13—22no—
258D4×C13—22no—
259D4×C13—22no—
260D4×C13—41no—
261D4×C13—41no—
262D4×C13—41no—
263D4×C13—41no—
264D4×C13—84no—
265D4×C13—84no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
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—84no—
304C2×C4×C13—84no—
305C2×C4×C13C2×#4111yescharacteristic
306C2×C4×C13C2×#4111yescharacteristic
307C2×C4×C13C2×#4111yescharacteristic
308C2×C4×C13C2×#4111yescharacteristic
309C2×C4×C13H(5,𝔽2)11yescharacteristic
310C2×C4×C13H(5,𝔽2)11yescharacteristic
311C8×C13—41no—
312C8×C13—41no—
313C8×C13—41no—
314C8×C13—41no—
315C22×D8C22×C1311yescharacteristic
316C2×#121C22×C1311yescharacteristic
317C2×#121C22×C1311yescharacteristic
318C2×C4×D4C22×C1311yescharacteristic
319C2×C4×D4C22×C1311yescharacteristic
320C2×#117C22×C1311yescharacteristic
321C2×#107C22×C1311yescharacteristic
322C2×#106C22×C1311yescharacteristic
323C2×#106C22×C1311yescharacteristic
324C2×#102C22×C1311yescharacteristic
325C2×#102C22×C1311yescharacteristic
326C2×#102C22×C1311yescharacteristic
327C2×#102C22×C1311yescharacteristic
328C2×#102C22×C1311yescharacteristic
329C2×#102C22×C1311yescharacteristic
330C2×C22⋊C8C22×C1311yescharacteristic
331C2×C22⋊C8C22×C1311yescharacteristic
332#390—21no—
333#390—21no—
334#390C22×C1311yescharacteristic
335#390C22×C1311yescharacteristic
336#389C22×C1311yescharacteristic
337#389C22×C1311yescharacteristic
338#388—21no—
339#388—21no—
340#386—21no—
341#386—21no—
342#385—21no—
343#385—21no—
344#380C22×C1311yescharacteristic
345#380C22×C1311yescharacteristic
346C4×C4⋊C4C22×C1311yescharacteristic
347C4×C4⋊C4C22×C1311yescharacteristic
348#340C22×C1311yescharacteristic
349#340C22×C1311yescharacteristic
350#340C22×C1311yescharacteristic
351#340C22×C1311yescharacteristic
352#340C22×C1311yescharacteristic
353#340C22×C1311yescharacteristic
354#336C22×C1311yescharacteristic
355#336C22×C1311yescharacteristic
356#336C22×C1311yescharacteristic
357#336C22×C1311yescharacteristic
358C22×C13—41no—
359C22×C13—42no—
360C22×C13—42no—
361C22×C13—41no—
362C22×C13—42no—
363C22×C13—41no—
364C22×C13—42no—
365C22×C13—41no—
366C22×C13—42no—
367C22×C13—41no—
368C22×C13—42no—
369C22×C13—41no—
370C22×C13—41no—
371C22×C13—81no—
372C22×C13—81no—
373C22×C13—81no—
374C22×C13—81no—
375C22×C13—81no—
376C22×C13—81no—
377C22×C13—81no—
378C22×C13—81no—
379C22×C13#52511yescharacteristic
380C22×C13#52511yescharacteristic
381C22×C13#53411yescharacteristic
382C22×C13#57611yescharacteristic
383C22×C13#57611yescharacteristic
384C22×C13#57711yescharacteristic
385C22×C13#57711yescharacteristic
386C4×C13—41no—
387C4×C13—42no—
388C4×C13—42no—
389C4×C13—41no—
390C4×C13—41no—
391C4×C13—41no—
392C4×C13—41no—
393C4×C13—81no—
394C4×C13—81no—
395C4×C13—81no—
396C4×C13—81no—
397C4×C13#55111yescharacteristic
398C4×C13#55311yescharacteristic
399C4×C13#55311yescharacteristic
400C4×C13#55911yescharacteristic
401C22×D4—21no—
402C22×D4—21no—
403C22×D4C23×C1311yescharacteristic
404C22×D4C23×C1311yescharacteristic
405C23×C4—21no—
406C23×C4—21no—
407C23×C4C23×C1311yescharacteristic
408C2×D8—22no—
409C2×D8—22no—
410C2×D8—41no—
411C22×C8C23×C1311yescharacteristic
412C22×C8C23×C1311yescharacteristic
413C22×C8C23×C1311yescharacteristic
414C22×C8C23×C1311yescharacteristic
415#121—22no—
416#121—22no—
417#121—22no—
418#121—22no—
419C4×D4—41no—
420C4×D4—41no—
421C4×D4—41no—
422C4×D4—41no—
423#117—41no—
424#117—41no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4D4×C1311yescharacteristic
428C2×C4⋊C4D4×C1311yescharacteristic
429C2×C4⋊C4C23×C1311yescharacteristic
430C2×C4⋊C4C23×C1311yescharacteristic
431C2×C4⋊C4C23×C1311yescharacteristic
432C2×C4⋊C4C23×C1311yescharacteristic
433C2×C4⋊C4C23×C1311yescharacteristic
434C2×C4⋊C4C23×C1311yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4D4×C1311yescharacteristic
446C2×C22⋊C4D4×C1311yescharacteristic
447C2×C42—21no—
448C2×C42—21no—
449C2×C42C23×C1311yescharacteristic
450C2×C42C23×C1311yescharacteristic
451#107—22no—
452#106—22no—
453#106—41no—
454#102—22no—
455#102—22no—
456#102—22no—
457#102—22no—
458#102—41no—
459#102—41no—
460C22⋊C8—41no—
461C22⋊C8—41no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468C2×C13—81no—
469C2×C13—82no—
470C2×C13—82no—
471C2×C13#260011yescharacteristic
472C2×C13#311811yescharacteristic
473C2×C13#311911yescharacteristic
474C2×C13#312211yescharacteristic
475C2×C13#312511yescharacteristic
476C2×C13#319811yescharacteristic
477C2×C13#319811yescharacteristic
478C24—21no—
479C24—21no—
480C24C2×D4×C1311yescharacteristic
481C2×D4—24no—
482C2×D4—24no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—81no—
494C2×D4—81no—
495C2×D4—81no—
496C2×D4—81no—
497C2×D4C13×#4112yes—
498C2×D4C13×#4112yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—81no—
514C22×C4—81no—
515C22×C4—81no—
516C22×C4—81no—
517C22×C4C2×D4×C1311yescharacteristic
518C22×C4C2×D4×C1311yescharacteristic
519C22×C4C2×D4×C1311yescharacteristic
520C22×C4C2×D4×C1311yescharacteristic
521C22×C4C2×D4×C1311yescharacteristic
522C22×C4C24×C1311yescharacteristic
523D8—44no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—81no—
549C4⋊C4—81no—
550C4⋊C4C13×#4112yes—
551C4⋊C4C13×#4112yes—
552C22⋊C4—24no—
553C22⋊C4—24no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—81no—
569C42—81no—
570C13#2941811yescharacteristic, direct product factor, Sylow
571C23—22no—
572C23—22no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23C22×D4×C1311yescharacteristic
593D4—22no—
594D4—22no—
595D4—22no—
596D4—22no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—84no—
602D4—84no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—84no—
641C2×C4—84no—
642C2×C4C2×C13×#4111yescharacteristic
643C2×C4C2×C13×#4111yescharacteristic
644C2×C4C2×C13×#4111yescharacteristic
645C2×C4C2×C13×#4111yescharacteristic
646C2×C4C13×H(5,𝔽2)11yescharacteristic
647C2×C4C13×H(5,𝔽2)11yescharacteristic
648C8—41no—
649C8—41no—
650C8—41no—
651C8—41no—
652C22—41no—
653C22—42no—
654C22—42no—
655C22—41no—
656C22—42no—
657C22—41no—
658C22—42no—
659C22—41no—
660C22—42no—
661C22—41no—
662C22—42no—
663C22—41no—
664C22—41no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22C13×#52511yescharacteristic
674C22C13×#52511yescharacteristic
675C22C13×#53411yescharacteristic
676C22C13×#57611yescharacteristic
677C22C13×#57611yescharacteristic
678C22C13×#57711yescharacteristic
679C22C13×#57711yescharacteristic
680C4—41no—
681C4—42no—
682C4—42no—
683C4—41no—
684C4—41no—
685C4—41no—
686C4—41no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4C13×#55111yescharacteristic
692C4C13×#55311yescharacteristic
693C4C13×#55311yescharacteristic
694C4C13×#55911yescharacteristic
695C2—81no—
696C2—82no—
697C2—82no—
698C2C13×#260011yescharacteristic
699C2C13×#311811yescharacteristic
700C2C13×#311911yescharacteristic
701C2C13×#312211yescharacteristic
702C2C13×#312511yescharacteristic
703C2C13×#319811yescharacteristic
704C2C13×#319811yescharacteristic
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×#2324C2semidirect
2. C13×#2324C2semidirect
3. C13×#2077C2semidirect
4. C13×#2034C2semidirect
5. C13×#2033C2semidirect
7. C13×#1926C2semidirect
8. C13×#1925C2semidirect
9. C13×#1919C2semidirect
10. C13×#1918C2semidirect
11. C13×#1879C2semidirect
12. C13×#1879C2semidirect
13. C13×#1864C2semidirect
14. C13×#1864C2semidirect
15. C13×#1818C2semidirect
126. #29418C13direct (N × H)
219. #2324C2×C13semidirect
220. #2324C2×C13semidirect
221. #2077C2×C13semidirect
222. #2034C2×C13semidirect
223. #2033C2×C13semidirect
225. #1926C2×C13semidirect
226. #1925C2×C13semidirect
227. #1919C2×C13semidirect
228. #1918C2×C13semidirect
229. #1879C2×C13semidirect
230. #1879C2×C13semidirect
231. #1864C2×C13semidirect
232. #1864C2×C13semidirect
233. #1818C2×C13semidirect
570. C13#29418direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23242
C13×#20772
C13×#20342
C13×#20332
C13×#19992
C13×#19262
C13×#19252
C13×#19192
C13×#19182
C13×#18792
C13×#18642
C13×#18182
#2941813