Finite Group Databasebeta

← C13×#15376 #15701715

Subgroups — C13×#15376 #15701715

Order 3328.

2370 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#394C211yesmaximal, characteristic, complemented
2C2×C13×#392C211yesmaximal, characteristic
3C2×C13×#386C211yesmaximal, characteristic, complemented
4C2×C13×#386C211yesmaximal, characteristic, complemented
5C2×C13×#386C211yesmaximal, characteristic, complemented
6C2×C13×#386C211yesmaximal, characteristic, complemented
7C2×C13×#385C211yesmaximal, characteristic, complemented
8C2×C13×#380C211yesmaximal, characteristic, complemented
9C13×#1443C211yesmaximal, characteristic, complemented
10C13×#1442C211yesmaximal, characteristic, complemented
11C13×#1440C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic, complemented
13C13×#1439C211yesmaximal, characteristic, complemented
14C13×#1439C211yesmaximal, characteristic, complemented
15C13×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C24×C4×C13C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C13×C22⋊C4C2211yescharacteristic
33C22×C13×C22⋊C4C2211yescharacteristic
34C22×C13×C22⋊C4C2211yescharacteristic
35C22×C13×C22⋊C4C2211yescharacteristic
36C22×C13×C22⋊C4C2211yescharacteristic
37C13×#394—24no—
38C13×#392—24no—
39C13×#386—24no—
40C13×#386—24no—
41C13×#386—24no—
42C13×#386—24no—
43C13×#385—24no—
44C13×#380—24no—
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C2×C13×#95C2211yescharacteristic
58C2×C13×#95C2211yescharacteristic
59C25×C13C2311yescharacteristic
60C25×C13C2311yescharacteristic
61C25×C13C2311yescharacteristic
62C22×D4×C13—22no—
63C22×D4×C13—22no—
64C22×D4×C13—22no—
65C22×D4×C13—22no—
66C22×D4×C13—22no—
67C22×D4×C13—22no—
68C22×D4×C13—22no—
69C22×D4×C13—22no—
70C22×D4×C13—22no—
71C22×D4×C13—22no—
72C22×D4×C13—22no—
73C22×D4×C13—22no—
74C22×D4×C13—22no—
75C22×D4×C13—22no—
76C22×D4×C13—41no—
77C22×D4×C13—41no—
78C22×D4×C13—41no—
79C22×D4×C13—41no—
80C22×D4×C13—41no—
81C22×D4×C13—41no—
82C22×D4×C13D414yes—
83C23×C4×C13—22no—
84C23×C4×C13—22no—
85C23×C4×C13—22no—
86C23×C4×C13—22no—
87C23×C4×C13—22no—
88C23×C4×C13—22no—
89C23×C4×C13—22no—
90C23×C4×C13—22no—
91C23×C4×C13—41no—
92C23×C4×C13—41no—
93C23×C4×C13—41no—
94C23×C4×C13—41no—
95C23×C4×C13—41no—
96C23×C4×C13—41no—
97C23×C4×C13C2311yescharacteristic
98C23×C4×C13C2311yescharacteristic
99C23×C4×C13C2311yescharacteristic
100C23×C4×C13C2311yescharacteristic
101C23×C4×C13C2311yescharacteristic
102C23×C4×C13C2311yescharacteristic
103C23×C4×C13C2311yescharacteristic
104C23×C4×C13C2311yescharacteristic
105C23×C4×C13C2311yescharacteristic
106C23×C4×C13C2311yescharacteristic
107C23×C4×C13C2311yescharacteristic
108C23×C4×C13C2311yescharacteristic
109C2×C13×C4⋊C4—22no—
110C2×C13×C4⋊C4—22no—
111C2×C13×C4⋊C4—22no—
112C2×C13×C4⋊C4—22no—
113C2×C13×C4⋊C4—22no—
114C2×C13×C4⋊C4—41no—
115C2×C13×C4⋊C4—41no—
116C2×C13×C4⋊C4—41no—
117C2×C13×C4⋊C4—41no—
118C2×C13×C22⋊C4—22no—
119C2×C13×C22⋊C4—22no—
120C2×C13×C22⋊C4—22no—
121C2×C13×C22⋊C4—22no—
122C2×C13×C22⋊C4—22no—
123C2×C13×C22⋊C4—22no—
124C2×C13×C22⋊C4—22no—
125C2×C13×C22⋊C4—22no—
126C2×C13×C22⋊C4—22no—
127C2×C13×C22⋊C4—22no—
128C2×C13×C22⋊C4—22no—
129C2×C13×C22⋊C4—22no—
130C2×C13×C22⋊C4—22no—
131C2×C13×C22⋊C4—22no—
132C2×C13×C22⋊C4—22no—
133C2×C13×C22⋊C4—22no—
134C2×C13×C22⋊C4—22no—
135C2×C13×C22⋊C4—22no—
136C2×C13×C22⋊C4—22no—
137C2×C13×C22⋊C4—22no—
138C2×C13×C22⋊C4—22no—
139C2×C13×C22⋊C4—22no—
140C2×C13×C22⋊C4—22no—
141C2×C13×C22⋊C4—22no—
142C2×C13×C22⋊C4—22no—
143C2×C13×C22⋊C4—22no—
144C2×C13×C22⋊C4—41no—
145C2×C13×C22⋊C4—41no—
146C2×C13×C22⋊C4—41no—
147C2×C13×C22⋊C4—41no—
148C2×C13×C22⋊C4—41no—
149C2×C13×C22⋊C4—41no—
150C2×C13×C22⋊C4—41no—
151C2×C13×C22⋊C4—41no—
152C2×C13×C22⋊C4—41no—
153C2×C13×C22⋊C4—41no—
154C2×C13×C22⋊C4—41no—
155C2×C13×C22⋊C4—41no—
156C2×C13×C22⋊C4D414yescomplemented
157C13×#95—22no—
158C13×#95—22no—
159C13×#95—22no—
160C13×#95—22no—
161C13×#95—22no—
162C13×#95—22no—
163C13×#95—22no—
164C13×#95—22no—
165C13×#95—22no—
166C13×#95—22no—
167C13×#95—41no—
168C13×#95—41no—
169C13×#95D414yescomplemented
170C13×#95D414yescomplemented
171#15376C1311yesmaximal, characteristic, direct product factor, Sylow
172C24×C13—21no—
173C24×C13—21no—
174C24×C13—21no—
175C24×C13—21no—
176C24×C13—21no—
177C24×C13—21no—
178C24×C13—21no—
179C24×C13—21no—
180C24×C13—21no—
181C24×C13—21no—
182C24×C13—21no—
183C24×C13—21no—
184C24×C13—21no—
185C24×C13—21no—
186C24×C13—21no—
187C24×C13—21no—
188C24×C13—21no—
189C24×C13—21no—
190C24×C13—21no—
191C24×C13—21no—
192C24×C13—21no—
193C24×C13—21no—
194C24×C13—21no—
195C24×C13—21no—
196C24×C13—21no—
197C24×C13—21no—
198C24×C13—21no—
199C24×C13—21no—
200C24×C13—21no—
201C24×C13—21no—
202C24×C13—21no—
203C24×C13—21no—
204C24×C13—21no—
205C24×C13—21no—
206C24×C13—21no—
207C24×C13—21no—
208C24×C13—21no—
209C24×C13—21no—
210C24×C13C2×D412yes—
211C24×C13C2×D412yes—
212C24×C13C2×D412yes—
213C24×C13#4112yes—
214C24×C13#4112yes—
215C24×C13#4112yes—
216C24×C13#4112yes—
217C24×C13C2411yescharacteristic
218C2×D4×C13—28no—
219C2×D4×C13—28no—
220C2×D4×C13—28no—
221C2×D4×C13—28no—
222C2×D4×C13—44no—
223C2×D4×C13—44no—
224C2×D4×C13—44no—
225C2×D4×C13—44no—
226C2×D4×C13—44no—
227C2×D4×C13—44no—
228C2×D4×C13—44no—
229C2×D4×C13—44no—
230C2×D4×C13—44no—
231C2×D4×C13—44no—
232C2×D4×C13—44no—
233C2×D4×C13—44no—
234C2×D4×C13—44no—
235C2×D4×C13—44no—
236C2×D4×C13—44no—
237C2×D4×C13—44no—
238C2×D4×C13—44no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—28no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×C13—21no—
253C22×C4×C13—21no—
254C22×C4×C13—21no—
255C22×C4×C13—21no—
256C22×C4×C13—21no—
257C22×C4×C13—21no—
258C22×C4×C13—21no—
259C22×C4×C13—21no—
260C22×C4×C13—21no—
261C22×C4×C13—21no—
262C22×C4×C13—21no—
263C22×C4×C13—21no—
264C22×C4×C13—21no—
265C22×C4×C13—21no—
266C22×C4×C13—21no—
267C22×C4×C13—21no—
268C22×C4×C13—21no—
269C22×C4×C13—21no—
270C22×C4×C13—21no—
271C22×C4×C13—21no—
272C22×C4×C13—21no—
273C22×C4×C13—21no—
274C22×C4×C13—21no—
275C22×C4×C13—21no—
276C22×C4×C13—21no—
277C22×C4×C13—21no—
278C22×C4×C13—21no—
279C22×C4×C13—21no—
280C22×C4×C13—21no—
281C22×C4×C13—21no—
282C22×C4×C13—21no—
283C22×C4×C13—21no—
284C22×C4×C13—21no—
285C22×C4×C13—21no—
286C22×C4×C13—21no—
287C22×C4×C13—21no—
288C22×C4×C13—21no—
289C22×C4×C13—21no—
290C22×C4×C13—21no—
291C22×C4×C13—21no—
292C22×C4×C13—21no—
293C22×C4×C13—21no—
294C22×C4×C13—21no—
295C22×C4×C13—21no—
296C22×C4×C13—21no—
297C22×C4×C13—21no—
298C22×C4×C13—21no—
299C22×C4×C13—21no—
300C22×C4×C13—21no—
301C22×C4×C13—21no—
302C22×C4×C13—21no—
303C22×C4×C13—21no—
304C22×C4×C13—21no—
305C22×C4×C13—21no—
306C22×C4×C13—21no—
307C22×C4×C13—21no—
308C22×C4×C13—21no—
309C22×C4×C13—21no—
310C22×C4×C13—21no—
311C22×C4×C13—21no—
312C22×C4×C13—21no—
313C22×C4×C13—21no—
314C22×C4×C13—44no—
315C22×C4×C13—44no—
316C22×C4×C13—44no—
317C22×C4×C13—44no—
318C22×C4×C13—44no—
319C22×C4×C13—44no—
320C22×C4×C13—44no—
321C22×C4×C13—44no—
322C22×C4×C13—44no—
323C22×C4×C13—44no—
324C22×C4×C13—44no—
325C22×C4×C13—44no—
326C22×C4×C13—44no—
327C22×C4×C13C2×D412yes—
328C22×C4×C13C2×D412yes—
329C22×C4×C13C2×D412yes—
330C22×C4×C13C2×D412yes—
331C22×C4×C13C2×D412yes—
332C22×C4×C13C2×D412yes—
333C22×C4×C13C2×D412yes—
334C22×C4×C13C2×D412yes—
335C22×C4×C13C2×D412yes—
336C22×C4×C13#4112yes—
337C13×C4⋊C4—44no—
338C13×C4⋊C4—44no—
339C13×C4⋊C4—44no—
340C13×C22⋊C4—28no—
341C13×C22⋊C4—44no—
342C13×C22⋊C4—44no—
343C13×C22⋊C4—44no—
344C13×C22⋊C4—44no—
345C13×C22⋊C4—44no—
346C13×C22⋊C4—44no—
347C13×C22⋊C4—44no—
348C13×C22⋊C4—44no—
349C13×C22⋊C4—44no—
350C13×C22⋊C4—44no—
351C13×C22⋊C4—44no—
352C13×C22⋊C4—44no—
353C2×#394C2×C1311yescharacteristic, complemented
354C2×#392C2×C1311yescharacteristic
355C2×#386C2×C1311yescharacteristic, complemented
356C2×#386C2×C1311yescharacteristic, complemented
357C2×#386C2×C1311yescharacteristic, complemented
358C2×#386C2×C1311yescharacteristic, complemented
359C2×#385C2×C1311yescharacteristic, complemented
360C2×#380C2×C1311yescharacteristic, complemented
361#1443C2×C1311yescharacteristic, complemented
362#1442C2×C1311yescharacteristic, complemented
363#1440C2×C1311yescharacteristic, complemented
364#1439C2×C1311yescharacteristic, complemented
365#1439C2×C1311yescharacteristic, complemented
366#1439C2×C1311yescharacteristic, complemented
367#1438C2×C1311yescharacteristic, complemented
368C23×C13—22no—
369C23×C13—22no—
370C23×C13—22no—
371C23×C13—22no—
372C23×C13—22no—
373C23×C13—22no—
374C23×C13—22no—
375C23×C13—22no—
376C23×C13—22no—
377C23×C13—22no—
378C23×C13—22no—
379C23×C13—22no—
380C23×C13—22no—
381C23×C13—22no—
382C23×C13—22no—
383C23×C13—22no—
384C23×C13—22no—
385C23×C13—22no—
386C23×C13—22no—
387C23×C13—22no—
388C23×C13—22no—
389C23×C13—22no—
390C23×C13—22no—
391C23×C13—22no—
392C23×C13—22no—
393C23×C13—22no—
394C23×C13—22no—
395C23×C13—22no—
396C23×C13—22no—
397C23×C13—22no—
398C23×C13—22no—
399C23×C13—22no—
400C23×C13—22no—
401C23×C13—22no—
402C23×C13—22no—
403C23×C13—22no—
404C23×C13—22no—
405C23×C13—22no—
406C23×C13—22no—
407C23×C13—22no—
408C23×C13—22no—
409C23×C13—22no—
410C23×C13—22no—
411C23×C13—41no—
412C23×C13—41no—
413C23×C13—41no—
414C23×C13—41no—
415C23×C13—41no—
416C23×C13—41no—
417C23×C13—41no—
418C23×C13—41no—
419C23×C13—41no—
420C23×C13—41no—
421C23×C13—41no—
422C23×C13—41no—
423C23×C13—41no—
424C23×C13—41no—
425C23×C13—41no—
426C23×C13—41no—
427C23×C13—41no—
428C23×C13—41no—
429C23×C13—41no—
430C23×C13—41no—
431C23×C13—41no—
432C23×C13—41no—
433C23×C13—41no—
434C23×C13—41no—
435C23×C13—41no—
436C23×C13—41no—
437C23×C13—41no—
438C23×C13—41no—
439C23×C13—41no—
440C23×C13—41no—
441C23×C13—41no—
442C23×C13—41no—
443C23×C13—41no—
444C23×C13—41no—
445C23×C13—41no—
446C23×C13—41no—
447C23×C13—41no—
448C23×C13—41no—
449C23×C13—41no—
450C23×C13—41no—
451C23×C13—41no—
452C23×C13—41no—
453C23×C13—41no—
454C23×C13—41no—
455C23×C13—41no—
456C23×C13—41no—
457C23×C13—41no—
458C23×C13—41no—
459C23×C13—41no—
460C23×C13—41no—
461C23×C13—41no—
462C23×C13—41no—
463C23×C13—41no—
464C23×C13—41no—
465C23×C13—41no—
466C23×C13—41no—
467C23×C13—41no—
468C23×C13—41no—
469C23×C13—41no—
470C23×C13—41no—
471C23×C13#12114yes—
472C23×C13#12314yes—
473C23×C13C22×D411yescharacteristic
474C23×C13C22×D411yescharacteristic
475C23×C13C22×D411yescharacteristic
476C23×C13C22×D411yescharacteristic
477C23×C13C2×#4111yescharacteristic
478C23×C13C2×#4111yescharacteristic
479C23×C13C2×#4111yescharacteristic
480C23×C13C2×#4111yescharacteristic
481C23×C13C2×#4111yescharacteristic
482C23×C13H(5,𝔽2)11yescharacteristic
483C23×C13H(5,𝔽2)11yescharacteristic
484C23×C13H(5,𝔽2)11yescharacteristic
485C23×C13H(5,𝔽2)11yescharacteristic
486C23×C13H(5,𝔽2)11yescharacteristic
487C23×C132−1+411yescharacteristic
488D4×C13—416no—
489D4×C13—416no—
490D4×C13—416no—
491C2×C4×C13—22no—
492C2×C4×C13—22no—
493C2×C4×C13—22no—
494C2×C4×C13—22no—
495C2×C4×C13—22no—
496C2×C4×C13—22no—
497C2×C4×C13—22no—
498C2×C4×C13—22no—
499C2×C4×C13—22no—
500C2×C4×C13—22no—
501C2×C4×C13—22no—
502C2×C4×C13—22no—
503C2×C4×C13—22no—
504C2×C4×C13—22no—
505C2×C4×C13—22no—
506C2×C4×C13—22no—
507C2×C4×C13—22no—
508C2×C4×C13—22no—
509C2×C4×C13—22no—
510C2×C4×C13—22no—
511C2×C4×C13—22no—
512C2×C4×C13—22no—
513C2×C4×C13—22no—
514C2×C4×C13—22no—
515C2×C4×C13—22no—
516C2×C4×C13—22no—
517C2×C4×C13—22no—
518C2×C4×C13—416no—
519C2×C4×C13—416no—
520C2×C4×C13—41no—
521C2×C4×C13—41no—
522C2×C4×C13—41no—
523C2×C4×C13—41no—
524C2×C4×C13—41no—
525C2×C4×C13—41no—
526C2×C4×C13—41no—
527C2×C4×C13—41no—
528C2×C4×C13—41no—
529C2×C4×C13—41no—
530C2×C4×C13—41no—
531C2×C4×C13—41no—
532C2×C4×C13—41no—
533C2×C4×C13—41no—
534C2×C4×C13—41no—
535C2×C4×C13—41no—
536C2×C4×C13—41no—
537C2×C4×C13—41no—
538C2×C4×C13—41no—
539C2×C4×C13—41no—
540C2×C4×C13—41no—
541C2×C4×C13—41no—
542C2×C4×C13—41no—
543C2×C4×C13—41no—
544C2×C4×C13—41no—
545C2×C4×C13—41no—
546C2×C4×C13—41no—
547C2×C4×C13—41no—
548C2×C4×C13—41no—
549C2×C4×C13—41no—
550C2×C4×C13—41no—
551C2×C4×C13—41no—
552C2×C4×C13—41no—
553C2×C4×C13—41no—
554C2×C4×C13—41no—
555C2×C4×C13—41no—
556C2×C4×C13—41no—
557C2×C4×C13—41no—
558C2×C4×C13—41no—
559C2×C4×C13—41no—
560C2×C4×C13—41no—
561C2×C4×C13—41no—
562C2×C4×C13—41no—
563C2×C4×C13—41no—
564C2×C4×C13—41no—
565C2×C4×C13—41no—
566C2×C4×C13—41no—
567C2×C4×C13—41no—
568C2×C4×C13—41no—
569C2×C4×C13—41no—
570C2×C4×C13—41no—
571C2×C4×C13—41no—
572C2×C4×C13—41no—
573C2×C4×C13—41no—
574C2×C4×C13—41no—
575C2×C4×C13—41no—
576C2×C4×C13#12114yes—
577C23×D4C22×C1311yescharacteristic
578C23×D4C22×C1311yescharacteristic
579C23×D4C22×C1311yescharacteristic
580C24×C4C22×C1311yescharacteristic
581C24×C4C22×C1311yescharacteristic
582C22×C4⋊C4C22×C1311yescharacteristic
583C22×C4⋊C4C22×C1311yescharacteristic
584C22×C4⋊C4C22×C1311yescharacteristic
585C22×C22⋊C4C22×C1311yescharacteristic
586C22×C22⋊C4C22×C1311yescharacteristic
587C22×C22⋊C4C22×C1311yescharacteristic
588C22×C22⋊C4C22×C1311yescharacteristic
589C22×C22⋊C4C22×C1311yescharacteristic
590C22×C22⋊C4C22×C1311yescharacteristic
591C22×C22⋊C4C22×C1311yescharacteristic
592C22×C22⋊C4C22×C1311yescharacteristic
593C22×C22⋊C4C22×C1311yescharacteristic
594C22×C22⋊C4C22×C1311yescharacteristic
595C22×C22⋊C4C22×C1311yescharacteristic
596C22×C22⋊C4C22×C1311yescharacteristic
597C22×C22⋊C4C22×C1311yescharacteristic
598#394—24no—
599#392—24no—
600#386—24no—
601#386—24no—
602#386—24no—
603#386—24no—
604#385—24no—
605#380—24no—
606C2×#95C22×C1311yescharacteristic
607C2×#95C22×C1311yescharacteristic
608C2×#95C22×C1311yescharacteristic
609C2×#95C22×C1311yescharacteristic
610C2×#95C22×C1311yescharacteristic
611C2×#95C22×C1311yescharacteristic
612C2×#95C22×C1311yescharacteristic
613C2×#95C22×C1311yescharacteristic
614C2×#95C22×C1311yescharacteristic
615C2×#95C22×C1311yescharacteristic
616C2×#95C22×C1311yescharacteristic
617C2×#95C22×C1311yescharacteristic
618C2×#95C22×C1311yescharacteristic
619C2×#95C22×C1311yescharacteristic
620C22×C13—24no—
621C22×C13—24no—
622C22×C13—24no—
623C22×C13—24no—
624C22×C13—24no—
625C22×C13—24no—
626C22×C13—42no—
627C22×C13—42no—
628C22×C13—42no—
629C22×C13—42no—
630C22×C13—42no—
631C22×C13—42no—
632C22×C13—42no—
633C22×C13—42no—
634C22×C13—42no—
635C22×C13—42no—
636C22×C13—42no—
637C22×C13—42no—
638C22×C13—42no—
639C22×C13—42no—
640C22×C13—42no—
641C22×C13—42no—
642C22×C13—42no—
643C22×C13—42no—
644C22×C13—42no—
645C22×C13—42no—
646C22×C13—42no—
647C22×C13—42no—
648C22×C13—42no—
649C22×C13—42no—
650C22×C13—42no—
651C22×C13—42no—
652C22×C13—42no—
653C22×C13—42no—
654C22×C13—42no—
655C22×C13—42no—
656C22×C13—42no—
657C22×C13—81no—
658C22×C13—81no—
659C22×C13—81no—
660C22×C13—81no—
661C22×C13—81no—
662C22×C13—81no—
663C22×C13—81no—
664C22×C13—81no—
665C22×C13C2×#12111yescharacteristic
666C22×C13C2×#12111yescharacteristic
667C22×C13C2×#12311yescharacteristic
668C22×C13#52511yescharacteristic
669C22×C13#52511yescharacteristic
670C22×C13#52511yescharacteristic
671C22×C13#53411yescharacteristic
672C22×C13#53511yescharacteristic
673C22×C13#53511yescharacteristic
674C22×C13#53711yescharacteristic
675C22×C13#53811yescharacteristic
676C22×C13#53811yescharacteristic
677C22×C13#53811yescharacteristic
678C22×C13#53911yescharacteristic
679C22×C13#53911yescharacteristic
680C22×C13D4211yescharacteristic
681C22×C13D4211yescharacteristic
682C22×C13D4211yescharacteristic
683C22×C13D4211yescharacteristic
684C22×C13#54611yescharacteristic
685C22×C13#54611yescharacteristic
686C22×C13#54611yescharacteristic
687C22×C13#54611yescharacteristic
688C22×C13#54611yescharacteristic
689C22×C13#54711yescharacteristic
690C22×C13#54811yescharacteristic
691C22×C13#54811yescharacteristic
692C22×C13#55111yescharacteristic
693C22×C13#55111yescharacteristic
694C22×C13#55111yescharacteristic
695C22×C13#55311yescharacteristic
696C22×C13#55311yescharacteristic
697C22×C13#55311yescharacteristic
698C22×C13#56011yescharacteristic
699C22×C13#56211yescharacteristic
700C4×C13—24no—
701C4×C13—42no—
702C4×C13—42no—
703C4×C13—42no—
704C4×C13—42no—
705C4×C13—42no—
706C4×C13—42no—
707C4×C13—42no—
708C4×C13—81no—
709C4×C13—81no—
710C4×C13—81no—
711C4×C13—81no—
712C25C23×C1311yescharacteristic
713C25C23×C1311yescharacteristic
714C25C23×C1311yescharacteristic
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4D4×C1314yes—
736C23×C4—22no—
737C23×C4—22no—
738C23×C4—22no—
739C23×C4—22no—
740C23×C4—22no—
741C23×C4—22no—
742C23×C4—22no—
743C23×C4—22no—
744C23×C4—41no—
745C23×C4—41no—
746C23×C4—41no—
747C23×C4—41no—
748C23×C4—41no—
749C23×C4—41no—
750C23×C4C23×C1311yescharacteristic
751C23×C4C23×C1311yescharacteristic
752C23×C4C23×C1311yescharacteristic
753C23×C4C23×C1311yescharacteristic
754C23×C4C23×C1311yescharacteristic
755C23×C4C23×C1311yescharacteristic
756C23×C4C23×C1311yescharacteristic
757C23×C4C23×C1311yescharacteristic
758C23×C4C23×C1311yescharacteristic
759C23×C4C23×C1311yescharacteristic
760C23×C4C23×C1311yescharacteristic
761C23×C4C23×C1311yescharacteristic
762C2×C4⋊C4—22no—
763C2×C4⋊C4—22no—
764C2×C4⋊C4—22no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4—22no—
767C2×C4⋊C4—41no—
768C2×C4⋊C4—41no—
769C2×C4⋊C4—41no—
770C2×C4⋊C4—41no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4D4×C1314yescomplemented
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—22no—
819#95—22no—
820#95—41no—
821#95—41no—
822#95D4×C1314yescomplemented
823#95D4×C1314yescomplemented
824C2×C13—44no—
825C2×C13—44no—
826C2×C13—82no—
827C2×C13#241211yescharacteristic
828C2×C13#241611yescharacteristic
829C2×C13#241811yescharacteristic
830C2×C13#242411yescharacteristic
831C2×C13#242411yescharacteristic
832C2×C13#244311yescharacteristic
833C2×C13#246311yescharacteristic
834C2×C13#253511yescharacteristic
835C2×C13#259811yescharacteristic
836C2×C13#266911yescharacteristic
837C2×C13#267611yescharacteristic
838C2×C13#269311yescharacteristic
839C2×C13#269611yescharacteristic
840C2×C13#270811yescharacteristic
841C2×C13#277811yescharacteristic
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24C2×D4×C1312yes—
881C24C2×D4×C1312yes—
882C24C2×D4×C1312yes—
883C24C13×#4112yes—
884C24C13×#4112yes—
885C24C13×#4112yes—
886C24C13×#4112yes—
887C24C24×C1311yescharacteristic
888C2×D4—28no—
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—28no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4C2×D4×C1312yes—
998C22×C4C2×D4×C1312yes—
999C22×C4C2×D4×C1312yes—
1000C22×C4C2×D4×C1312yes—
1001C22×C4C2×D4×C1312yes—
1002C22×C4C2×D4×C1312yes—
1003C22×C4C2×D4×C1312yes—
1004C22×C4C2×D4×C1312yes—
1005C22×C4C2×D4×C1312yes—
1006C22×C4C13×#4112yes—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C22⋊C4—28no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C13#1537611yescharacteristic, direct product factor, Sylow
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23C13×#12114yes—
1128C23C13×#12314yes—
1129C23C22×D4×C1311yescharacteristic
1130C23C22×D4×C1311yescharacteristic
1131C23C22×D4×C1311yescharacteristic
1132C23C22×D4×C1311yescharacteristic
1133C23C2×C13×#4111yescharacteristic
1134C23C2×C13×#4111yescharacteristic
1135C23C2×C13×#4111yescharacteristic
1136C23C2×C13×#4111yescharacteristic
1137C23C2×C13×#4111yescharacteristic
1138C23C13×H(5,𝔽2)11yescharacteristic
1139C23C13×H(5,𝔽2)11yescharacteristic
1140C23C13×H(5,𝔽2)11yescharacteristic
1141C23C13×H(5,𝔽2)11yescharacteristic
1142C23C13×H(5,𝔽2)11yescharacteristic
1143C23C13×2−1+411yescharacteristic
1144D4—416no—
1145D4—416no—
1146D4—416no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—416no—
1175C2×C4—416no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4C13×#12114yes—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22C2×C13×#12111yescharacteristic
1279C22C2×C13×#12111yescharacteristic
1280C22C2×C13×#12311yescharacteristic
1281C22C13×#52511yescharacteristic
1282C22C13×#52511yescharacteristic
1283C22C13×#52511yescharacteristic
1284C22C13×#53411yescharacteristic
1285C22C13×#53511yescharacteristic
1286C22C13×#53511yescharacteristic
1287C22C13×#53711yescharacteristic
1288C22C13×#53811yescharacteristic
1289C22C13×#53811yescharacteristic
1290C22C13×#53811yescharacteristic
1291C22C13×#53911yescharacteristic
1292C22C13×#53911yescharacteristic
1293C22D42×C1311yescharacteristic
1294C22D42×C1311yescharacteristic
1295C22D42×C1311yescharacteristic
1296C22D42×C1311yescharacteristic
1297C22C13×#54611yescharacteristic
1298C22C13×#54611yescharacteristic
1299C22C13×#54611yescharacteristic
1300C22C13×#54611yescharacteristic
1301C22C13×#54611yescharacteristic
1302C22C13×#54711yescharacteristic
1303C22C13×#54811yescharacteristic
1304C22C13×#54811yescharacteristic
1305C22C13×#55111yescharacteristic
1306C22C13×#55111yescharacteristic
1307C22C13×#55111yescharacteristic
1308C22C13×#55311yescharacteristic
1309C22C13×#55311yescharacteristic
1310C22C13×#55311yescharacteristic
1311C22C13×#56011yescharacteristic
1312C22C13×#56211yescharacteristic
1313C4—24no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C2—44no—
1326C2—44no—
1327C2—82no—
1328C2C13×#241211yescharacteristic
1329C2C13×#241611yescharacteristic
1330C2C13×#241811yescharacteristic
1331C2C13×#242411yescharacteristic
1332C2C13×#242411yescharacteristic
1333C2C13×#244311yescharacteristic
1334C2C13×#246311yescharacteristic
1335C2C13×#253511yescharacteristic
1336C2C13×#259811yescharacteristic
1337C2C13×#266911yescharacteristic
1338C2C13×#267611yescharacteristic
1339C2C13×#269311yescharacteristic
1340C2C13×#269611yescharacteristic
1341C2C13×#270811yescharacteristic
1342C2C13×#277811yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC2×C13×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#394C2semidirect
3. C2×C13×#386C2semidirect
4. C2×C13×#386C2semidirect
5. C2×C13×#386C2semidirect
6. C2×C13×#386C2semidirect
7. C2×C13×#385C2semidirect
8. C2×C13×#380C2semidirect
9. C13×#1443C2semidirect
10. C13×#1442C2semidirect
11. C13×#1440C2semidirect
12. C13×#1439C2semidirect
13. C13×#1439C2semidirect
14. C13×#1439C2semidirect
15. C13×#1438C2semidirect
156. C2×C13×C22⋊C4D4semidirect
169. C13×#95D4semidirect
170. C13×#95D4semidirect
171. #15376C13direct (N × H)
353. C2×#394C2×C13semidirect
355. C2×#386C2×C13semidirect
356. C2×#386C2×C13semidirect
357. C2×#386C2×C13semidirect
358. C2×#386C2×C13semidirect
359. C2×#385C2×C13semidirect
360. C2×#380C2×C13semidirect
361. #1443C2×C13semidirect
362. #1442C2×C13semidirect
363. #1440C2×C13semidirect
364. #1439C2×C13semidirect
365. #1439C2×C13semidirect
366. #1439C2×C13semidirect
367. #1438C2×C13semidirect
809. C2×C22⋊C4D4×C13semidirect
822. #95D4×C13semidirect
823. #95D4×C13semidirect
1023. C13#15376direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3942
C2×C13×#3922
C2×C13×#3862
C2×C13×#3852
C2×C13×#3802
C13×#14432
C13×#14422
C13×#14402
C13×#14392
C13×#14382
#1537613