Finite Group Databasebeta

← C13×#14751 #15701090

Subgroups — C13×#14751 #15701090

Order 3328.

2302 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#394C211yesmaximal, characteristic, complemented
2C2×C13×#394C211yesmaximal, characteristic, complemented
3C2×C13×#392C211yesmaximal, characteristic
4C2×C13×#390C211yesmaximal, characteristic, complemented
5C2×C13×#388C211yesmaximal, characteristic, complemented
6C2×C13×#386C211yesmaximal, characteristic, complemented
7C2×C13×#386C211yesmaximal, characteristic, complemented
8C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
9C13×#1441C211yesmaximal, characteristic, complemented
10C13×#1440C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic, complemented
13C13×#1438C211yesmaximal, characteristic, complemented
14C13×#1437C211yesmaximal, characteristic, complemented
15C13×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊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
37C22×C42×C13C2211yescharacteristic
38C22×C42×C13C2211yescharacteristic
39C13×#394—24no—
40C13×#394—24no—
41C13×#392—24no—
42C13×#390—24no—
43C13×#388—24no—
44C13×#386—24no—
45C13×#386—24no—
46C4×C13×C22⋊C4—24no—
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—22no—
77C22×D4×C13—41no—
78C22×D4×C13—41no—
79C22×D4×C13—41no—
80C22×D4×C13—41no—
81C22×D4×C13—41no—
82C22×D4×C13—41no—
83C23×C4×C13—22no—
84C23×C4×C13—22no—
85C23×C4×C13—22no—
86C23×C4×C13—22no—
87C23×C4×C13—22no—
88C23×C4×C13—41no—
89C23×C4×C13—41no—
90C23×C4×C13C2311yescharacteristic
91C23×C4×C13C2311yescharacteristic
92C23×C4×C13C2311yescharacteristic
93C23×C4×C13C2311yescharacteristic
94C23×C4×C13C2311yescharacteristic
95C23×C4×C13C2311yescharacteristic
96C23×C4×C13C2311yescharacteristic
97C23×C4×C13C2311yescharacteristic
98C23×C4×C13C2311yescharacteristic
99C23×C4×C13C2311yescharacteristic
100C23×C4×C13C2311yescharacteristic
101C23×C4×C13C2311yescharacteristic
102C2×C13×C4⋊C4—22no—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C4⋊C4—22no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—22no—
108C2×C13×C4⋊C4—41no—
109C2×C13×C4⋊C4—41no—
110C2×C13×C4⋊C4—41no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—22no—
114C2×C13×C22⋊C4—22no—
115C2×C13×C22⋊C4—22no—
116C2×C13×C22⋊C4—22no—
117C2×C13×C22⋊C4—22no—
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—41no—
141C2×C13×C22⋊C4—41no—
142C2×C13×C22⋊C4—41no—
143C2×C13×C22⋊C4—41no—
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⋊C4D414yes—
151C2×C13×C22⋊C4D414yescomplemented
152C2×C13×C22⋊C4D414yescomplemented
153C2×C42×C13—22no—
154C2×C42×C13—22no—
155C2×C42×C13—22no—
156C2×C42×C13—22no—
157C2×C42×C13—41no—
158C2×C42×C13—41no—
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—22no—
168C13×#95—22no—
169C13×#95—41no—
170C13×#95D414yescomplemented
171#14751C1311yesmaximal, 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×C13—21no—
211C24×C13—21no—
212C24×C13C2×D412yes—
213C24×C13C2×D412yes—
214C24×C13C2×D412yes—
215C24×C13#4112yes—
216C24×C13#4112yes—
217C24×C13C2411yescharacteristic
218C2×D4×C13—28no—
219C2×D4×C13—28no—
220C2×D4×C13—28no—
221C2×D4×C13—44no—
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—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—28no—
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—44no—
311C22×C4×C13—44no—
312C22×C4×C13—44no—
313C22×C4×C13—44no—
314C22×C4×C13—44no—
315C22×C4×C13—44no—
316C22×C4×C13C2×D412yes—
317C22×C4×C13C2×D412yes—
318C22×C4×C13C2×D412yes—
319C22×C4×C13C2×D412yes—
320C22×C4×C13C2×D412yes—
321C22×C4×C13C2×D412yes—
322C22×C4×C13C2×D412yes—
323C22×C4×C13C2×D412yes—
324C22×C4×C13C2×D412yes—
325C22×C4×C13#4112yes—
326C22×C4×C13#4112yes—
327C22×C4×C13#4112yes—
328C22×C4×C13#4112yes—
329C22×C4×C13#4112yes—
330C13×C4⋊C4—44no—
331C13×C4⋊C4—44no—
332C13×C4⋊C4—44no—
333C13×C22⋊C4—28no—
334C13×C22⋊C4—28no—
335C13×C22⋊C4—28no—
336C13×C22⋊C4—44no—
337C13×C22⋊C4—44no—
338C13×C22⋊C4—44no—
339C13×C22⋊C4—44no—
340C13×C22⋊C4—44no—
341C13×C22⋊C4—44no—
342C13×C22⋊C4—44no—
343C13×C22⋊C4—44no—
344C13×C22⋊C4—44no—
345C13×C22⋊C4—44no—
346C13×C22⋊C4—44no—
347C42×C13—44no—
348C42×C13—44no—
349C2×#394C2×C1311yescharacteristic, complemented
350C2×#394C2×C1311yescharacteristic, complemented
351C2×#392C2×C1311yescharacteristic
352C2×#390C2×C1311yescharacteristic, complemented
353C2×#388C2×C1311yescharacteristic, complemented
354C2×#386C2×C1311yescharacteristic, complemented
355C2×#386C2×C1311yescharacteristic, complemented
356C2×C4×C22⋊C4C2×C1311yescharacteristic, complemented
357#1441C2×C1311yescharacteristic, complemented
358#1440C2×C1311yescharacteristic, complemented
359#1439C2×C1311yescharacteristic, complemented
360#1439C2×C1311yescharacteristic, complemented
361#1438C2×C1311yescharacteristic, complemented
362#1437C2×C1311yescharacteristic, complemented
363#1436C2×C1311yescharacteristic, complemented
364C23×C13—22no—
365C23×C13—22no—
366C23×C13—22no—
367C23×C13—22no—
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—41no—
397C23×C13—41no—
398C23×C13—41no—
399C23×C13—41no—
400C23×C13—41no—
401C23×C13—41no—
402C23×C13—41no—
403C23×C13—41no—
404C23×C13—41no—
405C23×C13—41no—
406C23×C13—41no—
407C23×C13—41no—
408C23×C13—41no—
409C23×C13—41no—
410C23×C13—41no—
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#12114yes—
469C23×C13C22×D411yescharacteristic
470C23×C13C22×D411yescharacteristic
471C23×C13C22×D411yescharacteristic
472C23×C13C22×D411yescharacteristic
473C23×C13C2×#4111yescharacteristic
474C23×C13C2×#4111yescharacteristic
475C23×C13C2×#4111yescharacteristic
476C23×C13C2×#4111yescharacteristic
477C23×C13C2×#4111yescharacteristic
478C23×C13C2×#4111yescharacteristic
479C23×C13C2×#4111yescharacteristic
480C23×C13H(5,𝔽2)11yescharacteristic
481C23×C13H(5,𝔽2)11yescharacteristic
482C23×C13H(5,𝔽2)11yescharacteristic
483C23×C13H(5,𝔽2)11yescharacteristic
484D4×C13—416no—
485D4×C13—416no—
486D4×C13—416no—
487C2×C4×C13—22no—
488C2×C4×C13—22no—
489C2×C4×C13—22no—
490C2×C4×C13—22no—
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—22no—
519C2×C4×C13—22no—
520C2×C4×C13—22no—
521C2×C4×C13—22no—
522C2×C4×C13—22no—
523C2×C4×C13—416no—
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#12114yes—
571C2×C4×C13#12314yes—
572C23×D4C22×C1311yescharacteristic
573C23×D4C22×C1311yescharacteristic
574C23×D4C22×C1311yescharacteristic
575C24×C4C22×C1311yescharacteristic
576C22×C4⋊C4C22×C1311yescharacteristic
577C22×C4⋊C4C22×C1311yescharacteristic
578C22×C4⋊C4C22×C1311yescharacteristic
579C22×C22⋊C4C22×C1311yescharacteristic
580C22×C22⋊C4C22×C1311yescharacteristic
581C22×C22⋊C4C22×C1311yescharacteristic
582C22×C22⋊C4C22×C1311yescharacteristic
583C22×C22⋊C4C22×C1311yescharacteristic
584C22×C22⋊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×C42C22×C1311yescharacteristic
594C22×C42C22×C1311yescharacteristic
595#394—24no—
596#394—24no—
597#392—24no—
598#390—24no—
599#388—24no—
600#386—24no—
601#386—24no—
602C4×C22⋊C4—24no—
603C2×#95C22×C1311yescharacteristic
604C2×#95C22×C1311yescharacteristic
605C2×#95C22×C1311yescharacteristic
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
615C22×C13—24no—
616C22×C13—24no—
617C22×C13—24no—
618C22×C13—42no—
619C22×C13—42no—
620C22×C13—42no—
621C22×C13—42no—
622C22×C13—42no—
623C22×C13—42no—
624C22×C13—42no—
625C22×C13—42no—
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—81no—
645C22×C13—81no—
646C22×C13—81no—
647C22×C13—81no—
648C22×C13—81no—
649C22×C13—81no—
650C22×C13—81no—
651C22×C13—81no—
652C22×C13—81no—
653C22×C13—81no—
654C22×C13—81no—
655C22×C13—81no—
656C22×C13—81no—
657C22×C13—81no—
658C22×C13—81no—
659C22×C13—81no—
660C22×C13C2×#12111yescharacteristic
661C22×C13C2×#12111yescharacteristic
662C22×C13C2×#12311yescharacteristic
663C22×C13#52511yescharacteristic
664C22×C13#52511yescharacteristic
665C22×C13#52511yescharacteristic
666C22×C13#52511yescharacteristic
667C22×C13#52911yescharacteristic
668C22×C13#52911yescharacteristic
669C22×C13#52911yescharacteristic
670C22×C13#53211yescharacteristic
671C22×C13#53211yescharacteristic
672C22×C13#53211yescharacteristic
673C22×C13#53811yescharacteristic
674C22×C13#53811yescharacteristic
675C22×C13#53811yescharacteristic
676C22×C13#53811yescharacteristic
677C22×C13#54011yescharacteristic
678C22×C13#54011yescharacteristic
679C22×C13D4211yescharacteristic
680C22×C13D4211yescharacteristic
681C22×C13D4211yescharacteristic
682C22×C13D4211yescharacteristic
683C22×C13#54611yescharacteristic
684C22×C13#54611yescharacteristic
685C22×C13#54611yescharacteristic
686C22×C13#54611yescharacteristic
687C22×C13#54611yescharacteristic
688C22×C13#54611yescharacteristic
689C22×C13#54611yescharacteristic
690C22×C13#55011yescharacteristic
691C22×C13#55111yescharacteristic
692C22×C13#55311yescharacteristic
693C22×C13#55511yescharacteristic
694C22×C13#55911yescharacteristic
695C4×C13—24no—
696C4×C13—24no—
697C4×C13—42no—
698C4×C13—42no—
699C4×C13—42no—
700C4×C13—42no—
701C4×C13—42no—
702C4×C13—42no—
703C4×C13—42no—
704C4×C13—42no—
705C4×C13—81no—
706C4×C13—81no—
707C25C23×C1311yescharacteristic
708C25C23×C1311yescharacteristic
709C25C23×C1311yescharacteristic
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—22no—
714C22×D4—22no—
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—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C23×C4—22no—
732C23×C4—22no—
733C23×C4—22no—
734C23×C4—22no—
735C23×C4—22no—
736C23×C4—41no—
737C23×C4—41no—
738C23×C4C23×C1311yescharacteristic
739C23×C4C23×C1311yescharacteristic
740C23×C4C23×C1311yescharacteristic
741C23×C4C23×C1311yescharacteristic
742C23×C4C23×C1311yescharacteristic
743C23×C4C23×C1311yescharacteristic
744C23×C4C23×C1311yescharacteristic
745C23×C4C23×C1311yescharacteristic
746C23×C4C23×C1311yescharacteristic
747C23×C4C23×C1311yescharacteristic
748C23×C4C23×C1311yescharacteristic
749C23×C4C23×C1311yescharacteristic
750C2×C4⋊C4—22no—
751C2×C4⋊C4—22no—
752C2×C4⋊C4—22no—
753C2×C4⋊C4—22no—
754C2×C4⋊C4—22no—
755C2×C4⋊C4—22no—
756C2×C4⋊C4—41no—
757C2×C4⋊C4—41no—
758C2×C4⋊C4—41no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
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—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4D4×C1314yes—
799C2×C22⋊C4D4×C1314yescomplemented
800C2×C22⋊C4D4×C1314yescomplemented
801C2×C42—22no—
802C2×C42—22no—
803C2×C42—22no—
804C2×C42—22no—
805C2×C42—41no—
806C2×C42—41no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—41no—
818#95D4×C1314yescomplemented
819C2×C13—44no—
820C2×C13—82no—
821C2×C13—82no—
822C2×C13#239211yescharacteristic
823C2×C13#241811yescharacteristic
824C2×C13#242411yescharacteristic
825C2×C13#242411yescharacteristic
826C2×C13#242411yescharacteristic
827C2×C13#242811yescharacteristic
828C2×C13#244511yescharacteristic
829C2×C13#245911yescharacteristic
830C2×C13#246411yescharacteristic
831C2×C13#246711yescharacteristic
832C2×C13#247611yescharacteristic
833C2×C13#255511yescharacteristic
834C2×C13#255711yescharacteristic
835C2×C13#264811yescharacteristic
836C2×C13#285411yescharacteristic
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
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—
877C24C2×D4×C1312yes—
878C24C2×D4×C1312yes—
879C24C2×D4×C1312yes—
880C24C13×#4112yes—
881C24C13×#4112yes—
882C24C24×C1311yescharacteristic
883C2×D4—28no—
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
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—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—28no—
913C22×C4—21no—
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—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4C2×D4×C1312yes—
982C22×C4C2×D4×C1312yes—
983C22×C4C2×D4×C1312yes—
984C22×C4C2×D4×C1312yes—
985C22×C4C2×D4×C1312yes—
986C22×C4C2×D4×C1312yes—
987C22×C4C2×D4×C1312yes—
988C22×C4C2×D4×C1312yes—
989C22×C4C2×D4×C1312yes—
990C22×C4C13×#4112yes—
991C22×C4C13×#4112yes—
992C22×C4C13×#4112yes—
993C22×C4C13×#4112yes—
994C22×C4C13×#4112yes—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C22⋊C4—28no—
999C22⋊C4—28no—
1000C22⋊C4—28no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C42—44no—
1013C42—44no—
1014C13#1475111yescharacteristic, direct product factor, Sylow
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
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—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
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—
1119C23C13×#12114yes—
1120C23C22×D4×C1311yescharacteristic
1121C23C22×D4×C1311yescharacteristic
1122C23C22×D4×C1311yescharacteristic
1123C23C22×D4×C1311yescharacteristic
1124C23C2×C13×#4111yescharacteristic
1125C23C2×C13×#4111yescharacteristic
1126C23C2×C13×#4111yescharacteristic
1127C23C2×C13×#4111yescharacteristic
1128C23C2×C13×#4111yescharacteristic
1129C23C2×C13×#4111yescharacteristic
1130C23C2×C13×#4111yescharacteristic
1131C23C13×H(5,𝔽2)11yescharacteristic
1132C23C13×H(5,𝔽2)11yescharacteristic
1133C23C13×H(5,𝔽2)11yescharacteristic
1134C23C13×H(5,𝔽2)11yescharacteristic
1135D4—416no—
1136D4—416no—
1137D4—416no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
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—41no—
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×C4C13×#12114yes—
1222C2×C4C13×#12314yes—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
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—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22C2×C13×#12111yescharacteristic
1269C22C2×C13×#12111yescharacteristic
1270C22C2×C13×#12311yescharacteristic
1271C22C13×#52511yescharacteristic
1272C22C13×#52511yescharacteristic
1273C22C13×#52511yescharacteristic
1274C22C13×#52511yescharacteristic
1275C22C13×#52911yescharacteristic
1276C22C13×#52911yescharacteristic
1277C22C13×#52911yescharacteristic
1278C22C13×#53211yescharacteristic
1279C22C13×#53211yescharacteristic
1280C22C13×#53211yescharacteristic
1281C22C13×#53811yescharacteristic
1282C22C13×#53811yescharacteristic
1283C22C13×#53811yescharacteristic
1284C22C13×#53811yescharacteristic
1285C22C13×#54011yescharacteristic
1286C22C13×#54011yescharacteristic
1287C22D42×C1311yescharacteristic
1288C22D42×C1311yescharacteristic
1289C22D42×C1311yescharacteristic
1290C22D42×C1311yescharacteristic
1291C22C13×#54611yescharacteristic
1292C22C13×#54611yescharacteristic
1293C22C13×#54611yescharacteristic
1294C22C13×#54611yescharacteristic
1295C22C13×#54611yescharacteristic
1296C22C13×#54611yescharacteristic
1297C22C13×#54611yescharacteristic
1298C22C13×#55011yescharacteristic
1299C22C13×#55111yescharacteristic
1300C22C13×#55311yescharacteristic
1301C22C13×#55511yescharacteristic
1302C22C13×#55911yescharacteristic
1303C4—24no—
1304C4—24no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—81no—
1314C4—81no—
1315C2—44no—
1316C2—82no—
1317C2—82no—
1318C2C13×#239211yescharacteristic
1319C2C13×#241811yescharacteristic
1320C2C13×#242411yescharacteristic
1321C2C13×#242411yescharacteristic
1322C2C13×#242411yescharacteristic
1323C2C13×#242811yescharacteristic
1324C2C13×#244511yescharacteristic
1325C2C13×#245911yescharacteristic
1326C2C13×#246411yescharacteristic
1327C2C13×#246711yescharacteristic
1328C2C13×#247611yescharacteristic
1329C2C13×#255511yescharacteristic
1330C2C13×#255711yescharacteristic
1331C2C13×#264811yescharacteristic
1332C2C13×#285411yescharacteristic
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
2. C2×C13×#394C2semidirect
4. C2×C13×#390C2semidirect
5. C2×C13×#388C2semidirect
6. C2×C13×#386C2semidirect
7. C2×C13×#386C2semidirect
8. C2×C4×C13×C22⋊C4C2semidirect
9. C13×#1441C2semidirect
10. C13×#1440C2semidirect
11. C13×#1439C2semidirect
12. C13×#1439C2semidirect
13. C13×#1438C2semidirect
14. C13×#1437C2semidirect
15. C13×#1436C2semidirect
151. C2×C13×C22⋊C4D4semidirect
152. C2×C13×C22⋊C4D4semidirect
170. C13×#95D4semidirect
171. #14751C13direct (N × H)
349. C2×#394C2×C13semidirect
350. C2×#394C2×C13semidirect
352. C2×#390C2×C13semidirect
353. C2×#388C2×C13semidirect
354. C2×#386C2×C13semidirect
355. C2×#386C2×C13semidirect
356. C2×C4×C22⋊C4C2×C13semidirect
357. #1441C2×C13semidirect
358. #1440C2×C13semidirect
359. #1439C2×C13semidirect
360. #1439C2×C13semidirect
361. #1438C2×C13semidirect
362. #1437C2×C13semidirect
363. #1436C2×C13semidirect
799. C2×C22⋊C4D4×C13semidirect
800. C2×C22⋊C4D4×C13semidirect
818. #95D4×C13semidirect
1014. C13#14751direct (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×#3902
C2×C13×#3882
C2×C13×#3862
C2×C4×C13×C22⋊C42
C13×#14412
C13×#14402
C13×#14392
C13×#14382
C13×#14372
C13×#14362
#1475113