Finite Group Databasebeta

← C13×#15319 #15701658

Subgroups — C13×#15319 #15701658

Order 3328.

2350 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#121C211yesmaximal, characteristic
2C2×C13×#398C211yesmaximal, characteristic, complemented
3C2×C13×#394C211yesmaximal, characteristic, complemented
4C2×C13×#394C211yesmaximal, characteristic, complemented
5C2×C13×#390C211yesmaximal, characteristic, complemented
6C2×C13×#388C211yesmaximal, characteristic, complemented
7C13×#1440C211yesmaximal, characteristic, complemented
8C13×#1439C211yesmaximal, characteristic, complemented
9C13×#1439C211yesmaximal, characteristic, complemented
10C13×#1438C211yesmaximal, characteristic, complemented
11C13×#1438C211yesmaximal, characteristic, complemented
12C13×#1438C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×C22⋊#95C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C2×C13×#121—24no—
21C2×C13×#121—24no—
22C2×C13×#121—24no—
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊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×C13×C22⋊C4C2211yescharacteristic
38C22×C13×C22⋊C4C2211yescharacteristic
39C22×C13×C22⋊C4C2211yescharacteristic
40C22×C13×C22⋊C4C2211yescharacteristic
41C22×C42×C13C2211yescharacteristic
42C13×#398—24no—
43C13×#394—24no—
44C13×#394—24no—
45C13×#390—24no—
46C13×#388—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—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—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
102C13×#121—232no—
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—22no—
109C2×C13×C4⋊C4—22no—
110C2×C13×C4⋊C4—22no—
111C2×C13×C4⋊C4—22no—
112C2×C13×C4⋊C4—41no—
113C2×C13×C4⋊C4—41no—
114C2×C13×C4⋊C4D414yes—
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—41no—
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⋊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⋊C4D414yes—
156C2×C13×C22⋊C4D414yescomplemented
157C2×C42×C13—22no—
158C2×C42×C13—22no—
159C2×C42×C13—41no—
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×#95—41no—
171C13×#95—41no—
172#15319C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
213C24×C13C2×D412yes—
214C24×C13C2×D412yes—
215C24×C13C2×D412yes—
216C24×C13C2×D412yes—
217C24×C13#4112yes—
218C24×C13C2411yescharacteristic
219C2×D4×C13—28no—
220C2×D4×C13—28no—
221C2×D4×C13—28no—
222C2×D4×C13—28no—
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—
239C2×D4×C13—44no—
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—21no—
248C22×C4×C13—28no—
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—44no—
314C22×C4×C13—44no—
315C22×C4×C13—44no—
316C22×C4×C13—44no—
317C22×C4×C13—44no—
318C22×C4×C13—44no—
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×C13C2×D412yes—
326C22×C4×C13C2×D412yes—
327C22×C4×C13#4112yes—
328C22×C4×C13#4112yes—
329C22×C4×C13#4112yes—
330C22×C4×C13#4112yes—
331C13×C4⋊C4—28no—
332C13×C4⋊C4—44no—
333C13×C4⋊C4—44no—
334C13×C4⋊C4—44no—
335C13×C22⋊C4—28no—
336C13×C22⋊C4—28no—
337C13×C22⋊C4—28no—
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—
347C13×C22⋊C4—44no—
348C13×C22⋊C4—44no—
349C42×C13—44no—
350C22×#121C2×C1311yescharacteristic
351C2×#398C2×C1311yescharacteristic, complemented
352C2×#394C2×C1311yescharacteristic, complemented
353C2×#394C2×C1311yescharacteristic, complemented
354C2×#390C2×C1311yescharacteristic, complemented
355C2×#388C2×C1311yescharacteristic, complemented
356#1440C2×C1311yescharacteristic, complemented
357#1439C2×C1311yescharacteristic, complemented
358#1439C2×C1311yescharacteristic, complemented
359#1438C2×C1311yescharacteristic, complemented
360#1438C2×C1311yescharacteristic, complemented
361#1438C2×C1311yescharacteristic, complemented
362#1436C2×C1311yescharacteristic, complemented
363C22⋊#95C2×C1311yescharacteristic, complemented
364C22⋊#95C2×C1311yescharacteristic, complemented
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—22no—
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—41no—
469C23×C13#12114yes—
470C23×C13C22×D411yescharacteristic
471C23×C13C22×D411yescharacteristic
472C23×C13C22×D411yescharacteristic
473C23×C13C22×D411yescharacteristic
474C23×C13C2×#4111yescharacteristic
475C23×C13C2×#4111yescharacteristic
476C23×C13C2×#4111yescharacteristic
477C23×C13C2×#4111yescharacteristic
478C23×C13C2×#4111yescharacteristic
479C23×C13H(5,𝔽2)11yescharacteristic
480C23×C13H(5,𝔽2)11yescharacteristic
481C23×C13H(5,𝔽2)11yescharacteristic
482C23×C13H(5,𝔽2)11yescharacteristic
483C23×C13H(5,𝔽2)11yescharacteristic
484C23×C132−1+411yescharacteristic
485D4×C13—416no—
486D4×C13—416no—
487D4×C13—416no—
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—416no—
519C2×C4×C13—41no—
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#12014yes—
572C2×C4×C13#12414yes—
573C23×D4C22×C1311yescharacteristic
574C23×D4C22×C1311yescharacteristic
575C23×D4C22×C1311yescharacteristic
576C24×C4C22×C1311yescharacteristic
577C2×#121—24no—
578C2×#121—24no—
579C2×#121—24no—
580C22×C4⋊C4C22×C1311yescharacteristic
581C22×C4⋊C4C22×C1311yescharacteristic
582C22×C4⋊C4C22×C1311yescharacteristic
583C22×C4⋊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×C22⋊C4C22×C1311yescharacteristic
594C22×C22⋊C4C22×C1311yescharacteristic
595C22×C22⋊C4C22×C1311yescharacteristic
596C22×C22⋊C4C22×C1311yescharacteristic
597C22×C22⋊C4C22×C1311yescharacteristic
598C22×C42C22×C1311yescharacteristic
599#398—24no—
600#394—24no—
601#394—24no—
602#390—24no—
603#388—24no—
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
615C2×#95C22×C1311yescharacteristic
616C22×C13—24no—
617C22×C13—24no—
618C22×C13—24no—
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—42no—
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×C13—81no—
661C22×C13C2×#12011yescharacteristic
662C22×C13C2×#12111yescharacteristic
663C22×C13#52511yescharacteristic
664C22×C13C2×#12411yescharacteristic
665C22×C13#52911yescharacteristic
666C22×C13#53211yescharacteristic
667C22×C13#53411yescharacteristic
668C22×C13#53411yescharacteristic
669C22×C13#53511yescharacteristic
670C22×C13#53711yescharacteristic
671C22×C13#53911yescharacteristic
672C22×C13#54011yescharacteristic
673C22×C13#54011yescharacteristic
674C22×C13#54011yescharacteristic
675C22×C13#54211yescharacteristic
676C22×C13D4211yescharacteristic
677C22×C13D4211yescharacteristic
678C22×C13#54611yescharacteristic
679C22×C13#54611yescharacteristic
680C22×C13#54611yescharacteristic
681C22×C13#54611yescharacteristic
682C22×C13#54611yescharacteristic
683C22×C13#54611yescharacteristic
684C22×C13#54611yescharacteristic
685C22×C13#54611yescharacteristic
686C22×C13#54711yescharacteristic
687C22×C13#54711yescharacteristic
688C22×C13#54811yescharacteristic
689C22×C13#55011yescharacteristic
690C22×C13#55311yescharacteristic
691C22×C13#55311yescharacteristic
692C22×C13#55311yescharacteristic
693C22×C13#55511yescharacteristic
694C22×C13#56011yescharacteristic
695C22×C13#56211yescharacteristic
696C4×C13—24no—
697C4×C13—24no—
698C4×C13—42no—
699C4×C13—42no—
700C4×C13—42no—
701C4×C13—42no—
702C4×C13—42no—
703C4×C13—42no—
704C4×C13—81no—
705C4×C13—81no—
706C4×C13—81no—
707C4×C13—81no—
708C25C23×C1311yescharacteristic
709C25C23×C1311yescharacteristic
710C25C23×C1311yescharacteristic
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—
731C22×D4D4×C1314yes—
732C23×C4—22no—
733C23×C4—22no—
734C23×C4—22no—
735C23×C4—22no—
736C23×C4—22no—
737C23×C4—41no—
738C23×C4—41no—
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
750C23×C4C23×C1311yescharacteristic
751#121—232no—
752C2×C4⋊C4—22no—
753C2×C4⋊C4—22no—
754C2×C4⋊C4—22no—
755C2×C4⋊C4—22no—
756C2×C4⋊C4—22no—
757C2×C4⋊C4—22no—
758C2×C4⋊C4—22no—
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—41no—
762C2×C4⋊C4—41no—
763C2×C4⋊C4D4×C1314yes—
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⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4D4×C1314yes—
805C2×C22⋊C4D4×C1314yescomplemented
806C2×C42—22no—
807C2×C42—22no—
808C2×C42—41no—
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—22no—
818#95—41no—
819#95—41no—
820#95—41no—
821C2×C13—44no—
822C2×C13—82no—
823C2×C13—82no—
824C2×C13#240711yescharacteristic
825C2×C13#241011yescharacteristic
826C2×C13#242511yescharacteristic
827C2×C13#243511yescharacteristic
828C2×C13#246411yescharacteristic
829C2×C13#247611yescharacteristic
830C2×C13#249011yescharacteristic
831C2×C13#249111yescharacteristic
832C2×C13#254311yescharacteristic
833C2×C13#267111yescharacteristic
834C2×C13#267311yescharacteristic
835C2×C13#269111yescharacteristic
836C2×C13#269911yescharacteristic
837C2×C13#270111yescharacteristic
838C2×C13#271111yescharacteristic
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—
877C24—21no—
878C24—21no—
879C24C2×D4×C1312yes—
880C24C2×D4×C1312yes—
881C24C2×D4×C1312yes—
882C24C2×D4×C1312yes—
883C24C13×#4112yes—
884C24C24×C1311yescharacteristic
885C2×D4—28no—
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—28no—
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—
904C2×D4—44no—
905C2×D4—44no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—28no—
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—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4C2×D4×C1312yes—
986C22×C4C2×D4×C1312yes—
987C22×C4C2×D4×C1312yes—
988C22×C4C2×D4×C1312yes—
989C22×C4C2×D4×C1312yes—
990C22×C4C2×D4×C1312yes—
991C22×C4C2×D4×C1312yes—
992C22×C4C2×D4×C1312yes—
993C22×C4C13×#4112yes—
994C22×C4C13×#4112yes—
995C22×C4C13×#4112yes—
996C22×C4C13×#4112yes—
997C4⋊C4—28no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C42—44no—
1016C13#1531911yescharacteristic, direct product factor, Sylow
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—22no—
1048C23—22no—
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—
1119C23—41no—
1120C23—41no—
1121C23C13×#12114yes—
1122C23C22×D4×C1311yescharacteristic
1123C23C22×D4×C1311yescharacteristic
1124C23C22×D4×C1311yescharacteristic
1125C23C22×D4×C1311yescharacteristic
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
1135C23C13×H(5,𝔽2)11yescharacteristic
1136C23C13×2−1+411yescharacteristic
1137D4—416no—
1138D4—416no—
1139D4—416no—
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—416no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
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×C4—41no—
1222C2×C4—41no—
1223C2×C4C13×#12014yes—
1224C2×C4C13×#12414yes—
1225C22—24no—
1226C22—24no—
1227C22—24no—
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—42no—
1253C22—42no—
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—
1268C22—81no—
1269C22—81no—
1270C22C2×C13×#12011yescharacteristic
1271C22C2×C13×#12111yescharacteristic
1272C22C13×#52511yescharacteristic
1273C22C2×C13×#12411yescharacteristic
1274C22C13×#52911yescharacteristic
1275C22C13×#53211yescharacteristic
1276C22C13×#53411yescharacteristic
1277C22C13×#53411yescharacteristic
1278C22C13×#53511yescharacteristic
1279C22C13×#53711yescharacteristic
1280C22C13×#53911yescharacteristic
1281C22C13×#54011yescharacteristic
1282C22C13×#54011yescharacteristic
1283C22C13×#54011yescharacteristic
1284C22C13×#54211yescharacteristic
1285C22D42×C1311yescharacteristic
1286C22D42×C1311yescharacteristic
1287C22C13×#54611yescharacteristic
1288C22C13×#54611yescharacteristic
1289C22C13×#54611yescharacteristic
1290C22C13×#54611yescharacteristic
1291C22C13×#54611yescharacteristic
1292C22C13×#54611yescharacteristic
1293C22C13×#54611yescharacteristic
1294C22C13×#54611yescharacteristic
1295C22C13×#54711yescharacteristic
1296C22C13×#54711yescharacteristic
1297C22C13×#54811yescharacteristic
1298C22C13×#55011yescharacteristic
1299C22C13×#55311yescharacteristic
1300C22C13×#55311yescharacteristic
1301C22C13×#55311yescharacteristic
1302C22C13×#55511yescharacteristic
1303C22C13×#56011yescharacteristic
1304C22C13×#56211yescharacteristic
1305C4—24no—
1306C4—24no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C2—44no—
1318C2—82no—
1319C2—82no—
1320C2C13×#240711yescharacteristic
1321C2C13×#241011yescharacteristic
1322C2C13×#242511yescharacteristic
1323C2C13×#243511yescharacteristic
1324C2C13×#246411yescharacteristic
1325C2C13×#247611yescharacteristic
1326C2C13×#249011yescharacteristic
1327C2C13×#249111yescharacteristic
1328C2C13×#254311yescharacteristic
1329C2C13×#267111yescharacteristic
1330C2C13×#267311yescharacteristic
1331C2C13×#269111yescharacteristic
1332C2C13×#269911yescharacteristic
1333C2C13×#270111yescharacteristic
1334C2C13×#271111yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC22×C13×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#398C2semidirect
3. C2×C13×#394C2semidirect
4. C2×C13×#394C2semidirect
5. C2×C13×#390C2semidirect
6. C2×C13×#388C2semidirect
7. C13×#1440C2semidirect
8. C13×#1439C2semidirect
9. C13×#1439C2semidirect
10. C13×#1438C2semidirect
11. C13×#1438C2semidirect
12. C13×#1438C2semidirect
13. C13×#1436C2semidirect
14. C13×C22⋊#95C2semidirect
15. C13×C22⋊#95C2semidirect
156. C2×C13×C22⋊C4D4semidirect
172. #15319C13direct (N × H)
351. C2×#398C2×C13semidirect
352. C2×#394C2×C13semidirect
353. C2×#394C2×C13semidirect
354. C2×#390C2×C13semidirect
355. C2×#388C2×C13semidirect
356. #1440C2×C13semidirect
357. #1439C2×C13semidirect
358. #1439C2×C13semidirect
359. #1438C2×C13semidirect
360. #1438C2×C13semidirect
361. #1438C2×C13semidirect
362. #1436C2×C13semidirect
363. C22⋊#95C2×C13semidirect
364. C22⋊#95C2×C13semidirect
805. C2×C22⋊C4D4×C13semidirect
1016. C13#15319direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×#1212
C2×C13×#3982
C2×C13×#3942
C2×C13×#3902
C2×C13×#3882
C13×#14402
C13×#14392
C13×#14382
C13×#14362
C13×C22⋊#952
#1531913