Finite Group Databasebeta

← C13×#14534 #15700873

Subgroups — C13×#14534 #15700873

Order 3328.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#392C211yesmaximal, characteristic
2C2×C13×#390C211yesmaximal, characteristic, complemented
3C2×C13×#390C211yesmaximal, characteristic, complemented
4C2×C13×#388C211yesmaximal, characteristic, complemented
5C2×C13×#386C211yesmaximal, characteristic, complemented
6C2×C13×#386C211yesmaximal, characteristic, complemented
7C2×C13×#385C211yesmaximal, characteristic, complemented
8C13×#1440C211yesmaximal, characteristic, complemented
9C13×#1439C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic, complemented
11C13×#1438C211yesmaximal, characteristic, complemented
12C13×#1438C211yesmaximal, characteristic, complemented
13C13×#1437C211yesmaximal, characteristic, complemented
14C13×#1436C211yesmaximal, 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×#392C418yescomplemented
40C13×#390—24no—
41C13×#390—24no—
42C13×#388—24no—
43C13×#386—24no—
44C13×#386—24no—
45C13×#385—24no—
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
58C25×C13C2311yescharacteristic
59C25×C13C2311yescharacteristic
60C25×C13C2311yescharacteristic
61C22×D4×C13—22no—
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—41no—
70C22×D4×C13—41no—
71C22×D4×C13—41no—
72C22×D4×C13—41no—
73C22×D4×C13—41no—
74C22×D4×C13—41no—
75C22×D4×C13—41no—
76C22×D4×C13—41no—
77C22×D4×C13—41no—
78C22×D4×C13—41no—
79C22×D4×C13C2×C414yes—
80C22×D4×C13C2×C414yes—
81C22×D4×C13C2×C414yescomplemented
82C23×C4×C13—22no—
83C23×C4×C13—22no—
84C23×C4×C13—22no—
85C23×C4×C13—41no—
86C23×C4×C13—41no—
87C23×C4×C13—41no—
88C23×C4×C13—41no—
89C23×C4×C13C2311yescharacteristic
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
101C2×C13×C4⋊C4—22no—
102C2×C13×C4⋊C4—22no—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C4⋊C4—41no—
106C2×C13×C4⋊C4—41no—
107C2×C13×C4⋊C4—41no—
108C2×C13×C4⋊C4—41no—
109C2×C13×C4⋊C4D414yescomplemented
110C2×C13×C22⋊C4—22no—
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—41no—
131C2×C13×C22⋊C4—41no—
132C2×C13×C22⋊C4—41no—
133C2×C13×C22⋊C4—41no—
134C2×C13×C22⋊C4—41no—
135C2×C13×C22⋊C4—41no—
136C2×C13×C22⋊C4—41no—
137C2×C13×C22⋊C4—41no—
138C2×C13×C22⋊C4—41no—
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⋊C4C2×C414yes—
149C2×C13×C22⋊C4C2×C414yescomplemented
150C2×C13×C22⋊C4C2×C414yescomplemented
151C2×C13×C22⋊C4D414yescomplemented
152C2×C42×C13—22no—
153C2×C42×C13—22no—
154C2×C42×C13—22no—
155C2×C42×C13—41no—
156C2×C42×C13—41no—
157C2×C42×C13—41no—
158C13×#95—22no—
159C13×#95—22no—
160C13×#95—22no—
161C13×#95—22no—
162C13×#95—22no—
163C13×#95—22no—
164C13×#95—22no—
165C13×#95—41no—
166C13×#95—41no—
167C13×#95—41no—
168C13×#95C2×C414yescomplemented
169C13×#95D414yescomplemented
170#14534C1311yesmaximal, characteristic, direct product factor, Sylow
171C24×C13—21no—
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×C13C22×C412yes—
212C24×C13C22×C412yes—
213C24×C13C22×C412yes—
214C24×C13C2×D412yes—
215C24×C13#4112yes—
216C24×C13C2411yescharacteristic
217C2×D4×C13—28no—
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—
238C22×C4×C13—21no—
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—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—44no—
309C22×C4×C13—44no—
310C22×C4×C13—44no—
311C22×C4×C13—44no—
312C22×C4×C13—44no—
313C22×C4×C13—44no—
314C22×C4×C13—44no—
315C22×C4×C13C22×C412yes—
316C22×C4×C13C22×C412yes—
317C22×C4×C13C22×C412yes—
318C22×C4×C13C22×C412yes—
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—
329C13×C4⋊C4—44no—
330C13×C4⋊C4—44no—
331C13×C4⋊C4—44no—
332C13×C22⋊C4—28no—
333C13×C22⋊C4—28no—
334C13×C22⋊C4—44no—
335C13×C22⋊C4—44no—
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—
346C42×C13—44no—
347C42×C13—44no—
348C2×#392C2×C1311yescharacteristic
349C2×#390C2×C1311yescharacteristic, complemented
350C2×#390C2×C1311yescharacteristic, complemented
351C2×#388C2×C1311yescharacteristic, complemented
352C2×#386C2×C1311yescharacteristic, complemented
353C2×#386C2×C1311yescharacteristic, complemented
354C2×#385C2×C1311yescharacteristic, complemented
355#1440C2×C1311yescharacteristic, complemented
356#1439C2×C1311yescharacteristic, complemented
357#1439C2×C1311yescharacteristic, complemented
358#1438C2×C1311yescharacteristic, complemented
359#1438C2×C1311yescharacteristic, complemented
360#1437C2×C1311yescharacteristic, complemented
361#1436C2×C1311yescharacteristic, complemented
362#1436C2×C1311yescharacteristic, complemented
363C23×C13—22no—
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—41no—
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×C13C4×D414yes—
468C23×C13C23×C411yescharacteristic
469C23×C13C22×D411yescharacteristic
470C23×C13C22×D411yescharacteristic
471C23×C13C22×D411yescharacteristic
472C23×C13C2×#4111yescharacteristic
473C23×C13C2×#4111yescharacteristic
474C23×C13C2×#4111yescharacteristic
475C23×C13H(5,𝔽2)11yescharacteristic
476C23×C13H(5,𝔽2)11yescharacteristic
477C23×C13H(5,𝔽2)11yescharacteristic
478C23×C13H(5,𝔽2)11yescharacteristic
479C23×C13H(5,𝔽2)11yescharacteristic
480C23×C13H(5,𝔽2)11yescharacteristic
481C23×C13H(5,𝔽2)11yescharacteristic
482C23×C132−1+411yescharacteristic
483D4×C13—416no—
484D4×C13—416no—
485D4×C13—416no—
486C2×C4×C13—22no—
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—416no—
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×C13C4×D414yes—
570C2×C4×C13C4×D414yes—
571C23×D4C22×C1311yescharacteristic
572C23×D4C22×C1311yescharacteristic
573C23×D4C22×C1311yescharacteristic
574C24×C4C22×C1311yescharacteristic
575C22×C4⋊C4C22×C1311yescharacteristic
576C22×C4⋊C4C22×C1311yescharacteristic
577C22×C4⋊C4C22×C1311yescharacteristic
578C22×C22⋊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×C42C22×C1311yescharacteristic
593C22×C42C22×C1311yescharacteristic
594#392C4×C1318yescomplemented
595#390—24no—
596#390—24no—
597#388—24no—
598#386—24no—
599#386—24no—
600#385—24no—
601C2×#95C22×C1311yescharacteristic
602C2×#95C22×C1311yescharacteristic
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
613C22×C13—24no—
614C22×C13—24no—
615C22×C13—24no—
616C22×C13—42no—
617C22×C13—42no—
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—81no—
643C22×C13—81no—
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×C13C2×C4×D411yescharacteristic
659C22×C13C2×C4×D411yescharacteristic
660C22×C13C2×C4×D411yescharacteristic
661C22×C13#51811yescharacteristic
662C22×C13#51811yescharacteristic
663C22×C13#51811yescharacteristic
664C22×C13#52011yescharacteristic
665C22×C13#53411yescharacteristic
666C22×C13#53411yescharacteristic
667C22×C13#53511yescharacteristic
668C22×C13#53511yescharacteristic
669C22×C13#53511yescharacteristic
670C22×C13#53711yescharacteristic
671C22×C13#53811yescharacteristic
672C22×C13#53811yescharacteristic
673C22×C13#53811yescharacteristic
674C22×C13#53811yescharacteristic
675C22×C13#54011yescharacteristic
676C22×C13#54211yescharacteristic
677C22×C13D4211yescharacteristic
678C22×C13D4211yescharacteristic
679C22×C13D4211yescharacteristic
680C22×C13#54611yescharacteristic
681C22×C13#54611yescharacteristic
682C22×C13#54711yescharacteristic
683C22×C13#54811yescharacteristic
684C22×C13#55011yescharacteristic
685C22×C13#55011yescharacteristic
686C22×C13#55111yescharacteristic
687C22×C13#55311yescharacteristic
688C22×C13#55911yescharacteristic
689C22×C13#56011yescharacteristic
690C22×C13#56011yescharacteristic
691C22×C13#56211yescharacteristic
692C22×C13#56211yescharacteristic
693C4×C13—24no—
694C4×C13—24no—
695C4×C13—42no—
696C4×C13—42no—
697C4×C13—42no—
698C4×C13—42no—
699C4×C13—42no—
700C4×C13—42no—
701C4×C13—42no—
702C4×C13—42no—
703C4×C13—81no—
704C4×C13—81no—
705C25C23×C1311yescharacteristic
706C25C23×C1311yescharacteristic
707C25C23×C1311yescharacteristic
708C22×D4—22no—
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—22no—
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—41no—
717C22×D4—41no—
718C22×D4—41no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4C2×C4×C1314yes—
727C22×D4C2×C4×C1314yes—
728C22×D4C2×C4×C1314yescomplemented
729C23×C4—22no—
730C23×C4—22no—
731C23×C4—22no—
732C23×C4—41no—
733C23×C4—41no—
734C23×C4—41no—
735C23×C4—41no—
736C23×C4C23×C1311yescharacteristic
737C23×C4C23×C1311yescharacteristic
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
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—22no—
751C2×C4⋊C4—22no—
752C2×C4⋊C4—41no—
753C2×C4⋊C4—41no—
754C2×C4⋊C4—41no—
755C2×C4⋊C4—41no—
756C2×C4⋊C4D4×C1314yescomplemented
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
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—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
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⋊C4C2×C4×C1314yes—
796C2×C22⋊C4C2×C4×C1314yescomplemented
797C2×C22⋊C4C2×C4×C1314yescomplemented
798C2×C22⋊C4D4×C1314yescomplemented
799C2×C42—22no—
800C2×C42—22no—
801C2×C42—22no—
802C2×C42—41no—
803C2×C42—41no—
804C2×C42—41no—
805#95—22no—
806#95—22no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—41no—
813#95—41no—
814#95—41no—
815#95C2×C4×C1314yescomplemented
816#95D4×C1314yescomplemented
817C2×C13—44no—
818C2×C13—82no—
819C2×C13—82no—
820C2×C13#232111yescharacteristic
821C2×C13#232111yescharacteristic
822C2×C13#232411yescharacteristic
823C2×C13#235811yescharacteristic
824C2×C13#236111yescharacteristic
825C2×C13#236611yescharacteristic
826C2×C13#237711yescharacteristic
827C2×C13#266911yescharacteristic
828C2×C13#267311yescharacteristic
829C2×C13#267611yescharacteristic
830C2×C13#268211yescharacteristic
831C2×C13#271011yescharacteristic
832C2×C13#271411yescharacteristic
833C2×C13#273011yescharacteristic
834C2×C13#279711yescharacteristic
835C24—21no—
836C24—21no—
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—
875C24C22×C4×C1312yes—
876C24C22×C4×C1312yes—
877C24C22×C4×C1312yes—
878C24C2×D4×C1312yes—
879C24C13×#4112yes—
880C24C24×C1311yescharacteristic
881C2×D4—28no—
882C2×D4—28no—
883C2×D4—28no—
884C2×D4—28no—
885C2×D4—44no—
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—
902C22×C4—21no—
903C22×C4—21no—
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—21no—
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—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4C22×C4×C1312yes—
980C22×C4C22×C4×C1312yes—
981C22×C4C22×C4×C1312yes—
982C22×C4C22×C4×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×C4C2×D4×C1312yes—
991C22×C4C13×#4112yes—
992C22×C4C13×#4112yes—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C22⋊C4—28no—
997C22⋊C4—28no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
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—
1010C42—44no—
1011C42—44no—
1012C13#1453411yescharacteristic, direct product factor, Sylow
1013C23—22no—
1014C23—22no—
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—41no—
1046C23—41no—
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—
1117C23C4×D4×C1314yes—
1118C23C23×C4×C1311yescharacteristic
1119C23C22×D4×C1311yescharacteristic
1120C23C22×D4×C1311yescharacteristic
1121C23C22×D4×C1311yescharacteristic
1122C23C2×C13×#4111yescharacteristic
1123C23C2×C13×#4111yescharacteristic
1124C23C2×C13×#4111yescharacteristic
1125C23C13×H(5,𝔽2)11yescharacteristic
1126C23C13×H(5,𝔽2)11yescharacteristic
1127C23C13×H(5,𝔽2)11yescharacteristic
1128C23C13×H(5,𝔽2)11yescharacteristic
1129C23C13×H(5,𝔽2)11yescharacteristic
1130C23C13×H(5,𝔽2)11yescharacteristic
1131C23C13×H(5,𝔽2)11yescharacteristic
1132C23C13×2−1+411yescharacteristic
1133D4—416no—
1134D4—416no—
1135D4—416no—
1136C2×C4—22no—
1137C2×C4—22no—
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—416no—
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×C4C4×D4×C1314yes—
1220C2×C4C4×D4×C1314yes—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—42no—
1225C22—42no—
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—81no—
1251C22—81no—
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—
1266C22C2×C4×D4×C1311yescharacteristic
1267C22C2×C4×D4×C1311yescharacteristic
1268C22C2×C4×D4×C1311yescharacteristic
1269C22C13×#51811yescharacteristic
1270C22C13×#51811yescharacteristic
1271C22C13×#51811yescharacteristic
1272C22C13×#52011yescharacteristic
1273C22C13×#53411yescharacteristic
1274C22C13×#53411yescharacteristic
1275C22C13×#53511yescharacteristic
1276C22C13×#53511yescharacteristic
1277C22C13×#53511yescharacteristic
1278C22C13×#53711yescharacteristic
1279C22C13×#53811yescharacteristic
1280C22C13×#53811yescharacteristic
1281C22C13×#53811yescharacteristic
1282C22C13×#53811yescharacteristic
1283C22C13×#54011yescharacteristic
1284C22C13×#54211yescharacteristic
1285C22D42×C1311yescharacteristic
1286C22D42×C1311yescharacteristic
1287C22D42×C1311yescharacteristic
1288C22C13×#54611yescharacteristic
1289C22C13×#54611yescharacteristic
1290C22C13×#54711yescharacteristic
1291C22C13×#54811yescharacteristic
1292C22C13×#55011yescharacteristic
1293C22C13×#55011yescharacteristic
1294C22C13×#55111yescharacteristic
1295C22C13×#55311yescharacteristic
1296C22C13×#55911yescharacteristic
1297C22C13×#56011yescharacteristic
1298C22C13×#56011yescharacteristic
1299C22C13×#56211yescharacteristic
1300C22C13×#56211yescharacteristic
1301C4—24no—
1302C4—24no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C2—44no—
1314C2—82no—
1315C2—82no—
1316C2C13×#232111yescharacteristic
1317C2C13×#232111yescharacteristic
1318C2C13×#232411yescharacteristic
1319C2C13×#235811yescharacteristic
1320C2C13×#236111yescharacteristic
1321C2C13×#236611yescharacteristic
1322C2C13×#237711yescharacteristic
1323C2C13×#266911yescharacteristic
1324C2C13×#267311yescharacteristic
1325C2C13×#267611yescharacteristic
1326C2C13×#268211yescharacteristic
1327C2C13×#271011yescharacteristic
1328C2C13×#271411yescharacteristic
1329C2C13×#273011yescharacteristic
1330C2C13×#279711yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC2×C13×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#390C2semidirect
3. C2×C13×#390C2semidirect
4. C2×C13×#388C2semidirect
5. C2×C13×#386C2semidirect
6. C2×C13×#386C2semidirect
7. C2×C13×#385C2semidirect
8. C13×#1440C2semidirect
9. C13×#1439C2semidirect
10. C13×#1439C2semidirect
11. C13×#1438C2semidirect
12. C13×#1438C2semidirect
13. C13×#1437C2semidirect
14. C13×#1436C2semidirect
15. C13×#1436C2semidirect
39. C13×#392C4semidirect
81. C22×D4×C13C2×C4semidirect
109. C2×C13×C4⋊C4D4semidirect
149. C2×C13×C22⋊C4C2×C4semidirect
150. C2×C13×C22⋊C4C2×C4semidirect
151. C2×C13×C22⋊C4D4semidirect
168. C13×#95C2×C4semidirect
169. C13×#95D4semidirect
170. #14534C13direct (N × H)
349. C2×#390C2×C13semidirect
350. C2×#390C2×C13semidirect
351. C2×#388C2×C13semidirect
352. C2×#386C2×C13semidirect
353. C2×#386C2×C13semidirect
354. C2×#385C2×C13semidirect
355. #1440C2×C13semidirect
356. #1439C2×C13semidirect
357. #1439C2×C13semidirect
358. #1438C2×C13semidirect
359. #1438C2×C13semidirect
360. #1437C2×C13semidirect
361. #1436C2×C13semidirect
362. #1436C2×C13semidirect
594. #392C4×C13semidirect
728. C22×D4C2×C4×C13semidirect
756. C2×C4⋊C4D4×C13semidirect
796. C2×C22⋊C4C2×C4×C13semidirect
797. C2×C22⋊C4C2×C4×C13semidirect
798. C2×C22⋊C4D4×C13semidirect
815. #95C2×C4×C13semidirect
816. #95D4×C13semidirect
1012. C13#14534direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3922
C2×C13×#3902
C2×C13×#3882
C2×C13×#3862
C2×C13×#3852
C13×#14402
C13×#14392
C13×#14382
C13×#14372
C13×#14362
#1453413