Finite Group Databasebeta

← C13×#14721 #15701060

Subgroups — C13×#14721 #15701060

Order 3328.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#123C211yesmaximal, characteristic, complemented
2C22×C4×D4×C13C211yesmaximal, characteristic, complemented
3C2×C13×#394C211yesmaximal, characteristic, complemented
4C2×C13×#392C211yesmaximal, characteristic
5C2×C13×#386C211yesmaximal, characteristic, complemented
6C2×C13×#385C211yesmaximal, characteristic, complemented
7C13×#1444C211yesmaximal, 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×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C24×C4×C13C2211yescharacteristic
21C2×C13×#123—24no—
22C2×C13×#123—24no—
23C2×C13×#123—24no—
24C2×C4×D4×C13—24no—
25C2×C4×D4×C13—24no—
26C2×C4×D4×C13—24no—
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C22×C13×C4⋊C4C2211yescharacteristic
30C22×C13×C4⋊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×C13×C22⋊C4C2211yescharacteristic
42C22×C13×C22⋊C4C2211yescharacteristic
43C22×C13×C22⋊C4C2211yescharacteristic
44C22×C42×C13C2211yescharacteristic
45C13×#394—24no—
46C13×#392—24no—
47C13×#386—24no—
48C13×#385—24no—
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
59C2×C13×#95C2211yescharacteristic
60C2×C13×#95C2211yescharacteristic
61C25×C13C2311yescharacteristic
62C25×C13C2311yescharacteristic
63C25×C13C2311yescharacteristic
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—22no—
78C22×D4×C13—22no—
79C22×D4×C13—22no—
80C22×D4×C13—41no—
81C22×D4×C13—41no—
82C22×D4×C13—41no—
83C22×D4×C13—41no—
84C22×D4×C13D414yes—
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—22no—
92C23×C4×C13—22no—
93C23×C4×C13—22no—
94C23×C4×C13—41no—
95C23×C4×C13—41no—
96C23×C4×C13—41no—
97C23×C4×C13—41no—
98C23×C4×C13D414yescomplemented
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
109C23×C4×C13C2311yescharacteristic
110C23×C4×C13C2311yescharacteristic
111C13×#123—232no—
112C4×D4×C13—232no—
113C2×C13×C4⋊C4—22no—
114C2×C13×C4⋊C4—22no—
115C2×C13×C4⋊C4—22no—
116C2×C13×C4⋊C4—22no—
117C2×C13×C4⋊C4—22no—
118C2×C13×C4⋊C4—22no—
119C2×C13×C4⋊C4—22no—
120C2×C13×C4⋊C4—22no—
121C2×C13×C4⋊C4—22no—
122C2×C13×C4⋊C4—22no—
123C2×C13×C4⋊C4—41no—
124C2×C13×C4⋊C4D414yescomplemented
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—22no—
145C2×C13×C22⋊C4—22no—
146C2×C13×C22⋊C4—22no—
147C2×C13×C22⋊C4—22no—
148C2×C13×C22⋊C4—22no—
149C2×C13×C22⋊C4—22no—
150C2×C13×C22⋊C4—22no—
151C2×C13×C22⋊C4—22no—
152C2×C13×C22⋊C4—22no—
153C2×C13×C22⋊C4—22no—
154C2×C13×C22⋊C4—22no—
155C2×C13×C22⋊C4—22no—
156C2×C13×C22⋊C4—41no—
157C2×C13×C22⋊C4—41no—
158C2×C13×C22⋊C4—41no—
159C2×C13×C22⋊C4—41no—
160C2×C13×C22⋊C4—41no—
161C2×C13×C22⋊C4—41no—
162C2×C13×C22⋊C4D414yescomplemented
163C2×C13×C22⋊C4D414yescomplemented
164C2×C42×C13—22no—
165C2×C42×C13—22no—
166C2×C42×C13—22no—
167C13×#95—22no—
168C13×#95—22no—
169C13×#95—22no—
170C13×#95—22no—
171C13×#95—22no—
172C13×#95—22no—
173C13×#95—22no—
174C13×#95—22no—
175C13×#95—22no—
176C13×#95—41no—
177C13×#95—41no—
178C13×#95—41no—
179#14721C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
214C24×C13—21no—
215C24×C13—21no—
216C24×C13—21no—
217C24×C13—21no—
218C24×C13C2×D412yes—
219C24×C13C2×D412yes—
220C24×C13C2×D412yes—
221C24×C13C2×D412yes—
222C24×C13C2×D412yes—
223C24×C13#4112yes—
224C24×C13#4112yes—
225C24×C13C2411yescharacteristic
226C2×D4×C13—28no—
227C2×D4×C13—28no—
228C2×D4×C13—28no—
229C2×D4×C13—28no—
230C2×D4×C13—28no—
231C2×D4×C13—28no—
232C2×D4×C13—28no—
233C2×D4×C13—28no—
234C2×D4×C13—28no—
235C2×D4×C13—44no—
236C2×D4×C13—44no—
237C2×D4×C13—44no—
238C2×D4×C13—44no—
239C2×D4×C13—44no—
240C2×D4×C13—44no—
241C2×D4×C13—44no—
242C2×D4×C13—44no—
243C2×D4×C13—44no—
244C2×D4×C13—44no—
245C2×D4×C13—44no—
246C2×D4×C13—44no—
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—28no—
256C22×C4×C13—28no—
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—28no—
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—21no—
315C22×C4×C13—21no—
316C22×C4×C13—21no—
317C22×C4×C13—21no—
318C22×C4×C13—21no—
319C22×C4×C13—21no—
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×C13—44no—
328C22×C4×C13—44no—
329C22×C4×C13—44no—
330C22×C4×C13—44no—
331C22×C4×C13C2×D412yes—
332C22×C4×C13C2×D412yes—
333C22×C4×C13C2×D412yes—
334C22×C4×C13C2×D412yes—
335C22×C4×C13C2×D412yes—
336C22×C4×C13C2×D412yes—
337C22×C4×C13C2×D412yes—
338C22×C4×C13C2×D412yes—
339C22×C4×C13C2×D412yes—
340C22×C4×C13C2×D412yes—
341C22×C4×C13#4112yes—
342C22×C4×C13#4112yes—
343C22×C4×C13#4112yes—
344C22×C4×C13#4112yes—
345C13×C4⋊C4—28no—
346C13×C4⋊C4—28no—
347C13×C4⋊C4—28no—
348C13×C4⋊C4—44no—
349C13×C22⋊C4—28no—
350C13×C22⋊C4—28no—
351C13×C22⋊C4—28no—
352C13×C22⋊C4—28no—
353C13×C22⋊C4—28no—
354C13×C22⋊C4—28no—
355C13×C22⋊C4—44no—
356C13×C22⋊C4—44no—
357C13×C22⋊C4—44no—
358C13×C22⋊C4—44no—
359C13×C22⋊C4—44no—
360C13×C22⋊C4—44no—
361C13×C22⋊C4—44no—
362C42×C13—28no—
363C22×#123C2×C1311yescharacteristic, complemented
364C22×C4×D4C2×C1311yescharacteristic, complemented
365C2×#394C2×C1311yescharacteristic, complemented
366C2×#392C2×C1311yescharacteristic
367C2×#386C2×C1311yescharacteristic, complemented
368C2×#385C2×C1311yescharacteristic, complemented
369#1444C2×C1311yescharacteristic, complemented
370#1440C2×C1311yescharacteristic, complemented
371#1439C2×C1311yescharacteristic, complemented
372#1439C2×C1311yescharacteristic, complemented
373#1438C2×C1311yescharacteristic, complemented
374#1438C2×C1311yescharacteristic, complemented
375#1437C2×C1311yescharacteristic, complemented
376#1436C2×C1311yescharacteristic, complemented
377C22⋊#95C2×C1311yescharacteristic, complemented
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—22no—
412C23×C13—22no—
413C23×C13—22no—
414C23×C13—22no—
415C23×C13—22no—
416C23×C13—22no—
417C23×C13—22no—
418C23×C13—22no—
419C23×C13—22no—
420C23×C13—22no—
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—41no—
472C23×C13—41no—
473C23×C13—41no—
474C23×C13—41no—
475C23×C13—41no—
476C23×C13—41no—
477C23×C13—41no—
478C23×C13—41no—
479C23×C13—41no—
480C23×C13—41no—
481C23×C13#12014yes—
482C23×C13#12314yescomplemented
483C23×C13C22×D411yescharacteristic
484C23×C13C22×D411yescharacteristic
485C23×C13C22×D411yescharacteristic
486C23×C13C22×D411yescharacteristic
487C23×C13C22×D411yescharacteristic
488C23×C13C2×#4111yescharacteristic
489C23×C13C2×#4111yescharacteristic
490C23×C13C2×#4111yescharacteristic
491C23×C13C2×#4111yescharacteristic
492C23×C13C2×#4111yescharacteristic
493C23×C13C2×#4111yescharacteristic
494C23×C13H(5,𝔽2)11yescharacteristic
495C23×C13H(5,𝔽2)11yescharacteristic
496C23×C13H(5,𝔽2)11yescharacteristic
497C23×C132−1+411yescharacteristic
498D4×C13—232no—
499D4×C13—416no—
500D4×C13—416no—
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—22no—
524C2×C4×C13—22no—
525C2×C4×C13—22no—
526C2×C4×C13—22no—
527C2×C4×C13—22no—
528C2×C4×C13—22no—
529C2×C4×C13—22no—
530C2×C4×C13—22no—
531C2×C4×C13—22no—
532C2×C4×C13—22no—
533C2×C4×C13—22no—
534C2×C4×C13—22no—
535C2×C4×C13—22no—
536C2×C4×C13—22no—
537C2×C4×C13—416no—
538C2×C4×C13—416no—
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—41no—
577C2×C4×C13—41no—
578C2×C4×C13—41no—
579C2×C4×C13—41no—
580C2×C4×C13—41no—
581C2×C4×C13—41no—
582C2×C4×C13—41no—
583C2×C4×C13—41no—
584C2×C4×C13—41no—
585C2×C4×C13#12014yes—
586C2×C4×C13#12314yescomplemented
587C23×D4C22×C1311yescharacteristic
588C23×D4C22×C1311yescharacteristic
589C23×D4C22×C1311yescharacteristic
590C24×C4C22×C1311yescharacteristic
591C24×C4C22×C1311yescharacteristic
592C2×#123—24no—
593C2×#123—24no—
594C2×#123—24no—
595C2×C4×D4—24no—
596C2×C4×D4—24no—
597C2×C4×D4—24no—
598C22×C4⋊C4C22×C1311yescharacteristic
599C22×C4⋊C4C22×C1311yescharacteristic
600C22×C4⋊C4C22×C1311yescharacteristic
601C22×C4⋊C4C22×C1311yescharacteristic
602C22×C22⋊C4C22×C1311yescharacteristic
603C22×C22⋊C4C22×C1311yescharacteristic
604C22×C22⋊C4C22×C1311yescharacteristic
605C22×C22⋊C4C22×C1311yescharacteristic
606C22×C22⋊C4C22×C1311yescharacteristic
607C22×C22⋊C4C22×C1311yescharacteristic
608C22×C22⋊C4C22×C1311yescharacteristic
609C22×C22⋊C4C22×C1311yescharacteristic
610C22×C22⋊C4C22×C1311yescharacteristic
611C22×C22⋊C4C22×C1311yescharacteristic
612C22×C22⋊C4C22×C1311yescharacteristic
613C22×C22⋊C4C22×C1311yescharacteristic
614C22×C22⋊C4C22×C1311yescharacteristic
615C22×C42C22×C1311yescharacteristic
616#394—24no—
617#392—24no—
618#386—24no—
619#385—24no—
620C2×#95C22×C1311yescharacteristic
621C2×#95C22×C1311yescharacteristic
622C2×#95C22×C1311yescharacteristic
623C2×#95C22×C1311yescharacteristic
624C2×#95C22×C1311yescharacteristic
625C2×#95C22×C1311yescharacteristic
626C2×#95C22×C1311yescharacteristic
627C2×#95C22×C1311yescharacteristic
628C2×#95C22×C1311yescharacteristic
629C2×#95C22×C1311yescharacteristic
630C2×#95C22×C1311yescharacteristic
631C2×#95C22×C1311yescharacteristic
632C22×C13—24no—
633C22×C13—24no—
634C22×C13—24no—
635C22×C13—24no—
636C22×C13—24no—
637C22×C13—24no—
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—42no—
658C22×C13—42no—
659C22×C13—42no—
660C22×C13—42no—
661C22×C13—42no—
662C22×C13—42no—
663C22×C13—42no—
664C22×C13—42no—
665C22×C13—42no—
666C22×C13—42no—
667C22×C13—42no—
668C22×C13—42no—
669C22×C13—81no—
670C22×C13—81no—
671C22×C13—81no—
672C22×C13—81no—
673C22×C13—81no—
674C22×C13—81no—
675C22×C13—81no—
676C22×C13—81no—
677C22×C13C2×#12011yescharacteristic
678C22×C13C2×#12011yescharacteristic
679C22×C13C2×#12311yescharacteristic
680C22×C13C2×#12311yescharacteristic
681C22×C13#52511yescharacteristic
682C22×C13#52511yescharacteristic
683C22×C13#52511yescharacteristic
684C22×C13#52511yescharacteristic
685C22×C13#52511yescharacteristic
686C22×C13#52511yescharacteristic
687C22×C13#53211yescharacteristic
688C22×C13#53211yescharacteristic
689C22×C13#53211yescharacteristic
690C22×C13#53411yescharacteristic
691C22×C13#53711yescharacteristic
692C22×C13#53811yescharacteristic
693C22×C13#53911yescharacteristic
694C22×C13#54011yescharacteristic
695C22×C13#54211yescharacteristic
696C22×C13D4211yescharacteristic
697C22×C13D4211yescharacteristic
698C22×C13D4211yescharacteristic
699C22×C13D4211yescharacteristic
700C22×C13#54611yescharacteristic
701C22×C13#54611yescharacteristic
702C22×C13#54611yescharacteristic
703C22×C13#54711yescharacteristic
704C22×C13#54711yescharacteristic
705C22×C13#54711yescharacteristic
706C22×C13#54811yescharacteristic
707C22×C13#55011yescharacteristic
708C22×C13#55111yescharacteristic
709C22×C13#55311yescharacteristic
710C22×C13#55311yescharacteristic
711C22×C13#55911yescharacteristic
712C4×C13—24no—
713C4×C13—24no—
714C4×C13—42no—
715C4×C13—42no—
716C4×C13—42no—
717C4×C13—42no—
718C4×C13—42no—
719C4×C13—42no—
720C4×C13—42no—
721C4×C13—42no—
722C4×C13—81no—
723C4×C13—81no—
724C25C23×C1311yescharacteristic
725C25C23×C1311yescharacteristic
726C25C23×C1311yescharacteristic
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4D4×C1314yes—
748C23×C4—22no—
749C23×C4—22no—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—41no—
758C23×C4—41no—
759C23×C4—41no—
760C23×C4—41no—
761C23×C4D4×C1314yescomplemented
762C23×C4C23×C1311yescharacteristic
763C23×C4C23×C1311yescharacteristic
764C23×C4C23×C1311yescharacteristic
765C23×C4C23×C1311yescharacteristic
766C23×C4C23×C1311yescharacteristic
767C23×C4C23×C1311yescharacteristic
768C23×C4C23×C1311yescharacteristic
769C23×C4C23×C1311yescharacteristic
770C23×C4C23×C1311yescharacteristic
771C23×C4C23×C1311yescharacteristic
772C23×C4C23×C1311yescharacteristic
773C23×C4C23×C1311yescharacteristic
774#123—232no—
775C4×D4—232no—
776C2×C4⋊C4—22no—
777C2×C4⋊C4—22no—
778C2×C4⋊C4—22no—
779C2×C4⋊C4—22no—
780C2×C4⋊C4—22no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—22no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—22no—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—41no—
787C2×C4⋊C4D4×C1314yescomplemented
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—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4D4×C1314yescomplemented
826C2×C22⋊C4D4×C1314yescomplemented
827C2×C42—22no—
828C2×C42—22no—
829C2×C42—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—41no—
840#95—41no—
841#95—41no—
842C2×C13—44no—
843C2×C13—44no—
844C2×C13—82no—
845C2×C13#238811yescharacteristic
846C2×C13#240311yescharacteristic
847C2×C13#240711yescharacteristic
848C2×C13#241811yescharacteristic
849C2×C13#242211yescharacteristic
850C2×C13#243011yescharacteristic
851C2×C13#244311yescharacteristic
852C2×C13#244511yescharacteristic
853C2×C13#245511yescharacteristic
854C2×C13#245611yescharacteristic
855C2×C13#246111yescharacteristic
856C2×C13#246411yescharacteristic
857C2×C13#260211yescharacteristic
858C2×C13#263011yescharacteristic
859C2×C13#284911yescharacteristic
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—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24C2×D4×C1312yes—
899C24C2×D4×C1312yes—
900C24C2×D4×C1312yes—
901C24C2×D4×C1312yes—
902C24C2×D4×C1312yes—
903C24C13×#4112yes—
904C24C13×#4112yes—
905C24C24×C1311yescharacteristic
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—28no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—44no—
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—28no—
936C22×C4—28no—
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—21no—
985C22×C4—28no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
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—
1010C22×C4—44no—
1011C22×C4C2×D4×C1312yes—
1012C22×C4C2×D4×C1312yes—
1013C22×C4C2×D4×C1312yes—
1014C22×C4C2×D4×C1312yes—
1015C22×C4C2×D4×C1312yes—
1016C22×C4C2×D4×C1312yes—
1017C22×C4C2×D4×C1312yes—
1018C22×C4C2×D4×C1312yes—
1019C22×C4C2×D4×C1312yes—
1020C22×C4C2×D4×C1312yes—
1021C22×C4C13×#4112yes—
1022C22×C4C13×#4112yes—
1023C22×C4C13×#4112yes—
1024C22×C4C13×#4112yes—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—44no—
1029C22⋊C4—28no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C42—28no—
1043C13#1472111yescharacteristic, direct product factor, Sylow
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—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
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—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23C13×#12014yes—
1148C23C13×#12314yescomplemented
1149C23C22×D4×C1311yescharacteristic
1150C23C22×D4×C1311yescharacteristic
1151C23C22×D4×C1311yescharacteristic
1152C23C22×D4×C1311yescharacteristic
1153C23C22×D4×C1311yescharacteristic
1154C23C2×C13×#4111yescharacteristic
1155C23C2×C13×#4111yescharacteristic
1156C23C2×C13×#4111yescharacteristic
1157C23C2×C13×#4111yescharacteristic
1158C23C2×C13×#4111yescharacteristic
1159C23C2×C13×#4111yescharacteristic
1160C23C13×H(5,𝔽2)11yescharacteristic
1161C23C13×H(5,𝔽2)11yescharacteristic
1162C23C13×H(5,𝔽2)11yescharacteristic
1163C23C13×2−1+411yescharacteristic
1164D4—232no—
1165D4—416no—
1166D4—416no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—416no—
1204C2×C4—416no—
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×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4C13×#12014yes—
1252C2×C4C13×#12314yescomplemented
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—24no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22C2×C13×#12011yescharacteristic
1299C22C2×C13×#12011yescharacteristic
1300C22C2×C13×#12311yescharacteristic
1301C22C2×C13×#12311yescharacteristic
1302C22C13×#52511yescharacteristic
1303C22C13×#52511yescharacteristic
1304C22C13×#52511yescharacteristic
1305C22C13×#52511yescharacteristic
1306C22C13×#52511yescharacteristic
1307C22C13×#52511yescharacteristic
1308C22C13×#53211yescharacteristic
1309C22C13×#53211yescharacteristic
1310C22C13×#53211yescharacteristic
1311C22C13×#53411yescharacteristic
1312C22C13×#53711yescharacteristic
1313C22C13×#53811yescharacteristic
1314C22C13×#53911yescharacteristic
1315C22C13×#54011yescharacteristic
1316C22C13×#54211yescharacteristic
1317C22D42×C1311yescharacteristic
1318C22D42×C1311yescharacteristic
1319C22D42×C1311yescharacteristic
1320C22D42×C1311yescharacteristic
1321C22C13×#54611yescharacteristic
1322C22C13×#54611yescharacteristic
1323C22C13×#54611yescharacteristic
1324C22C13×#54711yescharacteristic
1325C22C13×#54711yescharacteristic
1326C22C13×#54711yescharacteristic
1327C22C13×#54811yescharacteristic
1328C22C13×#55011yescharacteristic
1329C22C13×#55111yescharacteristic
1330C22C13×#55311yescharacteristic
1331C22C13×#55311yescharacteristic
1332C22C13×#55911yescharacteristic
1333C4—24no—
1334C4—24no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—81no—
1344C4—81no—
1345C2—44no—
1346C2—44no—
1347C2—82no—
1348C2C13×#238811yescharacteristic
1349C2C13×#240311yescharacteristic
1350C2C13×#240711yescharacteristic
1351C2C13×#241811yescharacteristic
1352C2C13×#242211yescharacteristic
1353C2C13×#243011yescharacteristic
1354C2C13×#244311yescharacteristic
1355C2C13×#244511yescharacteristic
1356C2C13×#245511yescharacteristic
1357C2C13×#245611yescharacteristic
1358C2C13×#246111yescharacteristic
1359C2C13×#246411yescharacteristic
1360C2C13×#260211yescharacteristic
1361C2C13×#263011yescharacteristic
1362C2C13×#284911yescharacteristic
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. C22×C13×#123C2semidirect
2. C22×C4×D4×C13C2semidirect
3. C2×C13×#394C2semidirect
5. C2×C13×#386C2semidirect
6. C2×C13×#385C2semidirect
7. C13×#1444C2semidirect
8. C13×#1440C2semidirect
9. C13×#1439C2semidirect
10. C13×#1439C2semidirect
11. C13×#1438C2semidirect
12. C13×#1438C2semidirect
13. C13×#1437C2semidirect
14. C13×#1436C2semidirect
15. C13×C22⋊#95C2semidirect
98. C23×C4×C13D4semidirect
124. C2×C13×C4⋊C4D4semidirect
162. C2×C13×C22⋊C4D4semidirect
163. C2×C13×C22⋊C4D4semidirect
179. #14721C13direct (N × H)
363. C22×#123C2×C13semidirect
364. C22×C4×D4C2×C13semidirect
365. C2×#394C2×C13semidirect
367. C2×#386C2×C13semidirect
368. C2×#385C2×C13semidirect
369. #1444C2×C13semidirect
370. #1440C2×C13semidirect
371. #1439C2×C13semidirect
372. #1439C2×C13semidirect
373. #1438C2×C13semidirect
374. #1438C2×C13semidirect
375. #1437C2×C13semidirect
376. #1436C2×C13semidirect
377. C22⋊#95C2×C13semidirect
482. C23×C13#123semidirect
586. C2×C4×C13#123semidirect
761. C23×C4D4×C13semidirect
787. C2×C4⋊C4D4×C13semidirect
825. C2×C22⋊C4D4×C13semidirect
826. C2×C22⋊C4D4×C13semidirect
1043. C13#14721direct (N × H)
1148. C23C13×#123semidirect
1252. C2×C4C13×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1232
C22×C4×D4×C132
C2×C13×#3942
C2×C13×#3922
C2×C13×#3862
C2×C13×#3852
C13×#14442
C13×#14402
C13×#14392
C13×#14382
C13×#14372
C13×#14362
C13×C22⋊#952
#1472113