Finite Group Databasebeta

← C13×#14576 #15700915

Subgroups — C13×#14576 #15700915

Order 3328.

1498 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#397C211yesmaximal, characteristic
2C2×C13×#388C211yesmaximal, characteristic
3C2×C13×#388C211yesmaximal, characteristic
4C13×#1444C211yesmaximal, characteristic, complemented
5C13×#1443C211yesmaximal, characteristic, complemented
6C13×#1443C211yesmaximal, characteristic, complemented
7C13×#1441C211yesmaximal, characteristic, complemented
8C13×#1439C211yesmaximal, characteristic
9C13×#1436C211yesmaximal, characteristic, complemented
10C13×#1436C211yesmaximal, characteristic, complemented
11C13×#1436C211yesmaximal, characteristic, complemented
12C13×#1434C211yesmaximal, characteristic, complemented
13C13×C22⋊#95C211yesmaximal, characteristic
14C13×C22⋊#95C211yesmaximal, characteristic
15C13×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C42×C13C2211yescharacteristic
28C22×C42×C13C2211yescharacteristic
29C13×#397C418yescomplemented
30C13×#388—24no—
31C13×#388—24no—
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C25×C13C2311yescharacteristic
55C23×C4×C13—22no—
56C23×C4×C13—22no—
57C23×C4×C13—22no—
58C23×C4×C13—41no—
59C23×C4×C13—41no—
60C23×C4×C13—41no—
61C23×C4×C13—41no—
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—41no—
81C2×C13×C4⋊C4—41no—
82C2×C13×C4⋊C4—41no—
83C2×C13×C4⋊C4—41no—
84C2×C13×C4⋊C4—41no—
85C2×C13×C4⋊C4—41no—
86C2×C13×C4⋊C4—41no—
87C2×C13×C4⋊C4C2×C414yescomplemented
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—22no—
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4—22no—
92C2×C13×C22⋊C4—22no—
93C2×C13×C22⋊C4—22no—
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—41no—
97C2×C13×C22⋊C4—41no—
98C2×C13×C22⋊C4—41no—
99C2×C13×C22⋊C4—41no—
100C2×C13×C22⋊C4—41no—
101C2×C13×C22⋊C4—41no—
102C2×C13×C22⋊C4C2×C414yes—
103C2×C13×C22⋊C4C2×C414yes—
104C2×C13×C22⋊C4C2×C414yes—
105C2×C13×C22⋊C4D414yes—
106C2×C42×C13—22no—
107C2×C42×C13—22no—
108C2×C42×C13—22no—
109C2×C42×C13—41no—
110C2×C42×C13—41no—
111C2×C42×C13—41no—
112C13×#95—22no—
113C13×#95—22no—
114C13×#95—22no—
115C13×#95—22no—
116C13×#95—22no—
117C13×#95—22no—
118C13×#95—22no—
119C13×#95—22no—
120C13×#95—22no—
121C13×#95—41no—
122C13×#95—41no—
123C13×#95—41no—
124C13×#95—41no—
125C13×#95—41no—
126C13×#95—41no—
127C13×#95—41no—
128C13×#95—41no—
129C13×#95—41no—
130C13×#95—41no—
131C13×#95C2×C414yescomplemented
132C13×#95C2×C414yescomplemented
133C13×#95C2×C414yescomplemented
134#14576C1311yesmaximal, characteristic, direct product factor, Sylow
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13C22×C412yes—
148C24×C13C2×D412yes—
149C24×C13#4112yes—
150C24×C13C2411yescharacteristic
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—44no—
238C22×C4×C13—44no—
239C22×C4×C13—44no—
240C22×C4×C13—44no—
241C22×C4×C13—44no—
242C22×C4×C13—44no—
243C22×C4×C13—44no—
244C22×C4×C13C22×C412yes—
245C22×C4×C13C22×C412yes—
246C22×C4×C13C22×C412yes—
247C22×C4×C13C22×C412yes—
248C22×C4×C13C22×C412yes—
249C22×C4×C13C22×C412yes—
250C22×C4×C13C2×D412yes—
251C22×C4×C13C2×D412yes—
252C22×C4×C13#4112yes—
253C22×C4×C13#4112yes—
254C22×C4×C13#4112yes—
255C22×C4×C13#4112yes—
256C13×C4⋊C4—44no—
257C13×C4⋊C4—44no—
258C13×C4⋊C4—44no—
259C13×C4⋊C4—44no—
260C13×C22⋊C4—28no—
261C13×C22⋊C4—28no—
262C13×C22⋊C4—44no—
263C13×C22⋊C4—44no—
264C13×C22⋊C4—44no—
265C13×C22⋊C4—44no—
266C42×C13—44no—
267C42×C13—44no—
268C2×#397C2×C1311yescharacteristic
269C2×#388C2×C1311yescharacteristic
270C2×#388C2×C1311yescharacteristic
271#1444C2×C1311yescharacteristic, complemented
272#1443C2×C1311yescharacteristic, complemented
273#1443C2×C1311yescharacteristic, complemented
274#1441C2×C1311yescharacteristic, complemented
275#1439C2×C1311yescharacteristic
276#1436C2×C1311yescharacteristic, complemented
277#1436C2×C1311yescharacteristic, complemented
278#1436C2×C1311yescharacteristic, complemented
279#1434C2×C1311yescharacteristic, complemented
280C22⋊#95C2×C1311yescharacteristic
281C22⋊#95C2×C1311yescharacteristic
282C22⋊#95C2×C1311yescharacteristic
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—41no—
302C23×C13—41no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13C4×D414yes—
318C23×C13C23×C411yescharacteristic
319C23×C13C22×D411yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13C2×#4111yescharacteristic
322C23×C13C2×#4111yescharacteristic
323C23×C13C2×#4111yescharacteristic
324C23×C13C2×#4111yescharacteristic
325C23×C13H(5,𝔽2)11yescharacteristic
326C23×C13H(5,𝔽2)11yescharacteristic
327C23×C13H(5,𝔽2)11yescharacteristic
328C23×C13H(5,𝔽2)11yescharacteristic
329C23×C13H(5,𝔽2)11yescharacteristic
330C23×C132−1+411yescharacteristic
331C23×C132−1+411yescharacteristic
332C23×C132−1+411yescharacteristic
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—416no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13—41no—
421C2×C4×C13—41no—
422C2×C4×C13—41no—
423C2×C4×C13—41no—
424C2×C4×C13—41no—
425C2×C4×C13—41no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—41no—
430C2×C4×C13—41no—
431C2×C4×C13—41no—
432C24×C4C22×C1311yescharacteristic
433C22×C4⋊C4C22×C1311yescharacteristic
434C22×C4⋊C4C22×C1311yescharacteristic
435C22×C4⋊C4C22×C1311yescharacteristic
436C22×C4⋊C4C22×C1311yescharacteristic
437C22×C22⋊C4C22×C1311yescharacteristic
438C22×C22⋊C4C22×C1311yescharacteristic
439C22×C22⋊C4C22×C1311yescharacteristic
440C22×C22⋊C4C22×C1311yescharacteristic
441C22×C22⋊C4C22×C1311yescharacteristic
442C22×C22⋊C4C22×C1311yescharacteristic
443C22×C42C22×C1311yescharacteristic
444C22×C42C22×C1311yescharacteristic
445#397C4×C1318yescomplemented
446#388—24no—
447#388—24no—
448C2×#95C22×C1311yescharacteristic
449C2×#95C22×C1311yescharacteristic
450C2×#95C22×C1311yescharacteristic
451C2×#95C22×C1311yescharacteristic
452C2×#95C22×C1311yescharacteristic
453C2×#95C22×C1311yescharacteristic
454C2×#95C22×C1311yescharacteristic
455C2×#95C22×C1311yescharacteristic
456C2×#95C22×C1311yescharacteristic
457C2×#95C22×C1311yescharacteristic
458C2×#95C22×C1311yescharacteristic
459C2×#95C22×C1311yescharacteristic
460C2×#95C22×C1311yescharacteristic
461C2×#95C22×C1311yescharacteristic
462C2×#95C22×C1311yescharacteristic
463C2×#95C22×C1311yescharacteristic
464C2×#95C22×C1311yescharacteristic
465C2×#95C22×C1311yescharacteristic
466C2×#95C22×C1311yescharacteristic
467C2×#95C22×C1311yescharacteristic
468C2×#95C22×C1311yescharacteristic
469C2×#95C22×C1311yescharacteristic
470C22×C13—24no—
471C22×C13—24no—
472C22×C13—24no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—42no—
483C22×C13—42no—
484C22×C13—42no—
485C22×C13C2×C4×D411yescharacteristic
486C22×C13C4×#4111yescharacteristic
487C22×C13C4×#4111yescharacteristic
488C22×C13#51811yescharacteristic
489C22×C13#52011yescharacteristic
490C22×C13#52011yescharacteristic
491C22×C13#52011yescharacteristic
492C22×C13#53411yescharacteristic
493C22×C13#53711yescharacteristic
494C22×C13#53811yescharacteristic
495C22×C13#53811yescharacteristic
496C22×C13#53811yescharacteristic
497C22×C13#53811yescharacteristic
498C22×C13#53911yescharacteristic
499C22×C13#53911yescharacteristic
500C22×C13#54011yescharacteristic
501C22×C13#54211yescharacteristic
502C22×C13#54211yescharacteristic
503C22×C13#54211yescharacteristic
504C22×C13#54611yescharacteristic
505C22×C13#54611yescharacteristic
506C22×C13#54711yescharacteristic
507C22×C13#54711yescharacteristic
508C22×C13#55111yescharacteristic
509C22×C13#55111yescharacteristic
510C22×C13#55111yescharacteristic
511C22×C13#55211yescharacteristic
512C22×C13#55211yescharacteristic
513C22×C13#55211yescharacteristic
514C22×C13#55311yescharacteristic
515C22×C13#55611yescharacteristic
516C22×C13#56011yescharacteristic
517C22×C13#56311yescharacteristic
518C22×C13#56311yescharacteristic
519C22×C13#56311yescharacteristic
520C4×C13—42no—
521C4×C13—42no—
522C4×C13—42no—
523C4×C13—42no—
524C4×C13—42no—
525C4×C13—42no—
526C4×C13—42no—
527C4×C13—42no—
528C4×C13—42no—
529C4×C13—42no—
530C4×C13—42no—
531C4×C13—42no—
532C4×C13—81no—
533C4×C13—81no—
534C25C23×C1311yescharacteristic
535C23×C4—22no—
536C23×C4—22no—
537C23×C4—22no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4—41no—
541C23×C4—41no—
542C23×C4C23×C1311yescharacteristic
543C23×C4C23×C1311yescharacteristic
544C23×C4C23×C1311yescharacteristic
545C23×C4C23×C1311yescharacteristic
546C23×C4C23×C1311yescharacteristic
547C23×C4C23×C1311yescharacteristic
548C23×C4C23×C1311yescharacteristic
549C23×C4C23×C1311yescharacteristic
550C23×C4C23×C1311yescharacteristic
551C23×C4C23×C1311yescharacteristic
552C23×C4C23×C1311yescharacteristic
553C23×C4C23×C1311yescharacteristic
554C23×C4C23×C1311yescharacteristic
555C23×C4C23×C1311yescharacteristic
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4C2×C4×C1314yescomplemented
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—41no—
579C2×C22⋊C4—41no—
580C2×C22⋊C4—41no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4C2×C4×C1314yes—
583C2×C22⋊C4C2×C4×C1314yes—
584C2×C22⋊C4C2×C4×C1314yes—
585C2×C22⋊C4D4×C1314yes—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—22no—
589C2×C42—41no—
590C2×C42—41no—
591C2×C42—41no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—41no—
602#95—41no—
603#95—41no—
604#95—41no—
605#95—41no—
606#95—41no—
607#95—41no—
608#95—41no—
609#95—41no—
610#95—41no—
611#95C2×C4×C1314yescomplemented
612#95C2×C4×C1314yescomplemented
613#95C2×C4×C1314yescomplemented
614C2×C13—44no—
615C2×C13#232511yescharacteristic
616C2×C13#233511yescharacteristic
617C2×C13#233711yescharacteristic
618C2×C13#235911yescharacteristic
619C2×C13#235911yescharacteristic
620C2×C13#237311yescharacteristic
621C2×C13#238311yescharacteristic
622C2×C13#268811yescharacteristic
623C2×C13#269511yescharacteristic
624C2×C13#271511yescharacteristic
625C2×C13#271711yescharacteristic
626C2×C13#273511yescharacteristic
627C2×C13#273811yescharacteristic
628C2×C13#274511yescharacteristic
629C2×C13#276511yescharacteristic
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24C22×C4×C1312yes—
643C24C2×D4×C1312yes—
644C24C13×#4112yes—
645C24C24×C1311yescharacteristic
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4C22×C4×C1312yes—
740C22×C4C22×C4×C1312yes—
741C22×C4C22×C4×C1312yes—
742C22×C4C22×C4×C1312yes—
743C22×C4C22×C4×C1312yes—
744C22×C4C22×C4×C1312yes—
745C22×C4C2×D4×C1312yes—
746C22×C4C2×D4×C1312yes—
747C22×C4C13×#4112yes—
748C22×C4C13×#4112yes—
749C22×C4C13×#4112yes—
750C22×C4C13×#4112yes—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C22⋊C4—28no—
756C22⋊C4—28no—
757C22⋊C4—44no—
758C22⋊C4—44no—
759C22⋊C4—44no—
760C22⋊C4—44no—
761C42—44no—
762C42—44no—
763C13#1457611yescharacteristic, direct product factor, Sylow
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23C4×D4×C1314yes—
799C23C23×C4×C1311yescharacteristic
800C23C22×D4×C1311yescharacteristic
801C23C2×C13×#4111yescharacteristic
802C23C2×C13×#4111yescharacteristic
803C23C2×C13×#4111yescharacteristic
804C23C2×C13×#4111yescharacteristic
805C23C2×C13×#4111yescharacteristic
806C23C13×H(5,𝔽2)11yescharacteristic
807C23C13×H(5,𝔽2)11yescharacteristic
808C23C13×H(5,𝔽2)11yescharacteristic
809C23C13×H(5,𝔽2)11yescharacteristic
810C23C13×H(5,𝔽2)11yescharacteristic
811C23C13×2−1+411yescharacteristic
812C23C13×2−1+411yescharacteristic
813C23C13×2−1+411yescharacteristic
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—416no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×C4×D4×C1311yescharacteristic
929C22C4×C13×#4111yescharacteristic
930C22C4×C13×#4111yescharacteristic
931C22C13×#51811yescharacteristic
932C22C13×#52011yescharacteristic
933C22C13×#52011yescharacteristic
934C22C13×#52011yescharacteristic
935C22C13×#53411yescharacteristic
936C22C13×#53711yescharacteristic
937C22C13×#53811yescharacteristic
938C22C13×#53811yescharacteristic
939C22C13×#53811yescharacteristic
940C22C13×#53811yescharacteristic
941C22C13×#53911yescharacteristic
942C22C13×#53911yescharacteristic
943C22C13×#54011yescharacteristic
944C22C13×#54211yescharacteristic
945C22C13×#54211yescharacteristic
946C22C13×#54211yescharacteristic
947C22C13×#54611yescharacteristic
948C22C13×#54611yescharacteristic
949C22C13×#54711yescharacteristic
950C22C13×#54711yescharacteristic
951C22C13×#55111yescharacteristic
952C22C13×#55111yescharacteristic
953C22C13×#55111yescharacteristic
954C22C13×#55211yescharacteristic
955C22C13×#55211yescharacteristic
956C22C13×#55211yescharacteristic
957C22C13×#55311yescharacteristic
958C22C13×#55611yescharacteristic
959C22C13×#56011yescharacteristic
960C22C13×#56311yescharacteristic
961C22C13×#56311yescharacteristic
962C22C13×#56311yescharacteristic
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—81no—
976C4—81no—
977C2—44no—
978C2C13×#232511yescharacteristic
979C2C13×#233511yescharacteristic
980C2C13×#233711yescharacteristic
981C2C13×#235911yescharacteristic
982C2C13×#235911yescharacteristic
983C2C13×#237311yescharacteristic
984C2C13×#238311yescharacteristic
985C2C13×#268811yescharacteristic
986C2C13×#269511yescharacteristic
987C2C13×#271511yescharacteristic
988C2C13×#271711yescharacteristic
989C2C13×#273511yescharacteristic
990C2C13×#273811yescharacteristic
991C2C13×#274511yescharacteristic
992C2C13×#276511yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C13×#1444C2semidirect
5. C13×#1443C2semidirect
6. C13×#1443C2semidirect
7. C13×#1441C2semidirect
9. C13×#1436C2semidirect
10. C13×#1436C2semidirect
11. C13×#1436C2semidirect
12. C13×#1434C2semidirect
29. C13×#397C4semidirect
87. C2×C13×C4⋊C4C2×C4semidirect
131. C13×#95C2×C4semidirect
132. C13×#95C2×C4semidirect
133. C13×#95C2×C4semidirect
134. #14576C13direct (N × H)
271. #1444C2×C13semidirect
272. #1443C2×C13semidirect
273. #1443C2×C13semidirect
274. #1441C2×C13semidirect
276. #1436C2×C13semidirect
277. #1436C2×C13semidirect
278. #1436C2×C13semidirect
279. #1434C2×C13semidirect
445. #397C4×C13semidirect
567. C2×C4⋊C4C2×C4×C13semidirect
611. #95C2×C4×C13semidirect
612. #95C2×C4×C13semidirect
613. #95C2×C4×C13semidirect
763. C13#14576direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3972
C2×C13×#3882
C13×#14442
C13×#14432
C13×#14412
C13×#14392
C13×#14362
C13×#14342
C13×C22⋊#952
#1457613