Finite Group Databasebeta

← C13×#14456 #15700795

Subgroups — C13×#14456 #15700795

Order 3328.

1450 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#385C211yesmaximal, characteristic
2C13×#1445C211yesmaximal, characteristic, complemented
3C13×#1443C211yesmaximal, characteristic, complemented
4C13×#1441C211yesmaximal, characteristic, complemented
5C13×#1441C211yesmaximal, characteristic, complemented
6C13×#1439C211yesmaximal, characteristic
7C13×#1439C211yesmaximal, characteristic
8C13×#1437C211yesmaximal, characteristic
9C13×#1437C211yesmaximal, characteristic
10C13×#1436C211yesmaximal, characteristic, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C13×#1434C211yesmaximal, characteristic, complemented
13C13×#1434C211yesmaximal, characteristic, complemented
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×#385C418yescomplemented
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
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
52C25×C13C2311yescharacteristic
53C23×C4×C13—41no—
54C23×C4×C13—41no—
55C23×C4×C13—41no—
56C23×C4×C13—41no—
57C23×C4×C13—41no—
58C23×C4×C13—41no—
59C23×C4×C13C2×C414yes—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
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
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—41no—
77C2×C13×C4⋊C4—41no—
78C2×C13×C4⋊C4—41no—
79C2×C13×C4⋊C4—41no—
80C2×C13×C4⋊C4—41no—
81C2×C13×C4⋊C4—41no—
82C2×C13×C4⋊C4—41no—
83C2×C13×C4⋊C4—41no—
84C2×C13×C4⋊C4C2×C414yes—
85C2×C13×C4⋊C4C2×C414yes—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—22no—
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—41no—
94C2×C13×C22⋊C4—41no—
95C2×C13×C22⋊C4—41no—
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⋊C4C2×C414yes—
102C2×C13×C22⋊C4C2×C414yes—
103C2×C13×C22⋊C4Q814yes—
104C2×C42×C13—22no—
105C2×C42×C13—22no—
106C2×C42×C13—22no—
107C2×C42×C13—41no—
108C2×C42×C13—41no—
109C2×C42×C13—41no—
110C13×#95—22no—
111C13×#95—22no—
112C13×#95—22no—
113C13×#95—41no—
114C13×#95—41no—
115C13×#95—41no—
116C13×#95—41no—
117C13×#95—41no—
118C13×#95—41no—
119C13×#95—41no—
120C13×#95—41no—
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×#95C2×C414yes—
131C13×#95C2×C414yes—
132#14456C1311yesmaximal, characteristic, direct product factor, Sylow
133C24×C13—21no—
134C24×C13—21no—
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×C13C22×C412yes—
146C24×C13C2×Q812yes—
147C24×C13#4112yes—
148C24×C13C2411yescharacteristic
149C22×C4×C13—21no—
150C22×C4×C13—21no—
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—44no—
236C22×C4×C13—44no—
237C22×C4×C13—44no—
238C22×C4×C13—44no—
239C22×C4×C13—44no—
240C22×C4×C13—44no—
241C22×C4×C13—44no—
242C22×C4×C13C22×C412yes—
243C22×C4×C13C22×C412yes—
244C22×C4×C13C22×C412yes—
245C22×C4×C13C22×C412yes—
246C22×C4×C13C22×C412yes—
247C22×C4×C13C22×C412yes—
248C22×C4×C13C2×Q812yes—
249C22×C4×C13C2×Q812yes—
250C22×C4×C13#4112yes—
251C22×C4×C13#4112yes—
252C22×C4×C13#4112yes—
253C22×C4×C13#4112yes—
254C13×C4⋊C4—44no—
255C13×C4⋊C4—44no—
256C13×C4⋊C4—44no—
257C13×C4⋊C4—44no—
258C13×C22⋊C4—28no—
259C13×C22⋊C4—44no—
260C13×C22⋊C4—44no—
261C13×C22⋊C4—44no—
262C13×C22⋊C4—44no—
263C13×C22⋊C4—44no—
264C42×C13—44no—
265C42×C13—44no—
266C2×#385C2×C1311yescharacteristic
267#1445C2×C1311yescharacteristic, complemented
268#1443C2×C1311yescharacteristic, complemented
269#1441C2×C1311yescharacteristic, complemented
270#1441C2×C1311yescharacteristic, complemented
271#1439C2×C1311yescharacteristic
272#1439C2×C1311yescharacteristic
273#1437C2×C1311yescharacteristic
274#1437C2×C1311yescharacteristic
275#1436C2×C1311yescharacteristic, complemented
276C4⋊#95C2×C1311yescharacteristic, complemented
277#1434C2×C1311yescharacteristic, complemented
278#1434C2×C1311yescharacteristic, complemented
279C22⋊#95C2×C1311yescharacteristic
280C22⋊#95C2×C1311yescharacteristic
281C23×C13—22no—
282C23×C13—22no—
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—41no—
300C23×C13—41no—
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×C13C4×Q814yes—
316C23×C13C23×C411yescharacteristic
317C23×C13C22×Q811yescharacteristic
318C23×C13C2×#4111yescharacteristic
319C23×C13C2×#4111yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13C2×#4111yescharacteristic
322C23×C13C2×#4111yescharacteristic
323C23×C13H(5,𝔽2)11yescharacteristic
324C23×C13H(5,𝔽2)11yescharacteristic
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
331C2×C4×C13—22no—
332C2×C4×C13—22no—
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—416no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
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#11714yes—
430C24×C4C22×C1311yescharacteristic
431C22×C4⋊C4C22×C1311yescharacteristic
432C22×C4⋊C4C22×C1311yescharacteristic
433C22×C4⋊C4C22×C1311yescharacteristic
434C22×C4⋊C4C22×C1311yescharacteristic
435C22×C22⋊C4C22×C1311yescharacteristic
436C22×C22⋊C4C22×C1311yescharacteristic
437C22×C22⋊C4C22×C1311yescharacteristic
438C22×C22⋊C4C22×C1311yescharacteristic
439C22×C22⋊C4C22×C1311yescharacteristic
440C22×C22⋊C4C22×C1311yescharacteristic
441C22×C42C22×C1311yescharacteristic
442C22×C42C22×C1311yescharacteristic
443#385C4×C1318yescomplemented
444C2×#95C22×C1311yescharacteristic
445C2×#95C22×C1311yescharacteristic
446C2×#95C22×C1311yescharacteristic
447C2×#95C22×C1311yescharacteristic
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
466C22×C13—24no—
467C22×C13—24no—
468C22×C13—24no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—42no—
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×C13C2×#11711yescharacteristic
482C22×C13C2×C4×Q811yescharacteristic
483C22×C13C4×#4111yescharacteristic
484C22×C13#51811yescharacteristic
485C22×C13#51811yescharacteristic
486C22×C13#51811yescharacteristic
487C22×C13#52011yescharacteristic
488C22×C13#53811yescharacteristic
489C22×C13#53811yescharacteristic
490C22×C13#53911yescharacteristic
491C22×C13#53911yescharacteristic
492C22×C13#54011yescharacteristic
493C22×C13#54011yescharacteristic
494C22×C13#54011yescharacteristic
495C22×C13#54211yescharacteristic
496C22×C13#54211yescharacteristic
497C22×C13#54211yescharacteristic
498C22×C13#54311yescharacteristic
499C22×C13#54411yescharacteristic
500C22×C13#55111yescharacteristic
501C22×C13#55111yescharacteristic
502C22×C13#55111yescharacteristic
503C22×C13#55111yescharacteristic
504C22×C13#55311yescharacteristic
505C22×C13#55311yescharacteristic
506C22×C13#55311yescharacteristic
507C22×C13#55311yescharacteristic
508C22×C13#55411yescharacteristic
509C22×C13#55411yescharacteristic
510C22×C13#55411yescharacteristic
511C22×C13#55411yescharacteristic
512C22×C13#56011yescharacteristic
513C22×C13#56011yescharacteristic
514C22×C13#56011yescharacteristic
515C22×C13H(3,𝔽4)11yescharacteristic
516C4×C13—24no—
517C4×C13—42no—
518C4×C13—42no—
519C4×C13—42no—
520C4×C13—42no—
521C4×C13—42no—
522C4×C13—42no—
523C4×C13—42no—
524C4×C13—42no—
525C4×C13—42no—
526C4×C13—81no—
527C4×C13—81no—
528C4×C13—81no—
529C4×C13—81no—
530C25C23×C1311yescharacteristic
531C23×C4—41no—
532C23×C4—41no—
533C23×C4—41no—
534C23×C4—41no—
535C23×C4—41no—
536C23×C4—41no—
537C23×C4C2×C4×C1314yes—
538C23×C4C23×C1311yescharacteristic
539C23×C4C23×C1311yescharacteristic
540C23×C4C23×C1311yescharacteristic
541C23×C4C23×C1311yescharacteristic
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
552C2×C4⋊C4—22no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4—41no—
557C2×C4⋊C4—41no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—41no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4C2×C4×C1314yes—
563C2×C4⋊C4C2×C4×C1314yes—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—41no—
579C2×C22⋊C4C2×C4×C1314yes—
580C2×C22⋊C4C2×C4×C1314yes—
581C2×C22⋊C4Q8×C1314yes—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—41no—
586C2×C42—41no—
587C2×C42—41no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—41no—
592#95—41no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95—41no—
599#95—41no—
600#95—41no—
601#95—41no—
602#95—41no—
603#95—41no—
604#95—41no—
605#95—41no—
606#95—41no—
607#95—41no—
608#95C2×C4×C1314yes—
609#95C2×C4×C1314yes—
610C2×C13—44no—
611C2×C13#231911yescharacteristic
612C2×C13#232911yescharacteristic
613C2×C13#233511yescharacteristic
614C2×C13#234511yescharacteristic
615C2×C13#235311yescharacteristic
616C2×C13#236811yescharacteristic
617C2×C13#237511yescharacteristic
618C2×C13#274611yescharacteristic
619C2×C13#274811yescharacteristic
620C2×C13#274911yescharacteristic
621C2×C13#275311yescharacteristic
622C2×C13#275711yescharacteristic
623C2×C13#276311yescharacteristic
624C2×C13#278011yescharacteristic
625C2×C13#279011yescharacteristic
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24C22×C4×C1312yes—
639C24C2×Q8×C1312yes—
640C24C13×#4112yes—
641C24C24×C1311yescharacteristic
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
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—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4C22×C4×C1312yes—
736C22×C4C22×C4×C1312yes—
737C22×C4C22×C4×C1312yes—
738C22×C4C22×C4×C1312yes—
739C22×C4C22×C4×C1312yes—
740C22×C4C22×C4×C1312yes—
741C22×C4C2×Q8×C1312yes—
742C22×C4C2×Q8×C1312yes—
743C22×C4C13×#4112yes—
744C22×C4C13×#4112yes—
745C22×C4C13×#4112yes—
746C22×C4C13×#4112yes—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C22⋊C4—28no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C22⋊C4—44no—
757C42—44no—
758C42—44no—
759C13#1445611yescharacteristic, direct product factor, Sylow
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
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—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23C4×Q8×C1314yes—
795C23C23×C4×C1311yescharacteristic
796C23C22×Q8×C1311yescharacteristic
797C23C2×C13×#4111yescharacteristic
798C23C2×C13×#4111yescharacteristic
799C23C2×C13×#4111yescharacteristic
800C23C2×C13×#4111yescharacteristic
801C23C2×C13×#4111yescharacteristic
802C23C13×H(5,𝔽2)11yescharacteristic
803C23C13×H(5,𝔽2)11yescharacteristic
804C23C13×H(5,𝔽2)11yescharacteristic
805C23C13×H(5,𝔽2)11yescharacteristic
806C23C13×H(5,𝔽2)11yescharacteristic
807C23C13×H(5,𝔽2)11yescharacteristic
808C23C13×H(5,𝔽2)11yescharacteristic
809C23C13×2−1+411yescharacteristic
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
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—416no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
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×C4C13×#11714yes—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22C2×C13×#11711yescharacteristic
925C22C2×C4×Q8×C1311yescharacteristic
926C22C4×C13×#4111yescharacteristic
927C22C13×#51811yescharacteristic
928C22C13×#51811yescharacteristic
929C22C13×#51811yescharacteristic
930C22C13×#52011yescharacteristic
931C22C13×#53811yescharacteristic
932C22C13×#53811yescharacteristic
933C22C13×#53911yescharacteristic
934C22C13×#53911yescharacteristic
935C22C13×#54011yescharacteristic
936C22C13×#54011yescharacteristic
937C22C13×#54011yescharacteristic
938C22C13×#54211yescharacteristic
939C22C13×#54211yescharacteristic
940C22C13×#54211yescharacteristic
941C22C13×#54311yescharacteristic
942C22C13×#54411yescharacteristic
943C22C13×#55111yescharacteristic
944C22C13×#55111yescharacteristic
945C22C13×#55111yescharacteristic
946C22C13×#55111yescharacteristic
947C22C13×#55311yescharacteristic
948C22C13×#55311yescharacteristic
949C22C13×#55311yescharacteristic
950C22C13×#55311yescharacteristic
951C22C13×#55411yescharacteristic
952C22C13×#55411yescharacteristic
953C22C13×#55411yescharacteristic
954C22C13×#55411yescharacteristic
955C22C13×#56011yescharacteristic
956C22C13×#56011yescharacteristic
957C22C13×#56011yescharacteristic
958C22C13×H(3,𝔽4)11yescharacteristic
959C4—24no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—81no—
970C4—81no—
971C4—81no—
972C4—81no—
973C2—44no—
974C2C13×#231911yescharacteristic
975C2C13×#232911yescharacteristic
976C2C13×#233511yescharacteristic
977C2C13×#234511yescharacteristic
978C2C13×#235311yescharacteristic
979C2C13×#236811yescharacteristic
980C2C13×#237511yescharacteristic
981C2C13×#274611yescharacteristic
982C2C13×#274811yescharacteristic
983C2C13×#274911yescharacteristic
984C2C13×#275311yescharacteristic
985C2C13×#275711yescharacteristic
986C2C13×#276311yescharacteristic
987C2C13×#278011yescharacteristic
988C2C13×#279011yescharacteristic
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
2. C13×#1445C2semidirect
3. C13×#1443C2semidirect
4. C13×#1441C2semidirect
5. C13×#1441C2semidirect
10. C13×#1436C2semidirect
11. C13×C4⋊#95C2semidirect
12. C13×#1434C2semidirect
13. C13×#1434C2semidirect
29. C13×#385C4semidirect
132. #14456C13direct (N × H)
267. #1445C2×C13semidirect
268. #1443C2×C13semidirect
269. #1441C2×C13semidirect
270. #1441C2×C13semidirect
275. #1436C2×C13semidirect
276. C4⋊#95C2×C13semidirect
277. #1434C2×C13semidirect
278. #1434C2×C13semidirect
443. #385C4×C13semidirect
759. C13#14456direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3852
C13×#14452
C13×#14432
C13×#14412
C13×#14392
C13×#14372
C13×#14362
C13×C4⋊#952
C13×#14342
C13×C22⋊#952
#1445613