Finite Group Databasebeta

← C13×#14412 #15700751

Subgroups — C13×#14412 #15700751

Order 3328.

1398 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#388C211yesmaximal, characteristic
2C2×C13×#388C211yesmaximal, characteristic
3C2×C13×#382C211yesmaximal, characteristic, complemented
4C13×#1445C211yesmaximal, characteristic, complemented
5C13×#1442C211yesmaximal, characteristic, complemented
6C13×#1440C211yesmaximal, characteristic
7C13×#1439C211yesmaximal, characteristic
8C13×#1439C211yesmaximal, characteristic
9C13×#1439C211yesmaximal, characteristic
10C13×#1437C211yesmaximal, characteristic
11C13×#1436C211yesmaximal, characteristic, complemented
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×#1436C211yesmaximal, characteristic, complemented
15C13×C4⋊#95C211yesmaximal, characteristic, complemented
16C22×C13×C4⋊C4C2211yescharacteristic
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×C13×C22⋊C4C2211yescharacteristic
28C22×C42×C13C2211yescharacteristic
29C22×C42×C13C2211yescharacteristic
30C22×C42×C13C2211yescharacteristic
31C13×#388—24no—
32C13×#388C418yescomplemented
33C13×#382—24no—
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×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
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
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
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⋊C4C2×C414yes—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
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—41no—
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⋊C4—41no—
102C2×C13×C22⋊C4C2×C414yes—
103C2×C13×C22⋊C4C2×C414yes—
104C2×C13×C22⋊C4C2×C414yes—
105C2×C42×C13—22no—
106C2×C42×C13—22no—
107C2×C42×C13—22no—
108C2×C42×C13—41no—
109C2×C42×C13—41no—
110C2×C42×C13—41no—
111C2×C42×C13—41no—
112C2×C42×C13—41no—
113C2×C42×C13C2×C414yes—
114C13×#95—22no—
115C13×#95—22no—
116C13×#95—22no—
117C13×#95—22no—
118C13×#95—22no—
119C13×#95—22no—
120C13×#95—22no—
121C13×#95—22no—
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×C414yes—
132C13×#95C2×C414yes—
133C13×#95D414yes—
134#14412C1311yesmaximal, 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×C13—21no—
148C24×C13—21no—
149C24×C13C22×C412yes—
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×C13C22×C412yes—
236C22×C4×C13C22×C412yes—
237C22×C4×C13C22×C412yes—
238C22×C4×C13C22×C412yes—
239C22×C4×C13C22×C412yes—
240C22×C4×C13C22×C412yes—
241C22×C4×C13C2×D412yes—
242C22×C4×C13C2×D412yes—
243C22×C4×C13C2×D412yes—
244C22×C4×C13#4112yes—
245C22×C4×C13#4112yes—
246C22×C4×C13#4112yes—
247C22×C4×C13#4112yes—
248C22×C4×C13#4112yes—
249C13×C4⋊C4—44no—
250C13×C4⋊C4—44no—
251C13×C4⋊C4—44no—
252C13×C4⋊C4—44no—
253C13×C4⋊C4—44no—
254C13×C22⋊C4—28no—
255C13×C22⋊C4—28no—
256C13×C22⋊C4—44no—
257C13×C22⋊C4—44no—
258C13×C22⋊C4—44no—
259C13×C22⋊C4—44no—
260C13×C22⋊C4—44no—
261C42×C13—28no—
262C42×C13—44no—
263C42×C13—44no—
264C2×#388C2×C1311yescharacteristic
265C2×#388C2×C1311yescharacteristic
266C2×#382C2×C1311yescharacteristic, complemented
267#1445C2×C1311yescharacteristic, complemented
268#1442C2×C1311yescharacteristic, complemented
269#1440C2×C1311yescharacteristic
270#1439C2×C1311yescharacteristic
271#1439C2×C1311yescharacteristic
272#1439C2×C1311yescharacteristic
273#1437C2×C1311yescharacteristic
274#1436C2×C1311yescharacteristic, complemented
275#1436C2×C1311yescharacteristic, complemented
276#1436C2×C1311yescharacteristic, complemented
277#1436C2×C1311yescharacteristic, complemented
278C4⋊#95C2×C1311yescharacteristic, complemented
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—41no—
287C23×C13—41no—
288C23×C13—41no—
289C23×C13—41no—
290C23×C13—41no—
291C23×C13—41no—
292C23×C13—41no—
293C23×C13—41no—
294C23×C13—41no—
295C23×C13—41no—
296C23×C13—41no—
297C23×C13—41no—
298C23×C13—41no—
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×C13C23×C411yescharacteristic
315C23×C13C22×D411yescharacteristic
316C23×C13C2×#4111yescharacteristic
317C23×C13C2×#4111yescharacteristic
318C23×C13C2×#4111yescharacteristic
319C23×C13C2×#4111yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13H(5,𝔽2)11yescharacteristic
322C23×C13H(5,𝔽2)11yescharacteristic
323C23×C13H(5,𝔽2)11yescharacteristic
324C23×C13H(5,𝔽2)11yescharacteristic
325C23×C13H(5,𝔽2)11yescharacteristic
326C23×C132−1+411yescharacteristic
327C23×C132−1+411yescharacteristic
328C23×C132−1+411yescharacteristic
329C2×C4×C13—22no—
330C2×C4×C13—22no—
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—22no—
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#11714yes—
426C2×C4×C13C4×D414yes—
427C22×C4⋊C4C22×C1311yescharacteristic
428C22×C4⋊C4C22×C1311yescharacteristic
429C22×C4⋊C4C22×C1311yescharacteristic
430C22×C4⋊C4C22×C1311yescharacteristic
431C22×C4⋊C4C22×C1311yescharacteristic
432C22×C22⋊C4C22×C1311yescharacteristic
433C22×C22⋊C4C22×C1311yescharacteristic
434C22×C22⋊C4C22×C1311yescharacteristic
435C22×C22⋊C4C22×C1311yescharacteristic
436C22×C22⋊C4C22×C1311yescharacteristic
437C22×C22⋊C4C22×C1311yescharacteristic
438C22×C22⋊C4C22×C1311yescharacteristic
439C22×C42C22×C1311yescharacteristic
440C22×C42C22×C1311yescharacteristic
441C22×C42C22×C1311yescharacteristic
442#388—24no—
443#388C4×C1318yescomplemented
444#382—24no—
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
465C22×C13—42no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—81no—
473C22×C13—81no—
474C22×C13—81no—
475C22×C13—81no—
476C22×C13—81no—
477C22×C13—81no—
478C22×C13—81no—
479C22×C13—81no—
480C22×C13C2×#11711yescharacteristic
481C22×C13C2×C4×D411yescharacteristic
482C22×C13C4×#4111yescharacteristic
483C22×C13#51811yescharacteristic
484C22×C13#52011yescharacteristic
485C22×C13#52011yescharacteristic
486C22×C13#52011yescharacteristic
487C22×C13#53511yescharacteristic
488C22×C13#53711yescharacteristic
489C22×C13#53811yescharacteristic
490C22×C13#53911yescharacteristic
491C22×C13#54011yescharacteristic
492C22×C13#54011yescharacteristic
493C22×C13#54111yescharacteristic
494C22×C13#54111yescharacteristic
495C22×C13#54211yescharacteristic
496C22×C13#54211yescharacteristic
497C22×C13#54211yescharacteristic
498C22×C13#54211yescharacteristic
499C22×C13#54611yescharacteristic
500C22×C13#54611yescharacteristic
501C22×C13#54711yescharacteristic
502C22×C13#54811yescharacteristic
503C22×C13#55111yescharacteristic
504C22×C13#55211yescharacteristic
505C22×C13#55211yescharacteristic
506C22×C13#55311yescharacteristic
507C22×C13#55311yescharacteristic
508C22×C13#55311yescharacteristic
509C22×C13#55911yescharacteristic
510C22×C13#55911yescharacteristic
511C22×C13H(3,𝔽4)11yescharacteristic
512C22×C13#56211yescharacteristic
513C22×C13#56211yescharacteristic
514C22×C13#56311yescharacteristic
515C4×C13—24no—
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—81no—
526C4×C13—81no—
527C4×C13—81no—
528C4×C13—81no—
529C25C23×C1311yescharacteristic
530C23×C4C23×C1311yescharacteristic
531C23×C4C23×C1311yescharacteristic
532C23×C4C23×C1311yescharacteristic
533C23×C4C23×C1311yescharacteristic
534C23×C4C23×C1311yescharacteristic
535C23×C4C23×C1311yescharacteristic
536C23×C4C23×C1311yescharacteristic
537C23×C4C23×C1311yescharacteristic
538C23×C4C23×C1311yescharacteristic
539C23×C4C23×C1311yescharacteristic
540C23×C4C23×C1311yescharacteristic
541C23×C4C23×C1311yescharacteristic
542C23×C4C23×C1311yescharacteristic
543C23×C4C23×C1311yescharacteristic
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4—41no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4—41no—
557C2×C4⋊C4—41no—
558C2×C4⋊C4C2×C4×C1314yes—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—41no—
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⋊C4C2×C4×C1314yes—
578C2×C22⋊C4C2×C4×C1314yes—
579C2×C22⋊C4C2×C4×C1314yes—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—41no—
584C2×C42—41no—
585C2×C42—41no—
586C2×C42—41no—
587C2×C42—41no—
588C2×C42C2×C4×C1314yes—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—22no—
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#95C2×C4×C1314yes—
607#95C2×C4×C1314yes—
608#95D4×C1314yes—
609C2×C13—82no—
610C2×C13#231411yescharacteristic
611C2×C13#232411yescharacteristic
612C2×C13#233411yescharacteristic
613C2×C13#235211yescharacteristic
614C2×C13#235711yescharacteristic
615C2×C13#235911yescharacteristic
616C2×C13#237911yescharacteristic
617C2×C13#271011yescharacteristic
618C2×C13#271111yescharacteristic
619C2×C13#271211yescharacteristic
620C2×C13#272511yescharacteristic
621C2×C13#275311yescharacteristic
622C2×C13#275411yescharacteristic
623C2×C13#277211yescharacteristic
624C2×C13#277311yescharacteristic
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24C22×C4×C1312yes—
640C24C24×C1311yescharacteristic
641C22×C4—21no—
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×C4C22×C4×C1312yes—
726C22×C4C22×C4×C1312yes—
727C22×C4C22×C4×C1312yes—
728C22×C4C22×C4×C1312yes—
729C22×C4C22×C4×C1312yes—
730C22×C4C22×C4×C1312yes—
731C22×C4C2×D4×C1312yes—
732C22×C4C2×D4×C1312yes—
733C22×C4C2×D4×C1312yes—
734C22×C4C13×#4112yes—
735C22×C4C13×#4112yes—
736C22×C4C13×#4112yes—
737C22×C4C13×#4112yes—
738C22×C4C13×#4112yes—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C4⋊C4—44no—
743C4⋊C4—44no—
744C22⋊C4—28no—
745C22⋊C4—28no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—44no—
749C22⋊C4—44no—
750C22⋊C4—44no—
751C42—28no—
752C42—44no—
753C42—44no—
754C13#1441211yescharacteristic, direct product factor, Sylow
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23C23×C4×C1311yescharacteristic
791C23C22×D4×C1311yescharacteristic
792C23C2×C13×#4111yescharacteristic
793C23C2×C13×#4111yescharacteristic
794C23C2×C13×#4111yescharacteristic
795C23C2×C13×#4111yescharacteristic
796C23C2×C13×#4111yescharacteristic
797C23C13×H(5,𝔽2)11yescharacteristic
798C23C13×H(5,𝔽2)11yescharacteristic
799C23C13×H(5,𝔽2)11yescharacteristic
800C23C13×H(5,𝔽2)11yescharacteristic
801C23C13×H(5,𝔽2)11yescharacteristic
802C23C13×2−1+411yescharacteristic
803C23C13×2−1+411yescharacteristic
804C23C13×2−1+411yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
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—41no—
842C2×C4—41no—
843C2×C4—41no—
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×C4C13×#11714yes—
902C2×C4C4×D4×C1314yes—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22C2×C13×#11711yescharacteristic
919C22C2×C4×D4×C1311yescharacteristic
920C22C4×C13×#4111yescharacteristic
921C22C13×#51811yescharacteristic
922C22C13×#52011yescharacteristic
923C22C13×#52011yescharacteristic
924C22C13×#52011yescharacteristic
925C22C13×#53511yescharacteristic
926C22C13×#53711yescharacteristic
927C22C13×#53811yescharacteristic
928C22C13×#53911yescharacteristic
929C22C13×#54011yescharacteristic
930C22C13×#54011yescharacteristic
931C22C13×#54111yescharacteristic
932C22C13×#54111yescharacteristic
933C22C13×#54211yescharacteristic
934C22C13×#54211yescharacteristic
935C22C13×#54211yescharacteristic
936C22C13×#54211yescharacteristic
937C22C13×#54611yescharacteristic
938C22C13×#54611yescharacteristic
939C22C13×#54711yescharacteristic
940C22C13×#54811yescharacteristic
941C22C13×#55111yescharacteristic
942C22C13×#55211yescharacteristic
943C22C13×#55211yescharacteristic
944C22C13×#55311yescharacteristic
945C22C13×#55311yescharacteristic
946C22C13×#55311yescharacteristic
947C22C13×#55911yescharacteristic
948C22C13×#55911yescharacteristic
949C22C13×H(3,𝔽4)11yescharacteristic
950C22C13×#56211yescharacteristic
951C22C13×#56211yescharacteristic
952C22C13×#56311yescharacteristic
953C4—24no—
954C4—24no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—81no—
964C4—81no—
965C4—81no—
966C4—81no—
967C2—82no—
968C2C13×#231411yescharacteristic
969C2C13×#232411yescharacteristic
970C2C13×#233411yescharacteristic
971C2C13×#235211yescharacteristic
972C2C13×#235711yescharacteristic
973C2C13×#235911yescharacteristic
974C2C13×#237911yescharacteristic
975C2C13×#271011yescharacteristic
976C2C13×#271111yescharacteristic
977C2C13×#271211yescharacteristic
978C2C13×#272511yescharacteristic
979C2C13×#275311yescharacteristic
980C2C13×#275411yescharacteristic
981C2C13×#277211yescharacteristic
982C2C13×#277311yescharacteristic
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
3. C2×C13×#382C2semidirect
4. C13×#1445C2semidirect
5. C13×#1442C2semidirect
11. C13×#1436C2semidirect
12. C13×#1436C2semidirect
13. C13×#1436C2semidirect
14. C13×#1436C2semidirect
15. C13×C4⋊#95C2semidirect
32. C13×#388C4semidirect
134. #14412C13direct (N × H)
266. C2×#382C2×C13semidirect
267. #1445C2×C13semidirect
268. #1442C2×C13semidirect
274. #1436C2×C13semidirect
275. #1436C2×C13semidirect
276. #1436C2×C13semidirect
277. #1436C2×C13semidirect
278. C4⋊#95C2×C13semidirect
443. #388C4×C13semidirect
754. C13#14412direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3882
C2×C13×#3822
C13×#14452
C13×#14422
C13×#14402
C13×#14392
C13×#14372
C13×#14362
C13×C4⋊#952
#1441213