Finite Group Databasebeta

← C13×#14031 #15700370

Subgroups — C13×#14031 #15700370

Order 3328.

1594 conjugacy classes of subgroups.

The subgroup lattice has 1000 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×#388C211yesmaximal, characteristic
4C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
6C13×#1444C211yesmaximal, characteristic, complemented
7C13×#1443C211yesmaximal, characteristic, complemented
8C13×#1439C211yesmaximal, characteristic
9C13×#1439C211yesmaximal, characteristic
10C13×#1437C211yesmaximal, characteristic
11C13×#1437C211yesmaximal, characteristic
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×#1436C211yesmaximal, characteristic, complemented
15C13×#1434C211yesmaximal, 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
31C22×C42×C13C2211yescharacteristic
32C22×C42×C13C2211yescharacteristic
33C13×#388—24no—
34C13×#388—24no—
35C13×#388C418yescomplemented
36C4×C13×C4⋊C4—24no—
37C4×C13×C4⋊C4—24no—
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
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C25×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
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
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—22no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—41no—
84C2×C13×C4⋊C4C2×C414yes—
85C2×C13×C4⋊C4D414yes—
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—22no—
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—41no—
101C2×C13×C22⋊C4—41no—
102C2×C13×C22⋊C4—41no—
103C2×C13×C22⋊C4—41no—
104C2×C13×C22⋊C4C2×C414yes—
105C2×C13×C22⋊C4C2×C414yes—
106C2×C13×C22⋊C4C2×C414yes—
107C2×C42×C13—22no—
108C2×C42×C13—22no—
109C2×C42×C13—22no—
110C2×C42×C13—22no—
111C2×C42×C13—22no—
112C2×C42×C13—22no—
113C2×C42×C13—22no—
114C2×C42×C13—22no—
115C2×C42×C13—22no—
116C2×C42×C13—22no—
117C2×C42×C13—22no—
118C2×C42×C13—41no—
119C2×C42×C13—41no—
120C2×C42×C13—41no—
121C2×C42×C13C2×C414yes—
122C13×#95—22no—
123C13×#95—22no—
124C13×#95—22no—
125C13×#95—22no—
126C13×#95—22no—
127C13×#95—22no—
128C13×#95—22no—
129C13×#95—22no—
130C13×#95—22no—
131C13×#95—22no—
132C13×#95—22no—
133C13×#95—41no—
134C13×#95—41no—
135C13×#95—41no—
136C13×#95—41no—
137C13×#95C2×C414yes—
138C13×#95C2×C414yes—
139C13×#95D414yes—
140#14031C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13C22×C412yes—
156C24×C13C2411yescharacteristic
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×C13C2×D412yes—
245C22×C4×C13C2×D412yes—
246C22×C4×C13C2×D412yes—
247C22×C4×C13#4112yes—
248C22×C4×C13#4112yes—
249C22×C4×C13#4112yes—
250C22×C4×C13#4112yes—
251C22×C4×C13#4112yes—
252C22×C4×C13#4112yes—
253C22×C4×C13#4112yes—
254C22×C4×C13#4112yes—
255C13×C4⋊C4—28no—
256C13×C4⋊C4—28no—
257C13×C4⋊C4—28no—
258C13×C4⋊C4—28no—
259C13×C4⋊C4—44no—
260C13×C22⋊C4—28no—
261C13×C22⋊C4—28no—
262C13×C22⋊C4—28no—
263C13×C22⋊C4—44no—
264C13×C22⋊C4—44no—
265C13×C22⋊C4—44no—
266C13×C22⋊C4—44no—
267C42×C13—28no—
268C42×C13—28no—
269C42×C13—44no—
270C42×C13—44no—
271C42×C13—44no—
272C2×#388C2×C1311yescharacteristic
273C2×#388C2×C1311yescharacteristic
274C2×#388C2×C1311yescharacteristic
275C2×C4×C4⋊C4C2×C1311yescharacteristic, complemented
276C2×C4×C4⋊C4C2×C1311yescharacteristic, complemented
277#1444C2×C1311yescharacteristic, complemented
278#1443C2×C1311yescharacteristic, complemented
279#1439C2×C1311yescharacteristic
280#1439C2×C1311yescharacteristic
281#1437C2×C1311yescharacteristic
282#1437C2×C1311yescharacteristic
283#1436C2×C1311yescharacteristic, complemented
284#1436C2×C1311yescharacteristic, complemented
285#1436C2×C1311yescharacteristic, complemented
286#1434C2×C1311yescharacteristic, complemented
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
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×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13C23×C411yescharacteristic
323C23×C13C22×D411yescharacteristic
324C23×C13C22×D411yescharacteristic
325C23×C13C2×#4111yescharacteristic
326C23×C13C2×#4111yescharacteristic
327C23×C13C2×#4111yescharacteristic
328C23×C13C2×#4111yescharacteristic
329C23×C13C2×#4111yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13C2×#4111yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13H(5,𝔽2)11yescharacteristic
334C23×C13H(5,𝔽2)11yescharacteristic
335C23×C132−1+411yescharacteristic
336C23×C132−1+411yescharacteristic
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—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
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#11714yes—
432C2×C4×C13C4×D414yes—
433C2×C4×C13C4×D414yes—
434C2×C4×C13#12314yes—
435C22×C4⋊C4C22×C1311yescharacteristic
436C22×C4⋊C4C22×C1311yescharacteristic
437C22×C4⋊C4C22×C1311yescharacteristic
438C22×C4⋊C4C22×C1311yescharacteristic
439C22×C4⋊C4C22×C1311yescharacteristic
440C22×C22⋊C4C22×C1311yescharacteristic
441C22×C22⋊C4C22×C1311yescharacteristic
442C22×C22⋊C4C22×C1311yescharacteristic
443C22×C22⋊C4C22×C1311yescharacteristic
444C22×C22⋊C4C22×C1311yescharacteristic
445C22×C22⋊C4C22×C1311yescharacteristic
446C22×C22⋊C4C22×C1311yescharacteristic
447C22×C42C22×C1311yescharacteristic
448C22×C42C22×C1311yescharacteristic
449C22×C42C22×C1311yescharacteristic
450C22×C42C22×C1311yescharacteristic
451C22×C42C22×C1311yescharacteristic
452#388—24no—
453#388—24no—
454#388C4×C1318yescomplemented
455C4×C4⋊C4—24no—
456C4×C4⋊C4—24no—
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
470C2×#95C22×C1311yescharacteristic
471C2×#95C22×C1311yescharacteristic
472C2×#95C22×C1311yescharacteristic
473C2×#95C22×C1311yescharacteristic
474C2×#95C22×C1311yescharacteristic
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—81no—
483C22×C13—81no—
484C22×C13—81no—
485C22×C13—81no—
486C22×C13—81no—
487C22×C13—81no—
488C22×C13—81no—
489C22×C13—81no—
490C22×C13C2×#11711yescharacteristic
491C22×C13C2×C4×D411yescharacteristic
492C22×C13C2×C4×D411yescharacteristic
493C22×C13C4×#4111yescharacteristic
494C22×C13C4×#4111yescharacteristic
495C22×C13#52011yescharacteristic
496C22×C13#52011yescharacteristic
497C22×C13C2×#12311yescharacteristic
498C22×C13#52511yescharacteristic
499C22×C13#52511yescharacteristic
500C22×C13#52511yescharacteristic
501C22×C13#52911yescharacteristic
502C22×C13#52911yescharacteristic
503C22×C13#52911yescharacteristic
504C22×C13#52911yescharacteristic
505C22×C13#53811yescharacteristic
506C22×C13#53911yescharacteristic
507C22×C13#54111yescharacteristic
508C22×C13#54211yescharacteristic
509C22×C13D4211yescharacteristic
510C22×C13#54611yescharacteristic
511C22×C13#54711yescharacteristic
512C22×C13#54711yescharacteristic
513C22×C13#54811yescharacteristic
514C22×C13#54811yescharacteristic
515C22×C13#55011yescharacteristic
516C22×C13#55311yescharacteristic
517C22×C13#55311yescharacteristic
518C22×C13#55311yescharacteristic
519C22×C13#55511yescharacteristic
520C22×C13#55611yescharacteristic
521C22×C13#55611yescharacteristic
522C22×C13#55611yescharacteristic
523C22×C13#55611yescharacteristic
524C22×C13#55911yescharacteristic
525C4×C13—24no—
526C4×C13—24no—
527C4×C13—24no—
528C4×C13—24no—
529C4×C13—42no—
530C4×C13—42no—
531C4×C13—42no—
532C4×C13—42no—
533C4×C13—42no—
534C4×C13—42no—
535C4×C13—42no—
536C4×C13—42no—
537C4×C13—81no—
538C4×C13—81no—
539C25C23×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
552C23×C4C23×C1311yescharacteristic
553C23×C4C23×C1311yescharacteristic
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4C2×C4×C1314yes—
568C2×C4⋊C4D4×C1314yes—
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—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4C2×C4×C1314yes—
588C2×C22⋊C4C2×C4×C1314yes—
589C2×C22⋊C4C2×C4×C1314yes—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—22no—
595C2×C42—22no—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—41no—
602C2×C42—41no—
603C2×C42—41no—
604C2×C42C2×C4×C1314yes—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—41no—
617#95—41no—
618#95—41no—
619#95—41no—
620#95C2×C4×C1314yes—
621#95C2×C4×C1314yes—
622#95D4×C1314yes—
623C2×C13—82no—
624C2×C13#229011yescharacteristic
625C2×C13C4×#12311yescharacteristic
626C2×C13#233411yescharacteristic
627C2×C13#234711yescharacteristic
628C2×C13#235411yescharacteristic
629C2×C13#236111yescharacteristic
630C2×C13#236711yescharacteristic
631C2×C13#244311yescharacteristic
632C2×C13#244811yescharacteristic
633C2×C13#245611yescharacteristic
634C2×C13#246911yescharacteristic
635C2×C13#246911yescharacteristic
636C2×C13#247411yescharacteristic
637C2×C13#259311yescharacteristic
638C2×C13#259411yescharacteristic
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C22×C4×C1312yes—
654C24C24×C1311yescharacteristic
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—21no—
733C22×C4C22×C4×C1312yes—
734C22×C4C22×C4×C1312yes—
735C22×C4C22×C4×C1312yes—
736C22×C4C22×C4×C1312yes—
737C22×C4C22×C4×C1312yes—
738C22×C4C22×C4×C1312yes—
739C22×C4C2×D4×C1312yes—
740C22×C4C2×D4×C1312yes—
741C22×C4C2×D4×C1312yes—
742C22×C4C2×D4×C1312yes—
743C22×C4C2×D4×C1312yes—
744C22×C4C2×D4×C1312yes—
745C22×C4C13×#4112yes—
746C22×C4C13×#4112yes—
747C22×C4C13×#4112yes—
748C22×C4C13×#4112yes—
749C22×C4C13×#4112yes—
750C22×C4C13×#4112yes—
751C22×C4C13×#4112yes—
752C22×C4C13×#4112yes—
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—28no—
756C4⋊C4—28no—
757C4⋊C4—44no—
758C22⋊C4—28no—
759C22⋊C4—28no—
760C22⋊C4—28no—
761C22⋊C4—44no—
762C22⋊C4—44no—
763C22⋊C4—44no—
764C22⋊C4—44no—
765C42—28no—
766C42—28no—
767C42—44no—
768C42—44no—
769C42—44no—
770C13#1403111yescharacteristic, direct product factor, Sylow
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—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23C23×C4×C1311yescharacteristic
807C23C22×D4×C1311yescharacteristic
808C23C22×D4×C1311yescharacteristic
809C23C2×C13×#4111yescharacteristic
810C23C2×C13×#4111yescharacteristic
811C23C2×C13×#4111yescharacteristic
812C23C2×C13×#4111yescharacteristic
813C23C2×C13×#4111yescharacteristic
814C23C2×C13×#4111yescharacteristic
815C23C2×C13×#4111yescharacteristic
816C23C2×C13×#4111yescharacteristic
817C23C13×H(5,𝔽2)11yescharacteristic
818C23C13×H(5,𝔽2)11yescharacteristic
819C23C13×2−1+411yescharacteristic
820C23C13×2−1+411yescharacteristic
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—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
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—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4C13×#11714yes—
916C2×C4C4×D4×C1314yes—
917C2×C4C4×D4×C1314yes—
918C2×C4C13×#12314yes—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22C2×C13×#11711yescharacteristic
935C22C2×C4×D4×C1311yescharacteristic
936C22C2×C4×D4×C1311yescharacteristic
937C22C4×C13×#4111yescharacteristic
938C22C4×C13×#4111yescharacteristic
939C22C13×#52011yescharacteristic
940C22C13×#52011yescharacteristic
941C22C2×C13×#12311yescharacteristic
942C22C13×#52511yescharacteristic
943C22C13×#52511yescharacteristic
944C22C13×#52511yescharacteristic
945C22C13×#52911yescharacteristic
946C22C13×#52911yescharacteristic
947C22C13×#52911yescharacteristic
948C22C13×#52911yescharacteristic
949C22C13×#53811yescharacteristic
950C22C13×#53911yescharacteristic
951C22C13×#54111yescharacteristic
952C22C13×#54211yescharacteristic
953C22D42×C1311yescharacteristic
954C22C13×#54611yescharacteristic
955C22C13×#54711yescharacteristic
956C22C13×#54711yescharacteristic
957C22C13×#54811yescharacteristic
958C22C13×#54811yescharacteristic
959C22C13×#55011yescharacteristic
960C22C13×#55311yescharacteristic
961C22C13×#55311yescharacteristic
962C22C13×#55311yescharacteristic
963C22C13×#55511yescharacteristic
964C22C13×#55611yescharacteristic
965C22C13×#55611yescharacteristic
966C22C13×#55611yescharacteristic
967C22C13×#55611yescharacteristic
968C22C13×#55911yescharacteristic
969C4—24no—
970C4—24no—
971C4—24no—
972C4—24no—
973C4—42no—
974C4—42no—
975C4—42no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—81no—
982C4—81no—
983C2—82no—
984C2C13×#229011yescharacteristic
985C2C4×C13×#12311yescharacteristic
986C2C13×#233411yescharacteristic
987C2C13×#234711yescharacteristic
988C2C13×#235411yescharacteristic
989C2C13×#236111yescharacteristic
990C2C13×#236711yescharacteristic
991C2C13×#244311yescharacteristic
992C2C13×#244811yescharacteristic
993C2C13×#245611yescharacteristic
994C2C13×#246911yescharacteristic
995C2C13×#246911yescharacteristic
996C2C13×#247411yescharacteristic
997C2C13×#259311yescharacteristic
998C2C13×#259411yescharacteristic
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. C2×C4×C13×C4⋊C4C2semidirect
5. C2×C4×C13×C4⋊C4C2semidirect
6. C13×#1444C2semidirect
7. C13×#1443C2semidirect
12. C13×#1436C2semidirect
13. C13×#1436C2semidirect
14. C13×#1436C2semidirect
15. C13×#1434C2semidirect
35. C13×#388C4semidirect
140. #14031C13direct (N × H)
275. C2×C4×C4⋊C4C2×C13semidirect
276. C2×C4×C4⋊C4C2×C13semidirect
277. #1444C2×C13semidirect
278. #1443C2×C13semidirect
283. #1436C2×C13semidirect
284. #1436C2×C13semidirect
285. #1436C2×C13semidirect
286. #1434C2×C13semidirect
454. #388C4×C13semidirect
770. C13#14031direct (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×C4×C13×C4⋊C42
C13×#14442
C13×#14432
C13×#14392
C13×#14372
C13×#14362
C13×#14342
#1403113