Finite Group Databasebeta

← C13×#14102 #15700441

Subgroups — C13×#14102 #15700441

Order 3328.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#126C211yesmaximal, characteristic
2C2×C13×#388C211yesmaximal, characteristic
3C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
4C13×#1445C211yesmaximal, characteristic, complemented
5C13×#1441C211yesmaximal, characteristic, complemented
6C13×#1440C211yesmaximal, characteristic
7C13×#1440C211yesmaximal, characteristic
8C13×#1436C211yesmaximal, characteristic, complemented
9C13×#1436C211yesmaximal, characteristic, complemented
10C13×#1436C211yesmaximal, characteristic, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C13×#1434C211yesmaximal, characteristic, complemented
13C13×C22⋊#95C211yesmaximal, characteristic
14C13×C22⋊#95C211yesmaximal, characteristic
15C4×C13×#95C211yesmaximal, characteristic, complemented
16C24×C4×C13C2211yescharacteristic
17C2×C13×#126—24no—
18C2×C13×#126—24no—
19C2×C13×#126C418yescomplemented
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C42×C13C2211yescharacteristic
31C22×C42×C13C2211yescharacteristic
32C22×C42×C13C2211yescharacteristic
33C22×C42×C13C2211yescharacteristic
34C13×#388—24no—
35C4×C13×C22⋊C4—24no—
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
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C25×C13C2311yescharacteristic
57C23×C4×C13—22no—
58C23×C4×C13—22no—
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—41no—
63C23×C4×C13—41no—
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
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C13×#126—232no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—41no—
88C2×C13×C4⋊C4C2×C414yescomplemented
89C2×C13×C4⋊C4C2×C414yescomplemented
90C2×C13×C4⋊C4C2×C414yescomplemented
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—22no—
101C2×C13×C22⋊C4—22no—
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×C13×C22⋊C4D414yes—
108C2×C13×C22⋊C4D414yes—
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—41no—
118C2×C42×C13—41no—
119C2×C42×C13—41no—
120C2×C42×C13C2×C414yescomplemented
121C13×#95—22no—
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—22no—
134C13×#95—22no—
135C13×#95—22no—
136C13×#95—22no—
137C13×#95—41no—
138C13×#95—41no—
139C13×#95—41no—
140C13×#95—41no—
141#14102C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13C22×C412yes—
155C24×C13C2×D412yes—
156C24×C13C2×D412yes—
157C24×C13C2411yescharacteristic
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—28no—
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—21no—
238C22×C4×C13—21no—
239C22×C4×C13—44no—
240C22×C4×C13—44no—
241C22×C4×C13—44no—
242C22×C4×C13—44no—
243C22×C4×C13—44no—
244C22×C4×C13—44no—
245C22×C4×C13C22×C412yes—
246C22×C4×C13C22×C412yes—
247C22×C4×C13C22×C412yes—
248C22×C4×C13C22×C412yes—
249C22×C4×C13C22×C412yes—
250C22×C4×C13C22×C412yes—
251C22×C4×C13C2×D412yes—
252C22×C4×C13C2×D412yes—
253C22×C4×C13C2×D412yes—
254C22×C4×C13C2×D412yes—
255C22×C4×C13#4112yes—
256C22×C4×C13#4112yes—
257C22×C4×C13#4112yes—
258C22×C4×C13#4112yes—
259C22×C4×C13#4112yes—
260C22×C4×C13#4112yes—
261C22×C4×C13#4112yes—
262C22×C4×C13#4112yes—
263C13×C4⋊C4—28no—
264C13×C4⋊C4—28no—
265C13×C4⋊C4—28no—
266C13×C4⋊C4—44no—
267C13×C22⋊C4—28no—
268C13×C22⋊C4—28no—
269C13×C22⋊C4—28no—
270C13×C22⋊C4—44no—
271C13×C22⋊C4—44no—
272C13×C22⋊C4C22⋊C4116yes—
273C42×C13—28no—
274C42×C13—44no—
275C42×C13—44no—
276C42×C13—44no—
277C22×#126C2×C1311yescharacteristic
278C2×#388C2×C1311yescharacteristic
279C2×C4×C22⋊C4C2×C1311yescharacteristic
280#1445C2×C1311yescharacteristic, complemented
281#1441C2×C1311yescharacteristic, complemented
282#1440C2×C1311yescharacteristic
283#1440C2×C1311yescharacteristic
284#1436C2×C1311yescharacteristic, complemented
285#1436C2×C1311yescharacteristic, complemented
286#1436C2×C1311yescharacteristic, complemented
287C4⋊#95C2×C1311yescharacteristic, complemented
288#1434C2×C1311yescharacteristic, complemented
289C22⋊#95C2×C1311yescharacteristic
290C22⋊#95C2×C1311yescharacteristic
291C4×#95C2×C1311yescharacteristic, complemented
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—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
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×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13C2×C22⋊C414yes—
327C23×C13C23×C411yescharacteristic
328C23×C13C22×D411yescharacteristic
329C23×C13C22×D411yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13C2×#4111yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13C2×#4111yescharacteristic
334C23×C13C2×#4111yescharacteristic
335C23×C13C2×#4111yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C23×C13C2×#4111yescharacteristic
338C23×C13H(5,𝔽2)11yescharacteristic
339C23×C13H(5,𝔽2)11yescharacteristic
340C23×C132−1+411yescharacteristic
341C23×C132−1+411yescharacteristic
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—22no—
386C2×C4×C13—22no—
387C2×C4×C13—416no—
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—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—41no—
436C2×C4×C13—41no—
437C2×C4×C13—41no—
438C2×C4×C13C2×C22⋊C414yes—
439C2×C4×C13C2×C22⋊C414yes—
440C2×C4×C13#12614yescomplemented
441C24×C4C22×C1311yescharacteristic
442C2×#126—24no—
443C2×#126—24no—
444C2×#126C4×C1318yescomplemented
445C22×C4⋊C4C22×C1311yescharacteristic
446C22×C4⋊C4C22×C1311yescharacteristic
447C22×C4⋊C4C22×C1311yescharacteristic
448C22×C4⋊C4C22×C1311yescharacteristic
449C22×C22⋊C4C22×C1311yescharacteristic
450C22×C22⋊C4C22×C1311yescharacteristic
451C22×C22⋊C4C22×C1311yescharacteristic
452C22×C22⋊C4C22×C1311yescharacteristic
453C22×C22⋊C4C22×C1311yescharacteristic
454C22×C22⋊C4C22×C1311yescharacteristic
455C22×C42C22×C1311yescharacteristic
456C22×C42C22×C1311yescharacteristic
457C22×C42C22×C1311yescharacteristic
458C22×C42C22×C1311yescharacteristic
459#388—24no—
460C4×C22⋊C4—24no—
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
475C2×#95C22×C1311yescharacteristic
476C2×#95C22×C1311yescharacteristic
477C2×#95C22×C1311yescharacteristic
478C2×#95C22×C1311yescharacteristic
479C2×#95C22×C1311yescharacteristic
480C2×#95C22×C1311yescharacteristic
481C22×C13—24no—
482C22×C13—24no—
483C22×C13—24no—
484C22×C13—42no—
485C22×C13—42no—
486C22×C13—42no—
487C22×C13—42no—
488C22×C13—42no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13C22×C22⋊C411yescharacteristic
497C22×C13C4×#4111yescharacteristic
498C22×C13C4×#4111yescharacteristic
499C22×C13C4×#4111yescharacteristic
500C22×C13C4×#4111yescharacteristic
501C22×C13#52011yescharacteristic
502C22×C13#52011yescharacteristic
503C22×C13#52511yescharacteristic
504C22×C13#52511yescharacteristic
505C22×C13C2×#12611yescharacteristic
506C22×C13#52911yescharacteristic
507C22×C13#52911yescharacteristic
508C22×C13#52911yescharacteristic
509C22×C13#53211yescharacteristic
510C22×C13#53211yescharacteristic
511C22×C13#53811yescharacteristic
512C22×C13#53911yescharacteristic
513C22×C13#54111yescharacteristic
514C22×C13#54211yescharacteristic
515C22×C13#54611yescharacteristic
516C22×C13#54611yescharacteristic
517C22×C13#54611yescharacteristic
518C22×C13#54611yescharacteristic
519C22×C13#54711yescharacteristic
520C22×C13#54711yescharacteristic
521C22×C13#54711yescharacteristic
522C22×C13#54711yescharacteristic
523C22×C13#55111yescharacteristic
524C22×C13#55111yescharacteristic
525C22×C13#55211yescharacteristic
526C22×C13#55211yescharacteristic
527C22×C13#55311yescharacteristic
528C22×C13#55311yescharacteristic
529C22×C13#55611yescharacteristic
530C22×C13#55611yescharacteristic
531C4×C13—24no—
532C4×C13—24no—
533C4×C13—24no—
534C4×C13—42no—
535C4×C13—42no—
536C4×C13—42no—
537C4×C13—42no—
538C4×C13—42no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—42no—
542C4×C13—42no—
543C4×C13—81no—
544C4×C13—81no—
545C25C23×C1311yescharacteristic
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—22no—
550C23×C4—22no—
551C23×C4—41no—
552C23×C4—41no—
553C23×C4C23×C1311yescharacteristic
554C23×C4C23×C1311yescharacteristic
555C23×C4C23×C1311yescharacteristic
556C23×C4C23×C1311yescharacteristic
557C23×C4C23×C1311yescharacteristic
558C23×C4C23×C1311yescharacteristic
559C23×C4C23×C1311yescharacteristic
560C23×C4C23×C1311yescharacteristic
561C23×C4C23×C1311yescharacteristic
562C23×C4C23×C1311yescharacteristic
563C23×C4C23×C1311yescharacteristic
564C23×C4C23×C1311yescharacteristic
565C23×C4C23×C1311yescharacteristic
566C23×C4C23×C1311yescharacteristic
567#126—232no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4C2×C4×C1314yescomplemented
578C2×C4⋊C4C2×C4×C1314yescomplemented
579C2×C4⋊C4C2×C4×C1314yescomplemented
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—41no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4C2×C4×C1314yes—
594C2×C22⋊C4C2×C4×C1314yes—
595C2×C22⋊C4C2×C4×C1314yes—
596C2×C22⋊C4D4×C1314yes—
597C2×C22⋊C4D4×C1314yes—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—22no—
606C2×C42—41no—
607C2×C42—41no—
608C2×C42—41no—
609C2×C42C2×C4×C1314yescomplemented
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—22no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—41no—
627#95—41no—
628#95—41no—
629#95—41no—
630C2×C13—44no—
631C2×C13#229711yescharacteristic
632C2×C13C4×#12611yescharacteristic
633C2×C13#233411yescharacteristic
634C2×C13#233911yescharacteristic
635C2×C13#233911yescharacteristic
636C2×C13#237311yescharacteristic
637C2×C13#237311yescharacteristic
638C2×C13#246611yescharacteristic
639C2×C13#246811yescharacteristic
640C2×C13#247811yescharacteristic
641C2×C13#248011yescharacteristic
642C2×C13#249611yescharacteristic
643C2×C13#252111yescharacteristic
644C2×C13#255311yescharacteristic
645C2×C13#255911yescharacteristic
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24C22×C4×C1312yes—
659C24C2×D4×C1312yes—
660C24C2×D4×C1312yes—
661C24C24×C1311yescharacteristic
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—28no—
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×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4C22×C4×C1312yes—
750C22×C4C22×C4×C1312yes—
751C22×C4C22×C4×C1312yes—
752C22×C4C22×C4×C1312yes—
753C22×C4C22×C4×C1312yes—
754C22×C4C22×C4×C1312yes—
755C22×C4C2×D4×C1312yes—
756C22×C4C2×D4×C1312yes—
757C22×C4C2×D4×C1312yes—
758C22×C4C2×D4×C1312yes—
759C22×C4C13×#4112yes—
760C22×C4C13×#4112yes—
761C22×C4C13×#4112yes—
762C22×C4C13×#4112yes—
763C22×C4C13×#4112yes—
764C22×C4C13×#4112yes—
765C22×C4C13×#4112yes—
766C22×C4C13×#4112yes—
767C4⋊C4—28no—
768C4⋊C4—28no—
769C4⋊C4—28no—
770C4⋊C4—44no—
771C22⋊C4—28no—
772C22⋊C4—28no—
773C22⋊C4—28no—
774C22⋊C4—44no—
775C22⋊C4—44no—
776C22⋊C4C13×C22⋊C4116yes—
777C42—28no—
778C42—44no—
779C42—44no—
780C42—44no—
781C13#1410211yescharacteristic, direct product factor, Sylow
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23C2×C13×C22⋊C414yes—
817C23C23×C4×C1311yescharacteristic
818C23C22×D4×C1311yescharacteristic
819C23C22×D4×C1311yescharacteristic
820C23C2×C13×#4111yescharacteristic
821C23C2×C13×#4111yescharacteristic
822C23C2×C13×#4111yescharacteristic
823C23C2×C13×#4111yescharacteristic
824C23C2×C13×#4111yescharacteristic
825C23C2×C13×#4111yescharacteristic
826C23C2×C13×#4111yescharacteristic
827C23C2×C13×#4111yescharacteristic
828C23C13×H(5,𝔽2)11yescharacteristic
829C23C13×H(5,𝔽2)11yescharacteristic
830C23C13×2−1+411yescharacteristic
831C23C13×2−1+411yescharacteristic
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—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—416no—
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×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4C2×C13×C22⋊C414yes—
929C2×C4C2×C13×C22⋊C414yes—
930C2×C4C13×#12614yescomplemented
931C22—24no—
932C22—24no—
933C22—24no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22C22×C13×C22⋊C411yescharacteristic
947C22C4×C13×#4111yescharacteristic
948C22C4×C13×#4111yescharacteristic
949C22C4×C13×#4111yescharacteristic
950C22C4×C13×#4111yescharacteristic
951C22C13×#52011yescharacteristic
952C22C13×#52011yescharacteristic
953C22C13×#52511yescharacteristic
954C22C13×#52511yescharacteristic
955C22C2×C13×#12611yescharacteristic
956C22C13×#52911yescharacteristic
957C22C13×#52911yescharacteristic
958C22C13×#52911yescharacteristic
959C22C13×#53211yescharacteristic
960C22C13×#53211yescharacteristic
961C22C13×#53811yescharacteristic
962C22C13×#53911yescharacteristic
963C22C13×#54111yescharacteristic
964C22C13×#54211yescharacteristic
965C22C13×#54611yescharacteristic
966C22C13×#54611yescharacteristic
967C22C13×#54611yescharacteristic
968C22C13×#54611yescharacteristic
969C22C13×#54711yescharacteristic
970C22C13×#54711yescharacteristic
971C22C13×#54711yescharacteristic
972C22C13×#54711yescharacteristic
973C22C13×#55111yescharacteristic
974C22C13×#55111yescharacteristic
975C22C13×#55211yescharacteristic
976C22C13×#55211yescharacteristic
977C22C13×#55311yescharacteristic
978C22C13×#55311yescharacteristic
979C22C13×#55611yescharacteristic
980C22C13×#55611yescharacteristic
981C4—24no—
982C4—24no—
983C4—24no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—81no—
994C4—81no—
995C2—44no—
996C2C13×#229711yescharacteristic
997C2C4×C13×#12611yescharacteristic
998C2C13×#233411yescharacteristic
999C2C13×#233911yescharacteristic
1000C2C13×#233911yescharacteristic
1001C2C13×#237311yescharacteristic
1002C2C13×#237311yescharacteristic
1003C2C13×#246611yescharacteristic
1004C2C13×#246811yescharacteristic
1005C2C13×#247811yescharacteristic
1006C2C13×#248011yescharacteristic
1007C2C13×#249611yescharacteristic
1008C2C13×#252111yescharacteristic
1009C2C13×#255311yescharacteristic
1010C2C13×#255911yescharacteristic
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×#1445C2semidirect
5. C13×#1441C2semidirect
8. C13×#1436C2semidirect
9. C13×#1436C2semidirect
10. C13×#1436C2semidirect
11. C13×C4⋊#95C2semidirect
12. C13×#1434C2semidirect
15. C4×C13×#95C2semidirect
19. C2×C13×#126C4semidirect
88. C2×C13×C4⋊C4C2×C4semidirect
89. C2×C13×C4⋊C4C2×C4semidirect
90. C2×C13×C4⋊C4C2×C4semidirect
120. C2×C42×C13C2×C4semidirect
141. #14102C13direct (N × H)
280. #1445C2×C13semidirect
281. #1441C2×C13semidirect
284. #1436C2×C13semidirect
285. #1436C2×C13semidirect
286. #1436C2×C13semidirect
287. C4⋊#95C2×C13semidirect
288. #1434C2×C13semidirect
291. C4×#95C2×C13semidirect
440. C2×C4×C13#126semidirect
444. C2×#126C4×C13semidirect
577. C2×C4⋊C4C2×C4×C13semidirect
578. C2×C4⋊C4C2×C4×C13semidirect
579. C2×C4⋊C4C2×C4×C13semidirect
609. C2×C42C2×C4×C13semidirect
781. C13#14102direct (N × H)
930. C2×C4C13×#126semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1262
C2×C13×#3882
C2×C4×C13×C22⋊C42
C13×#14452
C13×#14412
C13×#14402
C13×#14362
C13×C4⋊#952
C13×#14342
C13×C22⋊#952
C4×C13×#952
#1410213