Finite Group Databasebeta

← C13×#14315 #15700654

Subgroups — C13×#14315 #15700654

Order 3328.

1558 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#396C211yesmaximal, characteristic
2C2×C13×#387C211yesmaximal, characteristic, complemented
3C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
4C13×#1445C211yesmaximal, characteristic, complemented
5C13×#1442C211yesmaximal, characteristic, complemented
6C13×#1441C211yesmaximal, characteristic, complemented
7C13×#1441C211yesmaximal, characteristic, complemented
8C13×#1439C211yesmaximal, characteristic
9C13×#1439C211yesmaximal, characteristic
10C13×#1439C211yesmaximal, characteristic
11C13×#1436C211yesmaximal, characteristic, complemented
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×C4⋊#95C211yesmaximal, 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×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C42×C13C2211yescharacteristic
30C22×C42×C13C2211yescharacteristic
31C13×#396C418yescomplemented
32C13×#387—24no—
33C4×C13×C22⋊C4—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×C13—22no—
56C23×C4×C13—22no—
57C23×C4×C13—41no—
58C23×C4×C13—41no—
59C23×C4×C13—41no—
60C23×C4×C13—41no—
61C23×C4×C13Q814yes—
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—41no—
82C2×C13×C4⋊C4—41no—
83C2×C13×C4⋊C4—41no—
84C2×C13×C4⋊C4—41no—
85C2×C13×C4⋊C4—41no—
86C2×C13×C4⋊C4—41no—
87C2×C13×C4⋊C4—41no—
88C2×C13×C4⋊C4—41no—
89C2×C13×C4⋊C4—41no—
90C2×C13×C4⋊C4—41no—
91C2×C13×C4⋊C4C2×C414yescomplemented
92C2×C13×C4⋊C4C2×C414yescomplemented
93C2×C13×C4⋊C4C2×C414yescomplemented
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—41no—
102C2×C13×C22⋊C4—41no—
103C2×C13×C22⋊C4—41no—
104C2×C13×C22⋊C4—41no—
105C2×C13×C22⋊C4—41no—
106C2×C13×C22⋊C4—41no—
107C2×C13×C22⋊C4—41no—
108C2×C13×C22⋊C4—41no—
109C2×C13×C22⋊C4C2×C414yes—
110C2×C13×C22⋊C4C2×C414yes—
111C2×C13×C22⋊C4C2×C414yes—
112C2×C42×C13—22no—
113C2×C42×C13—41no—
114C2×C42×C13—41no—
115C2×C42×C13—41no—
116C2×C42×C13—41no—
117C2×C42×C13D414yes—
118C13×#95—22no—
119C13×#95—22no—
120C13×#95—22no—
121C13×#95—22no—
122C13×#95—22no—
123C13×#95—22no—
124C13×#95—22no—
125C13×#95—22no—
126C13×#95—22no—
127C13×#95—41no—
128C13×#95—41no—
129C13×#95—41no—
130C13×#95—41no—
131C13×#95—41no—
132C13×#95—41no—
133C13×#95—41no—
134C13×#95—41no—
135C13×#95—41no—
136C13×#95—41no—
137C13×#95C2×C414yescomplemented
138#14315C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
150C24×C13—21no—
151C24×C13C22×C412yes—
152C24×C13C2×Q812yes—
153C24×C13#4112yes—
154C24×C13C2411yescharacteristic
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—28no—
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—21no—
240C22×C4×C13—44no—
241C22×C4×C13—44no—
242C22×C4×C13—44no—
243C22×C4×C13—44no—
244C22×C4×C13—44no—
245C22×C4×C13—44no—
246C22×C4×C13C22×C412yes—
247C22×C4×C13C22×C412yes—
248C22×C4×C13C22×C412yes—
249C22×C4×C13C22×C412yes—
250C22×C4×C13C22×C412yes—
251C22×C4×C13C22×C412yes—
252C22×C4×C13C2×D412yes—
253C22×C4×C13C2×D412yes—
254C22×C4×C13C2×D412yes—
255C22×C4×C13C2×Q812yes—
256C22×C4×C13C2×Q812yes—
257C22×C4×C13#4112yes—
258C22×C4×C13#4112yes—
259C22×C4×C13#4112yes—
260C13×C4⋊C4—28no—
261C13×C4⋊C4—44no—
262C13×C4⋊C4—44no—
263C13×C4⋊C4—44no—
264C13×C4⋊C4—44no—
265C13×C4⋊C4—44no—
266C13×C22⋊C4—28no—
267C13×C22⋊C4—28no—
268C13×C22⋊C4—44no—
269C13×C22⋊C4—44no—
270C13×C22⋊C4—44no—
271C13×C22⋊C4—44no—
272C42×C13—44no—
273C42×C13—44no—
274C2×#396C2×C1311yescharacteristic
275C2×#387C2×C1311yescharacteristic, complemented
276C2×C4×C22⋊C4C2×C1311yescharacteristic
277#1445C2×C1311yescharacteristic, complemented
278#1442C2×C1311yescharacteristic, complemented
279#1441C2×C1311yescharacteristic, complemented
280#1441C2×C1311yescharacteristic, complemented
281#1439C2×C1311yescharacteristic
282#1439C2×C1311yescharacteristic
283#1439C2×C1311yescharacteristic
284#1436C2×C1311yescharacteristic, complemented
285#1436C2×C1311yescharacteristic, complemented
286C4⋊#95C2×C1311yescharacteristic, complemented
287C22⋊#95C2×C1311yescharacteristic
288C22⋊#95C2×C1311yescharacteristic
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
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×C13—41no—
323C23×C13C4×Q814yes—
324C23×C13C23×C411yescharacteristic
325C23×C13C22×D411yescharacteristic
326C23×C13C22×Q811yescharacteristic
327C23×C13C2×#4111yescharacteristic
328C23×C13C2×#4111yescharacteristic
329C23×C13C2×#4111yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13H(5,𝔽2)11yescharacteristic
332C23×C13H(5,𝔽2)11yescharacteristic
333C23×C13H(5,𝔽2)11yescharacteristic
334C23×C13H(5,𝔽2)11yescharacteristic
335C23×C13H(5,𝔽2)11yescharacteristic
336C23×C13H(5,𝔽2)11yescharacteristic
337C23×C132−1+411yescharacteristic
338C23×C132−1+411yescharacteristic
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—416no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13—41no—
421C2×C4×C13—41no—
422C2×C4×C13—41no—
423C2×C4×C13—41no—
424C2×C4×C13—41no—
425C2×C4×C13—41no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—41no—
430C2×C4×C13—41no—
431C2×C4×C13—41no—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—41no—
436C2×C4×C13C4×D414yes—
437C2×C4×C13C22⋊Q814yes—
438C24×C4C22×C1311yescharacteristic
439C22×C4⋊C4C22×C1311yescharacteristic
440C22×C4⋊C4C22×C1311yescharacteristic
441C22×C4⋊C4C22×C1311yescharacteristic
442C22×C4⋊C4C22×C1311yescharacteristic
443C22×C4⋊C4C22×C1311yescharacteristic
444C22×C4⋊C4C22×C1311yescharacteristic
445C22×C22⋊C4C22×C1311yescharacteristic
446C22×C22⋊C4C22×C1311yescharacteristic
447C22×C22⋊C4C22×C1311yescharacteristic
448C22×C22⋊C4C22×C1311yescharacteristic
449C22×C22⋊C4C22×C1311yescharacteristic
450C22×C22⋊C4C22×C1311yescharacteristic
451C22×C42C22×C1311yescharacteristic
452C22×C42C22×C1311yescharacteristic
453#396C4×C1318yescomplemented
454#387—24no—
455C4×C22⋊C4—24no—
456C2×#95C22×C1311yescharacteristic
457C2×#95C22×C1311yescharacteristic
458C2×#95C22×C1311yescharacteristic
459C2×#95C22×C1311yescharacteristic
460C2×#95C22×C1311yescharacteristic
461C2×#95C22×C1311yescharacteristic
462C2×#95C22×C1311yescharacteristic
463C2×#95C22×C1311yescharacteristic
464C2×#95C22×C1311yescharacteristic
465C2×#95C22×C1311yescharacteristic
466C2×#95C22×C1311yescharacteristic
467C2×#95C22×C1311yescharacteristic
468C2×#95C22×C1311yescharacteristic
469C2×#95C22×C1311yescharacteristic
470C2×#95C22×C1311yescharacteristic
471C2×#95C22×C1311yescharacteristic
472C2×#95C22×C1311yescharacteristic
473C2×#95C22×C1311yescharacteristic
474C2×#95C22×C1311yescharacteristic
475C2×#95C22×C1311yescharacteristic
476C22×C13—24no—
477C22×C13—24no—
478C22×C13—24no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—42no—
483C22×C13—42no—
484C22×C13—42no—
485C22×C13—42no—
486C22×C13—42no—
487C22×C13—42no—
488C22×C13—42no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13C2×C4×D411yescharacteristic
492C22×C13C2×C4×Q811yescharacteristic
493C22×C13C4×#4111yescharacteristic
494C22×C13#51811yescharacteristic
495C22×C13#51811yescharacteristic
496C22×C13#52011yescharacteristic
497C22×C13#52011yescharacteristic
498C22×C13C2×C22⋊Q811yescharacteristic
499C22×C13#52511yescharacteristic
500C22×C13#52911yescharacteristic
501C22×C13#53311yescharacteristic
502C22×C13#53411yescharacteristic
503C22×C13#53511yescharacteristic
504C22×C13#53711yescharacteristic
505C22×C13#53711yescharacteristic
506C22×C13#53811yescharacteristic
507C22×C13#53811yescharacteristic
508C22×C13#53811yescharacteristic
509C22×C13#53811yescharacteristic
510C22×C13#53811yescharacteristic
511C22×C13#53811yescharacteristic
512C22×C13#53911yescharacteristic
513C22×C13#53911yescharacteristic
514C22×C13#53911yescharacteristic
515C22×C13#53911yescharacteristic
516C22×C13#54011yescharacteristic
517C22×C13#54011yescharacteristic
518C22×C13#54011yescharacteristic
519C22×C13#54111yescharacteristic
520C22×C13#54211yescharacteristic
521C22×C13#54211yescharacteristic
522C22×C13#54311yescharacteristic
523C22×C13#54311yescharacteristic
524C22×C13#54411yescharacteristic
525C22×C13#54411yescharacteristic
526C4×C13—24no—
527C4×C13—24no—
528C4×C13—42no—
529C4×C13—42no—
530C4×C13—42no—
531C4×C13—42no—
532C4×C13—42no—
533C4×C13—42no—
534C4×C13—42no—
535C4×C13—42no—
536C4×C13—81no—
537C4×C13—81no—
538C4×C13—81no—
539C4×C13—81no—
540C25C23×C1311yescharacteristic
541C23×C4—22no—
542C23×C4—22no—
543C23×C4—41no—
544C23×C4—41no—
545C23×C4—41no—
546C23×C4—41no—
547C23×C4Q8×C1314yes—
548C23×C4C23×C1311yescharacteristic
549C23×C4C23×C1311yescharacteristic
550C23×C4C23×C1311yescharacteristic
551C23×C4C23×C1311yescharacteristic
552C23×C4C23×C1311yescharacteristic
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
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—41no—
570C2×C4⋊C4—41no—
571C2×C4⋊C4—41no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—41no—
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—41no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4—41no—
591C2×C22⋊C4—41no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4—41no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4C2×C4×C1314yes—
596C2×C22⋊C4C2×C4×C1314yes—
597C2×C22⋊C4C2×C4×C1314yes—
598C2×C42—22no—
599C2×C42—41no—
600C2×C42—41no—
601C2×C42—41no—
602C2×C42—41no—
603C2×C42D4×C1314yes—
604#95—22no—
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—41no—
614#95—41no—
615#95—41no—
616#95—41no—
617#95—41no—
618#95—41no—
619#95—41no—
620#95—41no—
621#95—41no—
622#95—41no—
623#95C2×C4×C1314yescomplemented
624C2×C13—44no—
625C2×C13C4×C22⋊Q811yescharacteristic
626C2×C13#232411yescharacteristic
627C2×C13#232511yescharacteristic
628C2×C13#232911yescharacteristic
629C2×C13#232911yescharacteristic
630C2×C13#233311yescharacteristic
631C2×C13#233411yescharacteristic
632C2×C13#262611yescharacteristic
633C2×C13#262911yescharacteristic
634C2×C13#263011yescharacteristic
635C2×C13#263611yescharacteristic
636C2×C13#264811yescharacteristic
637C2×C13#265211yescharacteristic
638C2×C13#266511yescharacteristic
639C2×C13#266711yescharacteristic
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24C22×C4×C1312yes—
653C24C2×Q8×C1312yes—
654C24C13×#4112yes—
655C24C24×C1311yescharacteristic
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—28no—
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—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4C22×C4×C1312yes—
748C22×C4C22×C4×C1312yes—
749C22×C4C22×C4×C1312yes—
750C22×C4C22×C4×C1312yes—
751C22×C4C22×C4×C1312yes—
752C22×C4C22×C4×C1312yes—
753C22×C4C2×D4×C1312yes—
754C22×C4C2×D4×C1312yes—
755C22×C4C2×D4×C1312yes—
756C22×C4C2×Q8×C1312yes—
757C22×C4C2×Q8×C1312yes—
758C22×C4C13×#4112yes—
759C22×C4C13×#4112yes—
760C22×C4C13×#4112yes—
761C4⋊C4—28no—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C22⋊C4—28no—
768C22⋊C4—28no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C42—44no—
774C42—44no—
775C13#1431511yescharacteristic, direct product factor, Sylow
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
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—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C4×Q8×C1314yes—
811C23C23×C4×C1311yescharacteristic
812C23C22×D4×C1311yescharacteristic
813C23C22×Q8×C1311yescharacteristic
814C23C2×C13×#4111yescharacteristic
815C23C2×C13×#4111yescharacteristic
816C23C2×C13×#4111yescharacteristic
817C23C2×C13×#4111yescharacteristic
818C23C13×H(5,𝔽2)11yescharacteristic
819C23C13×H(5,𝔽2)11yescharacteristic
820C23C13×H(5,𝔽2)11yescharacteristic
821C23C13×H(5,𝔽2)11yescharacteristic
822C23C13×H(5,𝔽2)11yescharacteristic
823C23C13×H(5,𝔽2)11yescharacteristic
824C23C13×2−1+411yescharacteristic
825C23C13×2−1+411yescharacteristic
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—416no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
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×C4C4×D4×C1314yes—
924C2×C4C13×C22⋊Q814yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C2×C4×D4×C1311yescharacteristic
941C22C2×C4×Q8×C1311yescharacteristic
942C22C4×C13×#4111yescharacteristic
943C22C13×#51811yescharacteristic
944C22C13×#51811yescharacteristic
945C22C13×#52011yescharacteristic
946C22C13×#52011yescharacteristic
947C22C2×C13×C22⋊Q811yescharacteristic
948C22C13×#52511yescharacteristic
949C22C13×#52911yescharacteristic
950C22C13×#53311yescharacteristic
951C22C13×#53411yescharacteristic
952C22C13×#53511yescharacteristic
953C22C13×#53711yescharacteristic
954C22C13×#53711yescharacteristic
955C22C13×#53811yescharacteristic
956C22C13×#53811yescharacteristic
957C22C13×#53811yescharacteristic
958C22C13×#53811yescharacteristic
959C22C13×#53811yescharacteristic
960C22C13×#53811yescharacteristic
961C22C13×#53911yescharacteristic
962C22C13×#53911yescharacteristic
963C22C13×#53911yescharacteristic
964C22C13×#53911yescharacteristic
965C22C13×#54011yescharacteristic
966C22C13×#54011yescharacteristic
967C22C13×#54011yescharacteristic
968C22C13×#54111yescharacteristic
969C22C13×#54211yescharacteristic
970C22C13×#54211yescharacteristic
971C22C13×#54311yescharacteristic
972C22C13×#54311yescharacteristic
973C22C13×#54411yescharacteristic
974C22C13×#54411yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—81no—
987C4—81no—
988C4—81no—
989C2—44no—
990C2C4×C13×C22⋊Q811yescharacteristic
991C2C13×#232411yescharacteristic
992C2C13×#232511yescharacteristic
993C2C13×#232911yescharacteristic
994C2C13×#232911yescharacteristic
995C2C13×#233311yescharacteristic
996C2C13×#233411yescharacteristic
997C2C13×#262611yescharacteristic
998C2C13×#262911yescharacteristic
999C2C13×#263011yescharacteristic
1000C2C13×#263611yescharacteristic
1001C2C13×#264811yescharacteristic
1002C2C13×#265211yescharacteristic
1003C2C13×#266511yescharacteristic
1004C2C13×#266711yescharacteristic
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. C2×C13×#387C2semidirect
4. C13×#1445C2semidirect
5. C13×#1442C2semidirect
6. C13×#1441C2semidirect
7. C13×#1441C2semidirect
11. C13×#1436C2semidirect
12. C13×#1436C2semidirect
13. C13×C4⋊#95C2semidirect
31. C13×#396C4semidirect
91. C2×C13×C4⋊C4C2×C4semidirect
92. C2×C13×C4⋊C4C2×C4semidirect
93. C2×C13×C4⋊C4C2×C4semidirect
137. C13×#95C2×C4semidirect
138. #14315C13direct (N × H)
275. C2×#387C2×C13semidirect
277. #1445C2×C13semidirect
278. #1442C2×C13semidirect
279. #1441C2×C13semidirect
280. #1441C2×C13semidirect
284. #1436C2×C13semidirect
285. #1436C2×C13semidirect
286. C4⋊#95C2×C13semidirect
453. #396C4×C13semidirect
577. C2×C4⋊C4C2×C4×C13semidirect
578. C2×C4⋊C4C2×C4×C13semidirect
579. C2×C4⋊C4C2×C4×C13semidirect
623. #95C2×C4×C13semidirect
775. C13#14315direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3962
C2×C13×#3872
C2×C4×C13×C22⋊C42
C13×#14452
C13×#14422
C13×#14412
C13×#14392
C13×#14362
C13×C4⋊#952
C13×C22⋊#952
#1431513