Finite Group Databasebeta

← C13×#14045 #15700384

Subgroups — C13×#14045 #15700384

Order 3328.

1530 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#389C211yesmaximal, characteristic
2C2×C13×#389C211yesmaximal, characteristic
3C2×C13×#389C211yesmaximal, characteristic
4C2×C4×C13×C4⋊C4C211yesmaximal, characteristic
5C2×C4×C13×C4⋊C4C211yesmaximal, characteristic
6C13×#1444C212yesmaximal
7C13×#1441C212yesmaximal
8C13×#1436C212yesmaximal
9C13×C4⋊#95C211yesmaximal, characteristic
10C13×C4⋊#95C212yesmaximal
11C13×C4⋊#95C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2212yes—
19C22×C13×C4⋊C4C2212yes—
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×C42×C13C2212yes—
23C22×C42×C13C2211yescharacteristic
24C22×C42×C13C2211yescharacteristic
25C13×#389—24no—
26C13×#389—24no—
27C13×#389C418yescomplemented
28C4×C13×C4⋊C4—24no—
29C4×C13×C4⋊C4—24no—
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2212yes—
33C2×C13×#95C2212yes—
34C2×C13×#95C2212yes—
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C2×C13×#95C2212yes—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2312yes—
48C23×C4×C13C2311yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2311yescharacteristic
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—24no—
61C2×C13×C4⋊C4—24no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—24no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—42no—
67C2×C13×C4⋊C4—42no—
68C2×C13×C4⋊C4—42no—
69C2×C13×C4⋊C4—42no—
70C2×C13×C4⋊C4—42no—
71C2×C13×C4⋊C4C2×C414yes—
72C2×C13×C4⋊C4C2×C418yes—
73C2×C13×C4⋊C4C2×C414yes—
74C2×C13×C4⋊C4D414yes—
75C2×C13×C4⋊C4Q814yes—
76C2×C13×C4⋊C4Q814yes—
77C2×C13×C4⋊C4Q814yes—
78C2×C42×C13—22no—
79C2×C42×C13—22no—
80C2×C42×C13—22no—
81C2×C42×C13—22no—
82C2×C42×C13—24no—
83C2×C42×C13—22no—
84C2×C42×C13—22no—
85C2×C42×C13—24no—
86C2×C42×C13—22no—
87C2×C42×C13—42no—
88C2×C42×C13C2×C414yes—
89C2×C42×C13D414yes—
90C13×#95—22no—
91C13×#95—24no—
92C13×#95—22no—
93C13×#95—24no—
94C13×#95—24no—
95C13×#95—24no—
96C13×#95—42no—
97C13×#95—42no—
98C13×#95—42no—
99C13×#95C2×C418yes—
100#14045C1311yesmaximal, characteristic, direct product factor, Sylow
101C24×C13C2411yescharacteristic
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—22no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
120C22×C4×C13—22no—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—22no—
149C22×C4×C13—21no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13C22×C414yes—
158C22×C4×C13C22×C412yes—
159C22×C4×C13C22×C414yes—
160C22×C4×C13C22×C412yes—
161C22×C4×C13C22×C412yes—
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×D414yes—
164C22×C4×C13C2×D412yes—
165C22×C4×C13C2×D412yes—
166C22×C4×C13C2×D412yes—
167C22×C4×C13C2×Q812yes—
168C22×C4×C13C2×Q814yes—
169C22×C4×C13C2×Q814yes—
170C22×C4×C13C2×Q812yes—
171C22×C4×C13C2×Q812yes—
172C22×C4×C13C2×Q812yes—
173C22×C4×C13C2×Q812yes—
174C22×C4×C13#4112yes—
175C22×C4×C13#4112yes—
176C22×C4×C13#4112yes—
177C22×C4×C13#4112yes—
178C22×C4×C13#4112yes—
179C13×C4⋊C4—28no—
180C13×C4⋊C4—28no—
181C13×C4⋊C4—28no—
182C13×C4⋊C4—28no—
183C13×C4⋊C4—48no—
184C13×C4⋊C4—48no—
185C13×C4⋊C4—48no—
186C13×C4⋊C4—44no—
187C13×C4⋊C4C4⋊C4116yescomplemented
188C42×C13—28no—
189C42×C13—28no—
190C42×C13—48no—
191C42×C13—44no—
192C2×#389C2×C1311yescharacteristic
193C2×#389C2×C1311yescharacteristic
194C2×#389C2×C1311yescharacteristic
195C2×C4×C4⋊C4C2×C1311yescharacteristic
196C2×C4×C4⋊C4C2×C1311yescharacteristic
197#1444C2×C1312yes—
198#1441C2×C1312yes—
199#1436C2×C1312yes—
200C4⋊#95C2×C1311yescharacteristic
201C4⋊#95C2×C1312yes—
202C4⋊#95C2×C1311yescharacteristic
203C23×C13C23×C411yescharacteristic
204C23×C13C22×D411yescharacteristic
205C23×C13C22×D411yescharacteristic
206C23×C13C22×Q811yescharacteristic
207C23×C13C22×Q811yescharacteristic
208C23×C13C22×Q811yescharacteristic
209C23×C13C2×#4111yescharacteristic
210C23×C13C2×#4111yescharacteristic
211C23×C13C2×#4111yescharacteristic
212C23×C13C2×#4111yescharacteristic
213C23×C13C2×#4111yescharacteristic
214C23×C13H(5,𝔽2)11yescharacteristic
215C23×C13H(5,𝔽2)11yescharacteristic
216C23×C13H(5,𝔽2)11yescharacteristic
217C23×C132−1+411yescharacteristic
218C2×C4×C13—22no—
219C2×C4×C13—24no—
220C2×C4×C13—22no—
221C2×C4×C13—24no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—24no—
230C2×C4×C13—24no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—22no—
241C2×C4×C13—24no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—24no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—42no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—41no—
267C2×C4×C13—42no—
268C2×C4×C13—42no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—42no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—42no—
279C2×C4×C13—42no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13C2×C4⋊C418yes—
286C2×C4×C13C2×C4⋊C414yes—
287C2×C4×C13C4×D414yes—
288C2×C4×C13C4×Q814yes—
289C2×C4×C13C4×Q814yes—
290C2×C4×C13#12114yes—
291C2×C4×C13C22⋊Q814yes—
292C2×C4×C13C22⋊Q814yes—
293C2×C4×C13#12514yes—
294C2×C4×C13C4⋊Q814yes—
295C22×C4⋊C4C22×C1311yescharacteristic
296C22×C4⋊C4C22×C1311yescharacteristic
297C22×C4⋊C4C22×C1312yes—
298C22×C4⋊C4C22×C1311yescharacteristic
299C22×C4⋊C4C22×C1311yescharacteristic
300C22×C4⋊C4C22×C1311yescharacteristic
301C22×C4⋊C4C22×C1312yes—
302C22×C4⋊C4C22×C1312yes—
303C22×C4⋊C4C22×C1311yescharacteristic
304C22×C42C22×C1311yescharacteristic
305C22×C42C22×C1312yes—
306C22×C42C22×C1311yescharacteristic
307C22×C42C22×C1311yescharacteristic
308#389—24no—
309#389—24no—
310#389C4×C1318yescomplemented
311C4×C4⋊C4—24no—
312C4×C4⋊C4—24no—
313C2×#95C22×C1311yescharacteristic
314C2×#95C22×C1312yes—
315C2×#95C22×C1312yes—
316C2×#95C22×C1312yes—
317C2×#95C22×C1311yescharacteristic
318C2×#95C22×C1312yes—
319C2×#95C22×C1312yes—
320C2×#95C22×C1312yes—
321C2×#95C22×C1312yes—
322C2×#95C22×C1312yes—
323C22×C13C22×C4⋊C411yescharacteristic
324C22×C13C2×C4×D411yescharacteristic
325C22×C13C2×C4×Q811yescharacteristic
326C22×C13C2×C4×Q811yescharacteristic
327C22×C13C4×#4111yescharacteristic
328C22×C13#51811yescharacteristic
329C22×C13#52011yescharacteristic
330C22×C13C2×#12111yescharacteristic
331C22×C13C2×C22⋊Q811yescharacteristic
332C22×C13C2×C22⋊Q811yescharacteristic
333C22×C13#52511yescharacteristic
334C22×C13C2×#12511yescharacteristic
335C22×C13#52911yescharacteristic
336C22×C13C2×C4⋊Q811yescharacteristic
337C22×C13#53311yescharacteristic
338C22×C13#53511yescharacteristic
339C22×C13#53711yescharacteristic
340C22×C13#54011yescharacteristic
341C22×C13#54211yescharacteristic
342C22×C13#54611yescharacteristic
343C22×C13#54611yescharacteristic
344C22×C13D4×Q811yescharacteristic
345C22×C13#55011yescharacteristic
346C22×C13#55211yescharacteristic
347C22×C13#55311yescharacteristic
348C22×C13#55411yescharacteristic
349C22×C13#55411yescharacteristic
350C22×C13#55411yescharacteristic
351C22×C13#55411yescharacteristic
352C22×C13#55411yescharacteristic
353C22×C13#55511yescharacteristic
354C22×C13#55711yescharacteristic
355C22×C13#55711yescharacteristic
356C22×C13Q8211yescharacteristic
357C22×C13Q8211yescharacteristic
358C4×C13—28no—
359C4×C13—24no—
360C4×C13—24no—
361C4×C13—42no—
362C4×C13—44no—
363C4×C13—42no—
364C4×C13—42no—
365C4×C13—42no—
366C4×C13—44no—
367C4×C13—82no—
368C4×C13#38918yes—
369C23×C4C23×C1312yes—
370C23×C4C23×C1312yes—
371C23×C4C23×C1311yescharacteristic
372C23×C4C23×C1311yescharacteristic
373C23×C4C23×C1311yescharacteristic
374C23×C4C23×C1312yes—
375C23×C4C23×C1311yescharacteristic
376C23×C4C23×C1312yes—
377C23×C4C23×C1311yescharacteristic
378C23×C4C23×C1311yescharacteristic
379C23×C4C23×C1311yescharacteristic
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4C2×C4×C1314yes—
401C2×C4⋊C4C2×C4×C1318yes—
402C2×C4⋊C4C2×C4×C1314yes—
403C2×C4⋊C4D4×C1314yes—
404C2×C4⋊C4Q8×C1314yes—
405C2×C4⋊C4Q8×C1314yes—
406C2×C4⋊C4Q8×C1314yes—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—24no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—24no—
415C2×C42—22no—
416C2×C42—42no—
417C2×C42C2×C4×C1314yes—
418C2×C42D4×C1314yes—
419#95—22no—
420#95—24no—
421#95—22no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95C2×C4×C1318yes—
429C2×C13C2×#38911yescharacteristic
430C2×C13C4×C22⋊Q811yescharacteristic
431C2×C13#232411yescharacteristic
432C2×C13#234911yescharacteristic
433C2×C13Q8×C4⋊C411yescharacteristic
434C2×C13#236911yescharacteristic
435C2×C13#237011yescharacteristic
436C2×C13#241411yescharacteristic
437C2×C13#241711yescharacteristic
438C2×C13#245111yescharacteristic
439C2×C13#245411yescharacteristic
440C2×C13#250711yescharacteristic
441C2×C13#250811yescharacteristic
442C2×C13#256711yescharacteristic
443C2×C13#258411yescharacteristic
444C24C24×C1311yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4C22×C4×C1314yes—
501C22×C4C22×C4×C1312yes—
502C22×C4C22×C4×C1314yes—
503C22×C4C22×C4×C1312yes—
504C22×C4C22×C4×C1312yes—
505C22×C4C2×D4×C1312yes—
506C22×C4C2×D4×C1314yes—
507C22×C4C2×D4×C1312yes—
508C22×C4C2×D4×C1312yes—
509C22×C4C2×D4×C1312yes—
510C22×C4C2×Q8×C1312yes—
511C22×C4C2×Q8×C1314yes—
512C22×C4C2×Q8×C1314yes—
513C22×C4C2×Q8×C1312yes—
514C22×C4C2×Q8×C1312yes—
515C22×C4C2×Q8×C1312yes—
516C22×C4C2×Q8×C1312yes—
517C22×C4C13×#4112yes—
518C22×C4C13×#4112yes—
519C22×C4C13×#4112yes—
520C22×C4C13×#4112yes—
521C22×C4C13×#4112yes—
522C4⋊C4—28no—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—48no—
527C4⋊C4—48no—
528C4⋊C4—48no—
529C4⋊C4—44no—
530C4⋊C4C13×C4⋊C4116yescomplemented
531C42—28no—
532C42—28no—
533C42—48no—
534C42—44no—
535C13#1404511yescharacteristic, direct product factor, Sylow
536C23C23×C4×C1311yescharacteristic
537C23C22×D4×C1311yescharacteristic
538C23C22×D4×C1311yescharacteristic
539C23C22×Q8×C1311yescharacteristic
540C23C22×Q8×C1311yescharacteristic
541C23C22×Q8×C1311yescharacteristic
542C23C2×C13×#4111yescharacteristic
543C23C2×C13×#4111yescharacteristic
544C23C2×C13×#4111yescharacteristic
545C23C2×C13×#4111yescharacteristic
546C23C2×C13×#4111yescharacteristic
547C23C13×H(5,𝔽2)11yescharacteristic
548C23C13×H(5,𝔽2)11yescharacteristic
549C23C13×H(5,𝔽2)11yescharacteristic
550C23C13×2−1+411yescharacteristic
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4C2×C13×C4⋊C418yes—
619C2×C4C2×C13×C4⋊C414yes—
620C2×C4C4×D4×C1314yes—
621C2×C4C4×Q8×C1314yes—
622C2×C4C4×Q8×C1314yes—
623C2×C4C13×#12114yes—
624C2×C4C13×C22⋊Q814yes—
625C2×C4C13×C22⋊Q814yes—
626C2×C4C13×#12514yes—
627C2×C4C13×C4⋊Q814yes—
628C22C22×C13×C4⋊C411yescharacteristic
629C22C2×C4×D4×C1311yescharacteristic
630C22C2×C4×Q8×C1311yescharacteristic
631C22C2×C4×Q8×C1311yescharacteristic
632C22C4×C13×#4111yescharacteristic
633C22C13×#51811yescharacteristic
634C22C13×#52011yescharacteristic
635C22C2×C13×#12111yescharacteristic
636C22C2×C13×C22⋊Q811yescharacteristic
637C22C2×C13×C22⋊Q811yescharacteristic
638C22C13×#52511yescharacteristic
639C22C2×C13×#12511yescharacteristic
640C22C13×#52911yescharacteristic
641C22C2×C13×C4⋊Q811yescharacteristic
642C22C13×#53311yescharacteristic
643C22C13×#53511yescharacteristic
644C22C13×#53711yescharacteristic
645C22C13×#54011yescharacteristic
646C22C13×#54211yescharacteristic
647C22C13×#54611yescharacteristic
648C22C13×#54611yescharacteristic
649C22D4×Q8×C1311yescharacteristic
650C22C13×#55011yescharacteristic
651C22C13×#55211yescharacteristic
652C22C13×#55311yescharacteristic
653C22C13×#55411yescharacteristic
654C22C13×#55411yescharacteristic
655C22C13×#55411yescharacteristic
656C22C13×#55411yescharacteristic
657C22C13×#55411yescharacteristic
658C22C13×#55511yescharacteristic
659C22C13×#55711yescharacteristic
660C22C13×#55711yescharacteristic
661C22Q82×C1311yescharacteristic
662C22Q82×C1311yescharacteristic
663C4—24no—
664C4—28no—
665C4—24no—
666C4—42no—
667C4—44no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—44no—
672C4—82no—
673C4C13×#38918yes—
674C2C2×C13×#38911yescharacteristic
675C2C4×C13×C22⋊Q811yescharacteristic
676C2C13×#232411yescharacteristic
677C2C13×#234911yescharacteristic
678C2Q8×C13×C4⋊C411yescharacteristic
679C2C13×#236911yescharacteristic
680C2C13×#237011yescharacteristic
681C2C13×#241411yescharacteristic
682C2C13×#241711yescharacteristic
683C2C13×#245111yescharacteristic
684C2C13×#245411yescharacteristic
685C2C13×#250711yescharacteristic
686C2C13×#250811yescharacteristic
687C2C13×#256711yescharacteristic
688C2C13×#258411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
27. C13×#389C4semidirect
100. #14045C13direct (N × H)
187. C13×C4⋊C4C4⋊C4semidirect
310. #389C4×C13semidirect
530. C4⋊C4C13×C4⋊C4semidirect
535. C13#14045direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3892
C2×C4×C13×C4⋊C42
C13×#14442
C13×#14412
C13×#14362
C13×C4⋊#952
#1404513