Finite Group Databasebeta

← C2×C13×#3524 #15749131

Subgroups — C2×C13×#3524 #15749131

Order 3328.

7226 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3524C2132yesmaximal, direct product factor
2C2×C13×#559C213yesmaximal, complemented
3C2×C13×#557C211yesmaximal, characteristic, complemented
4C2×C13×#555C213yesmaximal, complemented
5C2×C13×#553C213yesmaximal, complemented
6C2×C13×#552C213yesmaximal, complemented
7C2×C13×#550C211yesmaximal, characteristic, complemented
8C2×C13×#548C211yesmaximal, characteristic, complemented
9C2×C13×#548C211yesmaximal, characteristic, complemented
10C2×C13×#542C213yesmaximal, complemented
11C2×C13×#540C213yesmaximal, complemented
12C2×C13×#529C213yesmaximal, complemented
13C2×C13×#529C213yesmaximal, complemented
14C2×C13×#520C211yesmaximal, characteristic, complemented
15C2×C13×#519C211yesmaximal, characteristic, complemented
16C2×C4×C13×#41C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C22×C13×#41C2211yescharacteristic
19C23×Q8×C13C2211yescharacteristic
20C13×#559C22148yescomplemented
21C13×#557C22116yescomplemented
22C13×#555C22148yescomplemented
23C13×#553C22148yescomplemented
24C13×#552C22148yescomplemented
25C13×#550C22116yescomplemented
26C13×#548C22116yescomplemented
27C13×#548C22116yescomplemented
28C13×#542C22148yescomplemented
29C13×#540C22148yescomplemented
30C2×C13×C4⋊Q8C2213yes—
31C2×C13×#127C2213yes—
32C13×#529C22148yescomplemented
33C13×#529C22148yescomplemented
34C2×C13×#126C2211yescharacteristic
35C2×C13×#126C2213yes—
36C2×C13×#126C2216yes—
37C2×C13×#125C2213yes—
38C2×C13×#125C2213yes—
39C2×C13×#125C2213yes—
40C2×C13×#124C2213yes—
41C2×C13×#124C2213yes—
42C2×C13×#124C2213yes—
43C2×C13×#124C2216yes—
44C2×C13×#123C2216yes—
45C2×C13×#123C2213yes—
46C2×C13×#123C2213yes—
47C2×C13×#123C2216yes—
48C2×C13×C22⋊Q8C2213yes—
49C2×C13×C22⋊Q8C2213yes—
50C2×C13×C22⋊Q8C2213yes—
51C2×C13×#121C2213yes—
52C2×C13×#121C2213yes—
53C2×C13×#121C2213yes—
54C2×C13×#121C2213yes—
55C2×C13×#121C2216yes—
56C2×C13×#121C2213yes—
57C13×#520C22116yescomplemented
58C13×#519C22116yescomplemented
59C4×C13×#41C22116yescomplemented
60C2×C4×Q8×C13C2211yescharacteristic
61C2×C4×Q8×C13C2211yescharacteristic
62C2×C4×Q8×C13C2213yes—
63C2×C4×Q8×C13C2211yescharacteristic
64C2×C4×Q8×C13C2213yes—
65C2×C4×Q8×C13C2211yescharacteristic
66C2×C4×Q8×C13C2213yes—
67C2×C4×D4×C13C2213yes—
68C2×C4×D4×C13C2213yes—
69C2×C4×D4×C13C2213yes—
70C2×C4×D4×C13C2213yes—
71C2×C4×D4×C13C2213yes—
72C2×C4×D4×C13C2213yes—
73C2×C4×D4×C13C2213yes—
74C2×C4×D4×C13C2216yes—
75C2×C13×#117C2213yes—
76C2×C13×#117C2213yes—
77C2×C13×#117C2213yes—
78C2×C13×#117C2213yes—
79C2×C13×#117C2216yes—
80C22×C13×C4⋊C4C2213yes—
81C22×C42×C13C2213yes—
82C2×C13×#41—28no—
83C2×C13×#41—28no—
84C2×C13×#41C2318yes—
85C2×C13×#41C2318yes—
86C22×Q8×C13—28no—
87C22×Q8×C13C2313yes—
88C22×Q8×C13C2318yes—
89C22×Q8×C13C2313yes—
90C22×Q8×C13C2311yescharacteristic
91C22×D4×C13C2313yes—
92C22×D4×C13C2313yes—
93C22×D4×C13C2313yes—
94C22×D4×C13C2313yes—
95C22×D4×C13C2316yes—
96C22×D4×C13C2313yes—
97C23×C4×C13C2313yes—
98C23×C4×C13C2313yes—
99C23×C4×C13C2313yes—
100C23×C4×C13C2313yes—
101C23×C4×C13C2313yes—
102C23×C4×C13C2316yes—
103C13×C4⋊Q8C23124yes—
104C13×#127C23124yes—
105C13×#126C2318yes—
106C13×#126C23124yes—
107C13×#126C23148yes—
108C13×#125C23124yes—
109C13×#125C23124yes—
110C13×#125C23124yes—
111C13×#124C23124yes—
112C13×#124C23124yes—
113C13×#124C23124yes—
114C13×#124C23148yes—
115C13×#123C23148yes—
116C13×#123C23124yes—
117C13×#123C23124yes—
118C13×#123C23148yes—
119C13×C22⋊Q8C23124yes—
120C13×C22⋊Q8C23124yes—
121C13×C22⋊Q8C23124yes—
122C13×#121C23124yes—
123C13×#121C23124yes—
124C13×#121C23124yes—
125C13×#121C23124yes—
126C13×#121C23148yes—
127C13×#121C23124yes—
128C4×Q8×C13C2318yes—
129C4×Q8×C13C2318yes—
130C4×Q8×C13C23124yes—
131C4×Q8×C13C2318yes—
132C4×Q8×C13C23124yes—
133C4×Q8×C13C2318yes—
134C4×Q8×C13C23124yes—
135C4×D4×C13C23124yes—
136C4×D4×C13C23124yes—
137C4×D4×C13C23124yes—
138C4×D4×C13C23124yes—
139C4×D4×C13C23124yes—
140C4×D4×C13C23124yes—
141C4×D4×C13C23124yes—
142C4×D4×C13C23148yes—
143C13×#117C23124yes—
144C13×#117C23124yes—
145C13×#117C23124yes—
146C13×#117C23124yes—
147C13×#117C23148yes—
148C2×C13×C4⋊C4C2313yes—
149C2×C13×C4⋊C4C2313yes—
150C2×C13×C4⋊C4C2313yes—
151C2×C13×C4⋊C4C23124yes—
152C2×C13×C4⋊C4C2311yescharacteristic
153C2×C13×C4⋊C4C2313yes—
154C2×C13×C4⋊C4C2313yes—
155C2×C13×C4⋊C4C2313yes—
156C2×C13×C4⋊C4C2313yes—
157C2×C13×C4⋊C4C2313yes—
158C2×C13×C4⋊C4C2316yes—
159C2×C13×C4⋊C4C2311yescharacteristic
160C2×C13×C4⋊C4C2313yes—
161C2×C13×C4⋊C4C2313yes—
162C2×C13×C4⋊C4C2311yescharacteristic
163C2×C13×C4⋊C4C2313yes—
164C2×C13×C22⋊C4C2311yescharacteristic
165C2×C13×C22⋊C4C2313yes—
166C2×C13×C22⋊C4C2313yes—
167C2×C13×C22⋊C4C2313yes—
168C2×C13×C22⋊C4C2316yes—
169C2×C13×C22⋊C4C2313yes—
170C2×C13×C22⋊C4C2316yes—
171C2×C13×C22⋊C4C2311yescharacteristic
172C2×C13×C22⋊C4C2313yes—
173C2×C13×C22⋊C4C2311yescharacteristic
174C2×C13×C22⋊C4C2313yes—
175C2×C13×C22⋊C4C2316yes—
176C2×C13×C22⋊C4C2313yes—
177C2×C42×C13C2311yescharacteristic
178C2×C42×C13C2313yes—
179C2×C42×C13C2313yes—
180C2×C42×C13C2313yes—
181C2×C42×C13C23124yes—
182C2×C42×C13C2316yes—
183C2×C42×C13C2313yes—
184C2×C42×C13C2313yes—
185C2×#3524C1311yesmaximal, characteristic, direct product factor, Sylow
186C24×C13C2411yescharacteristic
187C24×C13C2413yes—
188C24×C13C2413yes—
189C13×#41—232no—
190C13×#41—232no—
191C2×Q8×C13—232no—
192C2×Q8×C13—212no—
193C2×Q8×C13—46no—
194C2×Q8×C13#4118yes—
195C2×Q8×C13C24112yes—
196C2×Q8×C13C24112yes—
197C2×Q8×C13C2414yes—
198C2×D4×C13—212no—
199C2×D4×C13—212no—
200C2×D4×C13—46no—
201C2×D4×C13—46no—
202C2×D4×C13—46no—
203C2×D4×C13—412no—
204C2×D4×C13C24112yes—
205C2×D4×C13C24112yes—
206C2×D4×C13C24112yes—
207C2×D4×C13C24112yes—
208C2×D4×C13C24124yes—
209C2×D4×C13C24112yes—
210C22×C4×C13—212no—
211C22×C4×C13—212no—
212C22×C4×C13—212no—
213C22×C4×C13—46no—
214C22×C4×C13—412no—
215C22×C4×C13—46no—
216C22×C4×C13C24112yes—
217C22×C4×C13C24112yes—
218C22×C4×C13C24112yes—
219C22×C4×C13C2411yescharacteristic
220C22×C4×C13C2411yescharacteristic
221C22×C4×C13C2411yescharacteristic
222C22×C4×C13C2413yes—
223C22×C4×C13C2411yescharacteristic
224C22×C4×C13C2413yes—
225C22×C4×C13C2411yescharacteristic
226C22×C4×C13C2413yes—
227C22×C4×C13C2413yes—
228C22×C4×C13C2413yes—
229C22×C4×C13C2411yescharacteristic
230C22×C4×C13C24112yes—
231C22×C4×C13C24112yes—
232C22×C4×C13C24124yes—
233C22×C4×C13C2413yes—
234C13×C4⋊C4C24112yes—
235C13×C4⋊C4C24112yes—
236C13×C4⋊C4C24112yes—
237C13×C4⋊C4C2414yes—
238C13×C4⋊C4C24112yes—
239C13×C4⋊C4C24112yes—
240C13×C4⋊C4C24112yes—
241C13×C4⋊C4C24112yes—
242C13×C4⋊C4C24112yes—
243C13×C4⋊C4C24124yes—
244C13×C4⋊C4C2414yes—
245C13×C4⋊C4C24112yes—
246C13×C4⋊C4C24112yes—
247C13×C4⋊C4C2414yes—
248C13×C4⋊C4C24112yes—
249C13×C22⋊C4C2414yes—
250C13×C22⋊C4C24112yes—
251C13×C22⋊C4C24112yes—
252C13×C22⋊C4C24112yes—
253C13×C22⋊C4C24124yes—
254C13×C22⋊C4C24112yes—
255C13×C22⋊C4C24124yes—
256C13×C22⋊C4C2414yes—
257C13×C22⋊C4C24112yes—
258C13×C22⋊C4C2414yes—
259C13×C22⋊C4C24112yes—
260C13×C22⋊C4C24124yes—
261C13×C22⋊C4C24112yes—
262C42×C13C2414yes—
263C42×C13C24112yes—
264C42×C13C24112yes—
265C42×C13C24112yes—
266C42×C13C24124yes—
267C42×C13C24112yes—
268C42×C13C24112yes—
269#3524C2×C13132yesdirect product factor
270C2×#559C2×C1313yescomplemented
271C2×#557C2×C1311yescharacteristic, complemented
272C2×#555C2×C1313yescomplemented
273C2×#553C2×C1313yescomplemented
274C2×#552C2×C1313yescomplemented
275C2×#550C2×C1311yescharacteristic, complemented
276C2×#548C2×C1311yescharacteristic, complemented
277C2×#548C2×C1311yescharacteristic, complemented
278C2×#542C2×C1313yescomplemented
279C2×#540C2×C1313yescomplemented
280C2×#529C2×C1313yescomplemented
281C2×#529C2×C1313yescomplemented
282C2×#520C2×C1311yescharacteristic, complemented
283C2×#519C2×C1311yescharacteristic, complemented
284C2×C4×#41C2×C1311yescharacteristic, complemented
285C23×C13—22no—
286C23×C13—26no—
287C23×C13—26no—
288C23×C13—26no—
289C23×C13—26no—
290C23×C13—26no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—26no—
294C23×C13C2512yes—
295C23×C13C2516yes—
296C23×C13C2516yes—
297C23×C13C2511yescharacteristic
298Q8×C13—224no—
299Q8×C13—412no—
300Q8×C13C2×#41116yes—
301D4×C13—224no—
302D4×C13—224no—
303D4×C13—412no—
304D4×C13—412no—
305D4×C13—412no—
306D4×C13—424no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—26no—
310C2×C4×C13—22no—
311C2×C4×C13—26no—
312C2×C4×C13—22no—
313C2×C4×C13—26no—
314C2×C4×C13—26no—
315C2×C4×C13—22no—
316C2×C4×C13—26no—
317C2×C4×C13—22no—
318C2×C4×C13—224no—
319C2×C4×C13—224no—
320C2×C4×C13—224no—
321C2×C4×C13—412no—
322C2×C4×C13—424no—
323C2×C4×C13—412no—
324C2×C4×C13C2×#41112yes—
325C2×C4×C13C2512yes—
326C2×C4×C13C2512yes—
327C2×C4×C13C2512yes—
328C2×C4×C13C2516yes—
329C2×C4×C13C2512yes—
330C2×C4×C13C2516yes—
331C2×C4×C13C2512yes—
332C2×C4×C13C2516yes—
333C2×C4×C13C2516yes—
334C2×C4×C13C2516yes—
335C2×C4×C13C2512yes—
336C2×C4×C13C2516yes—
337C22×#41C22×C1311yescharacteristic
338C22×#41C22×C1311yescharacteristic
339C23×Q8C22×C1311yescharacteristic
340#559C22×C13148yescomplemented
341#557C22×C13116yescomplemented
342#555C22×C13148yescomplemented
343#553C22×C13148yescomplemented
344#552C22×C13148yescomplemented
345#550C22×C13116yescomplemented
346#548C22×C13116yescomplemented
347#548C22×C13116yescomplemented
348#542C22×C13148yescomplemented
349#540C22×C13148yescomplemented
350C2×C4⋊Q8C22×C1313yes—
351C2×#127C22×C1313yes—
352#529C22×C13148yescomplemented
353#529C22×C13148yescomplemented
354C2×#126C22×C1311yescharacteristic
355C2×#126C22×C1313yes—
356C2×#126C22×C1316yes—
357C2×#125C22×C1313yes—
358C2×#125C22×C1313yes—
359C2×#125C22×C1313yes—
360C2×#124C22×C1313yes—
361C2×#124C22×C1313yes—
362C2×#124C22×C1313yes—
363C2×#124C22×C1316yes—
364C2×#123C22×C1316yes—
365C2×#123C22×C1313yes—
366C2×#123C22×C1313yes—
367C2×#123C22×C1316yes—
368C2×C22⋊Q8C22×C1313yes—
369C2×C22⋊Q8C22×C1313yes—
370C2×C22⋊Q8C22×C1313yes—
371C2×#121C22×C1313yes—
372C2×#121C22×C1313yes—
373C2×#121C22×C1313yes—
374C2×#121C22×C1313yes—
375C2×#121C22×C1316yes—
376C2×#121C22×C1313yes—
377#520C22×C13116yescomplemented
378#519C22×C13116yescomplemented
379C4×#41C22×C13116yescomplemented
380C2×C4×Q8C22×C1311yescharacteristic
381C2×C4×Q8C22×C1311yescharacteristic
382C2×C4×Q8C22×C1313yes—
383C2×C4×Q8C22×C1311yescharacteristic
384C2×C4×Q8C22×C1313yes—
385C2×C4×Q8C22×C1311yescharacteristic
386C2×C4×Q8C22×C1313yes—
387C2×C4×D4C22×C1313yes—
388C2×C4×D4C22×C1313yes—
389C2×C4×D4C22×C1313yes—
390C2×C4×D4C22×C1313yes—
391C2×C4×D4C22×C1313yes—
392C2×C4×D4C22×C1313yes—
393C2×C4×D4C22×C1313yes—
394C2×C4×D4C22×C1316yes—
395C2×#117C22×C1313yes—
396C2×#117C22×C1313yes—
397C2×#117C22×C1313yes—
398C2×#117C22×C1313yes—
399C2×#117C22×C1316yes—
400C22×C4⋊C4C22×C1313yes—
401C22×C42C22×C1313yes—
402C22×C13—22no—
403C22×C13—26no—
404C22×C13—26no—
405C22×C13—26no—
406C22×C13—26no—
407C22×C13—26no—
408C22×C13—22no—
409C22×C13—22no—
410C22×C13—26no—
411C22×C13—44no—
412C22×C13—412no—
413C22×C13—412no—
414C22×C13C22×#4112yes—
415C22×C13#58512yes—
416C22×C13#58512yes—
417C22×C13C2611yescharacteristic
418C4×C13—22no—
419C4×C13—22no—
420C4×C13—26no—
421C4×C13—22no—
422C4×C13—26no—
423C4×C13—22no—
424C4×C13—26no—
425C4×C13—26no—
426C4×C13—22no—
427C4×C13—26no—
428C4×C13—22no—
429C4×C13C22×#41112yes—
430C2×#41—28no—
431C2×#41—28no—
432C2×#41C23×C1318yes—
433C2×#41C23×C1318yes—
434C22×Q8—28no—
435C22×Q8C23×C1313yes—
436C22×Q8C23×C1318yes—
437C22×Q8C23×C1313yes—
438C22×Q8C23×C1311yescharacteristic
439C22×D4C23×C1313yes—
440C22×D4C23×C1313yes—
441C22×D4C23×C1313yes—
442C22×D4C23×C1313yes—
443C22×D4C23×C1316yes—
444C22×D4C23×C1313yes—
445C23×C4C23×C1313yes—
446C23×C4C23×C1313yes—
447C23×C4C23×C1313yes—
448C23×C4C23×C1316yes—
449C23×C4C23×C1313yes—
450C23×C4C23×C1313yes—
451C4⋊Q8C23×C13124yes—
452#127C23×C13124yes—
453#126C23×C1318yes—
454#126C23×C13124yes—
455#126C23×C13148yes—
456#125C23×C13124yes—
457#125C23×C13124yes—
458#125C23×C13124yes—
459#124C23×C13124yes—
460#124C23×C13124yes—
461#124C23×C13124yes—
462#124C23×C13148yes—
463#123C23×C13148yes—
464#123C23×C13124yes—
465#123C23×C13124yes—
466#123C23×C13148yes—
467C22⋊Q8C23×C13124yes—
468C22⋊Q8C23×C13124yes—
469C22⋊Q8C23×C13124yes—
470#121C23×C13124yes—
471#121C23×C13124yes—
472#121C23×C13124yes—
473#121C23×C13124yes—
474#121C23×C13148yes—
475#121C23×C13124yes—
476C4×Q8C23×C1318yes—
477C4×Q8C23×C1318yes—
478C4×Q8C23×C13124yes—
479C4×Q8C23×C1318yes—
480C4×Q8C23×C13124yes—
481C4×Q8C23×C1318yes—
482C4×Q8C23×C13124yes—
483C4×D4C23×C13124yes—
484C4×D4C23×C13124yes—
485C4×D4C23×C13124yes—
486C4×D4C23×C13124yes—
487C4×D4C23×C13124yes—
488C4×D4C23×C13124yes—
489C4×D4C23×C13124yes—
490C4×D4C23×C13148yes—
491#117C23×C13124yes—
492#117C23×C13124yes—
493#117C23×C13124yes—
494#117C23×C13124yes—
495#117C23×C13148yes—
496C2×C4⋊C4C23×C1313yes—
497C2×C4⋊C4C23×C1313yes—
498C2×C4⋊C4C23×C1313yes—
499C2×C4⋊C4C23×C13124yes—
500C2×C4⋊C4C23×C1311yescharacteristic
501C2×C4⋊C4C23×C1313yes—
502C2×C4⋊C4C23×C1313yes—
503C2×C4⋊C4C23×C1313yes—
504C2×C4⋊C4C23×C1313yes—
505C2×C4⋊C4C23×C1313yes—
506C2×C4⋊C4C23×C1316yes—
507C2×C4⋊C4C23×C1311yescharacteristic
508C2×C4⋊C4C23×C1313yes—
509C2×C4⋊C4C23×C1313yes—
510C2×C4⋊C4C23×C1311yescharacteristic
511C2×C4⋊C4C23×C1313yes—
512C2×C22⋊C4C23×C1311yescharacteristic
513C2×C22⋊C4C23×C1313yes—
514C2×C22⋊C4C23×C1313yes—
515C2×C22⋊C4C23×C1313yes—
516C2×C22⋊C4C23×C1316yes—
517C2×C22⋊C4C23×C1313yes—
518C2×C22⋊C4C23×C1316yes—
519C2×C22⋊C4C23×C1311yescharacteristic
520C2×C22⋊C4C23×C1313yes—
521C2×C22⋊C4C23×C1311yescharacteristic
522C2×C22⋊C4C23×C1313yes—
523C2×C22⋊C4C23×C1316yes—
524C2×C22⋊C4C23×C1313yes—
525C2×C42C23×C1313yes—
526C2×C42C23×C1313yes—
527C2×C42C23×C1316yes—
528C2×C42C23×C1313yes—
529C2×C42C23×C1313yes—
530C2×C42C23×C1313yes—
531C2×C42C23×C13124yes—
532C2×C42C23×C1311yescharacteristic
533C2×C13—42no—
534C2×C13—46no—
535C2×C13—46no—
536C2×C13#352414yesdirect product factor
537C2×C13C23×#4111yescharacteristic
538C2×C13C2×#58511yescharacteristic
539C2×C13C2×#58511yescharacteristic
540C24C24×C1311yescharacteristic
541C24C24×C1313yes—
542C24C24×C1313yes—
543#41—232no—
544#41—232no—
545C2×Q8—232no—
546C2×Q8—212no—
547C2×Q8—46no—
548C2×Q8C13×#4118yes—
549C2×Q8C24×C13112yes—
550C2×Q8C24×C13112yes—
551C2×Q8C24×C1314yes—
552C2×D4—212no—
553C2×D4—212no—
554C2×D4—46no—
555C2×D4—46no—
556C2×D4—46no—
557C2×D4—412no—
558C2×D4C24×C13112yes—
559C2×D4C24×C13112yes—
560C2×D4C24×C13112yes—
561C2×D4C24×C13112yes—
562C2×D4C24×C13124yes—
563C2×D4C24×C13112yes—
564C22×C4—212no—
565C22×C4—212no—
566C22×C4—212no—
567C22×C4—46no—
568C22×C4—412no—
569C22×C4—46no—
570C22×C4C24×C1311yescharacteristic
571C22×C4C24×C1313yes—
572C22×C4C24×C1311yescharacteristic
573C22×C4C24×C1311yescharacteristic
574C22×C4C24×C1311yescharacteristic
575C22×C4C24×C1313yes—
576C22×C4C24×C1311yescharacteristic
577C22×C4C24×C1313yes—
578C22×C4C24×C1313yes—
579C22×C4C24×C13112yes—
580C22×C4C24×C1313yes—
581C22×C4C24×C1311yescharacteristic
582C22×C4C24×C13112yes—
583C22×C4C24×C13112yes—
584C22×C4C24×C13112yes—
585C22×C4C24×C13112yes—
586C22×C4C24×C13124yes—
587C22×C4C24×C1313yes—
588C4⋊C4C24×C13112yes—
589C4⋊C4C24×C13112yes—
590C4⋊C4C24×C13112yes—
591C4⋊C4C24×C1314yes—
592C4⋊C4C24×C13112yes—
593C4⋊C4C24×C13112yes—
594C4⋊C4C24×C13112yes—
595C4⋊C4C24×C13112yes—
596C4⋊C4C24×C13112yes—
597C4⋊C4C24×C13124yes—
598C4⋊C4C24×C1314yes—
599C4⋊C4C24×C13112yes—
600C4⋊C4C24×C13112yes—
601C4⋊C4C24×C1314yes—
602C4⋊C4C24×C13112yes—
603C22⋊C4C24×C1314yes—
604C22⋊C4C24×C13112yes—
605C22⋊C4C24×C13112yes—
606C22⋊C4C24×C13112yes—
607C22⋊C4C24×C13124yes—
608C22⋊C4C24×C13112yes—
609C22⋊C4C24×C13124yes—
610C22⋊C4C24×C1314yes—
611C22⋊C4C24×C13112yes—
612C22⋊C4C24×C1314yes—
613C22⋊C4C24×C13112yes—
614C22⋊C4C24×C13124yes—
615C22⋊C4C24×C13112yes—
616C42C24×C1314yes—
617C42C24×C13112yes—
618C42C24×C13112yes—
619C42C24×C13112yes—
620C42C24×C13124yes—
621C42C24×C13112yes—
622C42C24×C13112yes—
623C13C2×#352411yescharacteristic, direct product factor, Sylow
624C23—22no—
625C23—26no—
626C23—26no—
627C23—26no—
628C23—26no—
629C23—26no—
630C23—22no—
631C23—22no—
632C23—26no—
633C23C25×C1312yes—
634C23C25×C1316yes—
635C23C25×C1316yes—
636C23C25×C1311yescharacteristic
637Q8—224no—
638Q8—412no—
639Q8C2×C13×#41116yes—
640D4—224no—
641D4—224no—
642D4—412no—
643D4—412no—
644D4—412no—
645D4—424no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—26no—
649C2×C4—22no—
650C2×C4—26no—
651C2×C4—22no—
652C2×C4—26no—
653C2×C4—26no—
654C2×C4—22no—
655C2×C4—26no—
656C2×C4—22no—
657C2×C4—224no—
658C2×C4—224no—
659C2×C4—224no—
660C2×C4—412no—
661C2×C4—424no—
662C2×C4—412no—
663C2×C4C2×C13×#41112yes—
664C2×C4C25×C1312yes—
665C2×C4C25×C1312yes—
666C2×C4C25×C1312yes—
667C2×C4C25×C1316yes—
668C2×C4C25×C1312yes—
669C2×C4C25×C1316yes—
670C2×C4C25×C1312yes—
671C2×C4C25×C1316yes—
672C2×C4C25×C1316yes—
673C2×C4C25×C1316yes—
674C2×C4C25×C1312yes—
675C2×C4C25×C1316yes—
676C22—22no—
677C22—26no—
678C22—26no—
679C22—26no—
680C22—26no—
681C22—26no—
682C22—22no—
683C22—22no—
684C22—26no—
685C22—44no—
686C22—412no—
687C22—412no—
688C22C22×C13×#4112yes—
689C22C13×#58512yes—
690C22C13×#58512yes—
691C22C26×C1311yescharacteristic
692C4—22no—
693C4—22no—
694C4—26no—
695C4—22no—
696C4—26no—
697C4—22no—
698C4—26no—
699C4—26no—
700C4—22no—
701C4—26no—
702C4—22no—
703C4C22×C13×#41112yes—
704C2—42no—
705C2—46no—
706C2—46no—
707C2C13×#352414yesdirect product factor
708C2C23×C13×#4111yescharacteristic
709C2C2×C13×#58511yescharacteristic
710C2C2×C13×#58511yescharacteristic
subgroupG/H
center, socleC23×C13C25
commutator, Frattini, cosocleC22C26×C13
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3524C2direct (N × H)
2. C2×C13×#559C2semidirect
3. C2×C13×#557C2semidirect
4. C2×C13×#555C2semidirect
5. C2×C13×#553C2semidirect
6. C2×C13×#552C2semidirect
7. C2×C13×#550C2semidirect
8. C2×C13×#548C2semidirect
9. C2×C13×#548C2semidirect
10. C2×C13×#542C2semidirect
11. C2×C13×#540C2semidirect
12. C2×C13×#529C2semidirect
13. C2×C13×#529C2semidirect
14. C2×C13×#520C2semidirect
15. C2×C13×#519C2semidirect
16. C2×C4×C13×#41C2semidirect
20. C13×#559C22semidirect
21. C13×#557C22semidirect
22. C13×#555C22semidirect
23. C13×#553C22semidirect
24. C13×#552C22semidirect
25. C13×#550C22semidirect
26. C13×#548C22semidirect
27. C13×#548C22semidirect
28. C13×#542C22semidirect
29. C13×#540C22semidirect
32. C13×#529C22semidirect
33. C13×#529C22semidirect
57. C13×#520C22semidirect
58. C13×#519C22semidirect
59. C4×C13×#41C22semidirect
185. C2×#3524C13direct (N × H)
269. #3524C2×C13direct (N × H)
270. C2×#559C2×C13semidirect
271. C2×#557C2×C13semidirect
272. C2×#555C2×C13semidirect
273. C2×#553C2×C13semidirect
274. C2×#552C2×C13semidirect
275. C2×#550C2×C13semidirect
276. C2×#548C2×C13semidirect
277. C2×#548C2×C13semidirect
278. C2×#542C2×C13semidirect
279. C2×#540C2×C13semidirect
280. C2×#529C2×C13semidirect
281. C2×#529C2×C13semidirect
282. C2×#520C2×C13semidirect
283. C2×#519C2×C13semidirect
284. C2×C4×#41C2×C13semidirect
340. #559C22×C13semidirect
341. #557C22×C13semidirect
342. #555C22×C13semidirect
343. #553C22×C13semidirect
344. #552C22×C13semidirect
345. #550C22×C13semidirect
346. #548C22×C13semidirect
347. #548C22×C13semidirect
348. #542C22×C13semidirect
349. #540C22×C13semidirect
352. #529C22×C13semidirect
353. #529C22×C13semidirect
377. #520C22×C13semidirect
378. #519C22×C13semidirect
379. C4×#41C22×C13semidirect
536. C2×C13#3524direct (N × H)
623. C13C2×#3524direct (N × H)
707. C2C13×#3524direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35242
C2×C13×#5592
C2×C13×#5572
C2×C13×#5552
C2×C13×#5532
C2×C13×#5522
C2×C13×#5502
C2×C13×#5482
C2×C13×#5422
C2×C13×#5402
C2×C13×#5292
C2×C13×#5202
C2×C13×#5192
C2×C4×C13×#412
C2×#352413