Finite Group Databasebeta

← C2×C13×#3516 #15749124

Subgroups — C2×C13×#3516 #15749124

Order 3328.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3516C2132yesmaximal, direct product factor
2C2×C13×#557C211yesmaximal, characteristic, complemented
3C2×C13×#556C213yesmaximal, complemented
4C2×C13×#554C213yesmaximal, complemented
5C2×C13×#553C213yesmaximal, complemented
6C2×C13×#552C213yesmaximal, complemented
7C2×D4×Q8×C13C211yesmaximal, characteristic, complemented
8C2×C13×#548C211yesmaximal, characteristic, complemented
9C2×C13×#548C211yesmaximal, characteristic, complemented
10C2×C13×#542C213yesmaximal, complemented
11C2×C13×#541C213yesmaximal, complemented
12C2×C13×#529C213yesmaximal, complemented
13C2×C13×#529C213yesmaximal, complemented
14C2×C13×#520C211yesmaximal, characteristic, complemented
15C2×C13×#519C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C13C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C23×Q8×C13C2211yescharacteristic
19C23×Q8×C13C2211yescharacteristic
20C13×#557C22116yescomplemented
21C13×#556C22148yescomplemented
22C13×#554C22148yescomplemented
23C13×#553C22148yescomplemented
24C13×#552C22148yescomplemented
25D4×Q8×C13C22116yescomplemented
26C13×#548C22116yescomplemented
27C13×#548C22116yescomplemented
28C13×#542C22148yescomplemented
29C13×#541C22148yescomplemented
30C2×C13×C4⋊Q8C2213yes—
31C2×C13×C4⋊Q8C2213yes—
32C13×#529C22148yescomplemented
33C13×#529C22148yescomplemented
34C2×C13×#126C2216yes—
35C2×C13×#126C2213yes—
36C2×C13×#126C2213yes—
37C2×C13×#126C2216yes—
38C2×C13×#125C2213yes—
39C2×C13×#125C2213yes—
40C2×C13×#125C2216yes—
41C2×C13×#125C2213yes—
42C2×C13×#124C2213yes—
43C2×C13×#124C2213yes—
44C2×C13×#124C2213yes—
45C2×C13×#123C2211yescharacteristic
46C2×C13×#123C2213yes—
47C2×C13×#123C2216yes—
48C2×C13×C22⋊Q8C2213yes—
49C2×C13×C22⋊Q8C2213yes—
50C2×C13×C22⋊Q8C2213yes—
51C2×C13×C22⋊Q8C2213yes—
52C2×C13×C22⋊Q8C2213yes—
53C2×C13×C22⋊Q8C2216yes—
54C2×C13×#121C2213yes—
55C2×C13×#121C2213yes—
56C2×C13×#121C2213yes—
57C13×#520C22116yescomplemented
58C13×#519C22116yescomplemented
59C2×C4×Q8×C13C2211yescharacteristic
60C2×C4×Q8×C13C2213yes—
61C2×C4×Q8×C13C2211yescharacteristic
62C2×C4×Q8×C13C2213yes—
63C2×C4×Q8×C13C2213yes—
64C2×C4×Q8×C13C2211yescharacteristic
65C2×C4×Q8×C13C2213yes—
66C2×C4×Q8×C13C2211yescharacteristic
67C2×C4×Q8×C13C2213yes—
68C2×C4×Q8×C13C22116yescomplemented
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×#117C2216yes—
79C22×C13×C4⋊C4C2213yes—
80C22×C13×C4⋊C4C2213yes—
81C22×C42×C13C2213yes—
82C2×C13×#41—28no—
83C2×C13×#41C2318yes—
84C22×Q8×C13—28no—
85C22×Q8×C13—28no—
86C22×Q8×C13C2313yes—
87C22×Q8×C13C2313yes—
88C22×Q8×C13C2318yes—
89C22×Q8×C13C2318yes—
90C22×Q8×C13C2313yes—
91C22×Q8×C13C2311yescharacteristic
92C22×D4×C13C2313yes—
93C22×D4×C13C2311yescharacteristic
94C22×D4×C13C2313yes—
95C22×D4×C13C2313yes—
96C23×C4×C13C2311yescharacteristic
97C23×C4×C13C2313yes—
98C23×C4×C13C2313yes—
99C23×C4×C13C2313yes—
100C23×C4×C13C2313yes—
101C23×C4×C13C2316yes—
102C13×C4⋊Q8C23124yes—
103C13×C4⋊Q8C23124yes—
104C13×#126C23148yes—
105C13×#126C23124yes—
106C13×#126C23124yes—
107C13×#126C23148yes—
108C13×#125C23124yes—
109C13×#125C23124yes—
110C13×#125C23148yes—
111C13×#125C23124yes—
112C13×#124C23124yes—
113C13×#124C23124yes—
114C13×#124C23124yes—
115C13×#123C2318yes—
116C13×#123C23124yes—
117C13×#123C23148yes—
118C13×C22⋊Q8C23124yes—
119C13×C22⋊Q8C23124yes—
120C13×C22⋊Q8C23124yes—
121C13×C22⋊Q8C23124yes—
122C13×C22⋊Q8C23124yes—
123C13×C22⋊Q8C23148yes—
124C13×#121C23124yes—
125C13×#121C23124yes—
126C13×#121C23124yes—
127C4×Q8×C13C2318yes—
128C4×Q8×C13C23124yes—
129C4×Q8×C13C2318yes—
130C4×Q8×C13C23124yes—
131C4×Q8×C13C23124yes—
132C4×Q8×C13C2318yes—
133C4×Q8×C13C23124yes—
134C4×Q8×C13C2318yes—
135C4×Q8×C13C23124yes—
136C4×D4×C13C23124yes—
137C4×D4×C13C23124yes—
138C4×D4×C13C23124yes—
139C4×D4×C13C23124yes—
140C4×D4×C13C23124yes—
141C4×D4×C13C23148yes—
142C13×#117C23124yes—
143C13×#117C23124yes—
144C13×#117C23124yes—
145C13×#117C23148yes—
146C2×C13×C4⋊C4C2313yes—
147C2×C13×C4⋊C4C2313yes—
148C2×C13×C4⋊C4C2313yes—
149C2×C13×C4⋊C4C2313yes—
150C2×C13×C4⋊C4C2316yes—
151C2×C13×C4⋊C4C23124yes—
152C2×C13×C4⋊C4C23124yes—
153C2×C13×C4⋊C4C2311yescharacteristic
154C2×C13×C4⋊C4C2313yes—
155C2×C13×C4⋊C4C2313yes—
156C2×C13×C4⋊C4C2313yes—
157C2×C13×C4⋊C4C2313yes—
158C2×C13×C4⋊C4C2316yes—
159C2×C13×C4⋊C4C2313yes—
160C2×C13×C4⋊C4C2313yes—
161C2×C13×C4⋊C4C2316yes—
162C2×C13×C4⋊C4C2313yes—
163C2×C13×C4⋊C4C2311yescharacteristic
164C2×C13×C4⋊C4C2313yes—
165C2×C13×C22⋊C4C2313yes—
166C2×C13×C22⋊C4C2311yescharacteristic
167C2×C13×C22⋊C4C2313yes—
168C2×C13×C22⋊C4C2313yes—
169C2×C13×C22⋊C4C2313yes—
170C2×C13×C22⋊C4C2316yes—
171C2×C13×C22⋊C4C2311yescharacteristic
172C2×C13×C22⋊C4C2313yes—
173C2×C13×C22⋊C4C2311yescharacteristic
174C2×C13×C22⋊C4C2316yes—
175C2×C13×C22⋊C4C2313yes—
176C2×C13×C22⋊C4C2313yes—
177C2×C42×C13C2313yes—
178C2×C42×C13C2313yes—
179C2×C42×C13C2313yes—
180C2×C42×C13C2313yes—
181C2×C42×C13C23124yes—
182C2×C42×C13C2316yes—
183C2×C42×C13C2313yes—
184C2×C42×C13C2313yes—
185C2×#3516C1311yesmaximal, characteristic, direct product factor, Sylow
186C24×C13C2411yescharacteristic
187C24×C13C2413yes—
188C24×C13C2411yescharacteristic
189C13×#41—232no—
190C2×Q8×C13—232no—
191C2×Q8×C13—232no—
192C2×Q8×C13—212no—
193C2×Q8×C13—212no—
194C2×Q8×C13—46no—
195C2×Q8×C13#4118yes—
196C2×Q8×C13C24112yes—
197C2×Q8×C13C24112yes—
198C2×Q8×C13C24112yes—
199C2×Q8×C13C2414yes—
200C2×D4×C13—212no—
201C2×D4×C13—24no—
202C2×D4×C13—212no—
203C2×D4×C13—46no—
204C2×D4×C13C24112yes—
205C2×D4×C13C2414yes—
206C2×D4×C13C24112yes—
207C2×D4×C13C24112yes—
208C22×C4×C13—24no—
209C22×C4×C13—212no—
210C22×C4×C13—212no—
211C22×C4×C13—212no—
212C22×C4×C13—412no—
213C22×C4×C13—46no—
214C22×C4×C13C2414yes—
215C22×C4×C13C24112yes—
216C22×C4×C13C24112yes—
217C22×C4×C13C24112yes—
218C22×C4×C13C2411yescharacteristic
219C22×C4×C13C2411yescharacteristic
220C22×C4×C13C2413yes—
221C22×C4×C13C2411yescharacteristic
222C22×C4×C13C2413yes—
223C22×C4×C13C2411yescharacteristic
224C22×C4×C13C2413yes—
225C22×C4×C13C2413yes—
226C22×C4×C13C2413yes—
227C22×C4×C13C2413yes—
228C22×C4×C13C2411yescharacteristic
229C22×C4×C13C24112yes—
230C22×C4×C13C24124yes—
231C22×C4×C13C2413yes—
232C13×C4⋊C4C24112yes—
233C13×C4⋊C4C24112yes—
234C13×C4⋊C4C24112yes—
235C13×C4⋊C4C24112yes—
236C13×C4⋊C4C24124yes—
237C13×C4⋊C4C2414yes—
238C13×C4⋊C4C24112yes—
239C13×C4⋊C4C24112yes—
240C13×C4⋊C4C24112yes—
241C13×C4⋊C4C24112yes—
242C13×C4⋊C4C24124yes—
243C13×C4⋊C4C24112yes—
244C13×C4⋊C4C24112yes—
245C13×C4⋊C4C24124yes—
246C13×C4⋊C4C24112yes—
247C13×C4⋊C4C2414yes—
248C13×C4⋊C4C24112yes—
249C13×C22⋊C4C24112yes—
250C13×C22⋊C4C2414yes—
251C13×C22⋊C4C24112yes—
252C13×C22⋊C4C24112yes—
253C13×C22⋊C4C24112yes—
254C13×C22⋊C4C24124yes—
255C13×C22⋊C4C2414yes—
256C13×C22⋊C4C24112yes—
257C13×C22⋊C4C2414yes—
258C13×C22⋊C4C24124yes—
259C13×C22⋊C4C24112yes—
260C13×C22⋊C4C24112yes—
261C42×C13C24112yes—
262C42×C13C24112yes—
263C42×C13C24112yes—
264C42×C13C24112yes—
265C42×C13C24124yes—
266C42×C13C24112yes—
267C42×C13C24112yes—
268#3516C2×C13132yesdirect product factor
269C2×#557C2×C1311yescharacteristic, complemented
270C2×#556C2×C1313yescomplemented
271C2×#554C2×C1313yescomplemented
272C2×#553C2×C1313yescomplemented
273C2×#552C2×C1313yescomplemented
274C2×D4×Q8C2×C1311yescharacteristic, complemented
275C2×#548C2×C1311yescharacteristic, complemented
276C2×#548C2×C1311yescharacteristic, complemented
277C2×#542C2×C1313yescomplemented
278C2×#541C2×C1313yescomplemented
279C2×#529C2×C1313yescomplemented
280C2×#529C2×C1313yescomplemented
281C2×#520C2×C1311yescharacteristic, complemented
282C2×#519C2×C1311yescharacteristic, complemented
283C22×C4×Q8C2×C1311yescharacteristic, complemented
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—26no—
288C23×C13—22no—
289C23×C13—26no—
290C23×C13—26no—
291C23×C13—22no—
292C23×C132−1+414yes—
293C23×C13C2512yes—
294C23×C13C2516yes—
295C23×C13C2512yes—
296C23×C13C2511yescharacteristic
297Q8×C13—224no—
298Q8×C13—224no—
299Q8×C13—412no—
300Q8×C13C2×#41116yes—
301D4×C13—224no—
302D4×C13—28no—
303D4×C13—224no—
304D4×C13—412no—
305C2×C4×C13—22no—
306C2×C4×C13—26no—
307C2×C4×C13—26no—
308C2×C4×C13—28no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—26no—
312C2×C4×C13—22no—
313C2×C4×C13—26no—
314C2×C4×C13—26no—
315C2×C4×C13—26no—
316C2×C4×C13—22no—
317C2×C4×C13—224no—
318C2×C4×C13—224no—
319C2×C4×C13—224no—
320C2×C4×C13—424no—
321C2×C4×C13—412no—
322C2×C4×C13C2×#41112yes—
323C2×C4×C13C2512yes—
324C2×C4×C13C2512yes—
325C2×C4×C13C2516yes—
326C2×C4×C13C2512yes—
327C2×C4×C13C2516yes—
328C2×C4×C13C2512yes—
329C2×C4×C13C2516yes—
330C2×C4×C13C2516yes—
331C2×C4×C13C2516yes—
332C2×C4×C13C2516yes—
333C2×C4×C13C2512yes—
334C2×C4×C13C2516yes—
335C22×#41C22×C1311yescharacteristic
336C23×Q8C22×C1311yescharacteristic
337C23×Q8C22×C1311yescharacteristic
338#557C22×C13116yescomplemented
339#556C22×C13148yescomplemented
340#554C22×C13148yescomplemented
341#553C22×C13148yescomplemented
342#552C22×C13148yescomplemented
343D4×Q8C22×C13116yescomplemented
344#548C22×C13116yescomplemented
345#548C22×C13116yescomplemented
346#542C22×C13148yescomplemented
347#541C22×C13148yescomplemented
348C2×C4⋊Q8C22×C1313yes—
349C2×C4⋊Q8C22×C1313yes—
350#529C22×C13148yescomplemented
351#529C22×C13148yescomplemented
352C2×#126C22×C1316yes—
353C2×#126C22×C1313yes—
354C2×#126C22×C1313yes—
355C2×#126C22×C1316yes—
356C2×#125C22×C1313yes—
357C2×#125C22×C1313yes—
358C2×#125C22×C1316yes—
359C2×#125C22×C1313yes—
360C2×#124C22×C1313yes—
361C2×#124C22×C1313yes—
362C2×#124C22×C1313yes—
363C2×#123C22×C1311yescharacteristic
364C2×#123C22×C1313yes—
365C2×#123C22×C1316yes—
366C2×C22⋊Q8C22×C1313yes—
367C2×C22⋊Q8C22×C1313yes—
368C2×C22⋊Q8C22×C1313yes—
369C2×C22⋊Q8C22×C1313yes—
370C2×C22⋊Q8C22×C1313yes—
371C2×C22⋊Q8C22×C1316yes—
372C2×#121C22×C1313yes—
373C2×#121C22×C1313yes—
374C2×#121C22×C1313yes—
375#520C22×C13116yescomplemented
376#519C22×C13116yescomplemented
377C2×C4×Q8C22×C1311yescharacteristic
378C2×C4×Q8C22×C1313yes—
379C2×C4×Q8C22×C1311yescharacteristic
380C2×C4×Q8C22×C1313yes—
381C2×C4×Q8C22×C1313yes—
382C2×C4×Q8C22×C1311yescharacteristic
383C2×C4×Q8C22×C1313yes—
384C2×C4×Q8C22×C1311yescharacteristic
385C2×C4×Q8C22×C1313yes—
386C2×C4×Q8C22×C13116yescomplemented
387C2×C4×D4C22×C1313yes—
388C2×C4×D4C22×C1313yes—
389C2×C4×D4C22×C1313yes—
390C2×C4×D4C22×C1313yes—
391C2×C4×D4C22×C1313yes—
392C2×C4×D4C22×C1316yes—
393C2×#117C22×C1313yes—
394C2×#117C22×C1313yes—
395C2×#117C22×C1313yes—
396C2×#117C22×C1316yes—
397C22×C4⋊C4C22×C1313yes—
398C22×C4⋊C4C22×C1313yes—
399C22×C42C22×C1313yes—
400C22×C13—22no—
401C22×C13—22no—
402C22×C13—28no—
403C22×C13—22no—
404C22×C13—26no—
405C22×C13—22no—
406C22×C13—26no—
407C22×C13—26no—
408C22×C13—22no—
409C22×C13—44no—
410C22×C13—412no—
411C22×C13C22×#4112yes—
412C22×C13C2×2−1+414yes—
413C22×C13C2×2−1+412yes—
414C22×C13#58512yes—
415C22×C13C2611yescharacteristic
416C4×C13—22no—
417C4×C13—26no—
418C4×C13—26no—
419C4×C13—22no—
420C4×C13—22no—
421C4×C13—26no—
422C4×C13—22no—
423C4×C13—26no—
424C4×C13—26no—
425C4×C13—26no—
426C4×C13—22no—
427C4×C13C22×#41112yes—
428C2×#41—28no—
429C2×#41C23×C1318yes—
430C22×Q8—28no—
431C22×Q8—28no—
432C22×Q8C23×C1313yes—
433C22×Q8C23×C1313yes—
434C22×Q8C23×C1318yes—
435C22×Q8C23×C1318yes—
436C22×Q8C23×C1313yes—
437C22×Q8C23×C1311yescharacteristic
438C22×D4C23×C1313yes—
439C22×D4C23×C1311yescharacteristic
440C22×D4C23×C1313yes—
441C22×D4C23×C1313yes—
442C23×C4C23×C1313yes—
443C23×C4C23×C1313yes—
444C23×C4C23×C1313yes—
445C23×C4C23×C1311yescharacteristic
446C23×C4C23×C1313yes—
447C23×C4C23×C1316yes—
448C4⋊Q8C23×C13124yes—
449C4⋊Q8C23×C13124yes—
450#126C23×C13148yes—
451#126C23×C13124yes—
452#126C23×C13124yes—
453#126C23×C13148yes—
454#125C23×C13124yes—
455#125C23×C13124yes—
456#125C23×C13148yes—
457#125C23×C13124yes—
458#124C23×C13124yes—
459#124C23×C13124yes—
460#124C23×C13124yes—
461#123C23×C1318yes—
462#123C23×C13124yes—
463#123C23×C13148yes—
464C22⋊Q8C23×C13124yes—
465C22⋊Q8C23×C13124yes—
466C22⋊Q8C23×C13124yes—
467C22⋊Q8C23×C13124yes—
468C22⋊Q8C23×C13124yes—
469C22⋊Q8C23×C13148yes—
470#121C23×C13124yes—
471#121C23×C13124yes—
472#121C23×C13124yes—
473C4×Q8C23×C1318yes—
474C4×Q8C23×C13124yes—
475C4×Q8C23×C1318yes—
476C4×Q8C23×C13124yes—
477C4×Q8C23×C13124yes—
478C4×Q8C23×C1318yes—
479C4×Q8C23×C13124yes—
480C4×Q8C23×C1318yes—
481C4×Q8C23×C13124yes—
482C4×D4C23×C13124yes—
483C4×D4C23×C13124yes—
484C4×D4C23×C13124yes—
485C4×D4C23×C13124yes—
486C4×D4C23×C13124yes—
487C4×D4C23×C13148yes—
488#117C23×C13124yes—
489#117C23×C13124yes—
490#117C23×C13124yes—
491#117C23×C13148yes—
492C2×C4⋊C4C23×C1313yes—
493C2×C4⋊C4C23×C1313yes—
494C2×C4⋊C4C23×C1313yes—
495C2×C4⋊C4C23×C1313yes—
496C2×C4⋊C4C23×C1316yes—
497C2×C4⋊C4C23×C13124yes—
498C2×C4⋊C4C23×C13124yes—
499C2×C4⋊C4C23×C1311yescharacteristic
500C2×C4⋊C4C23×C1313yes—
501C2×C4⋊C4C23×C1313yes—
502C2×C4⋊C4C23×C1313yes—
503C2×C4⋊C4C23×C1313yes—
504C2×C4⋊C4C23×C1316yes—
505C2×C4⋊C4C23×C1313yes—
506C2×C4⋊C4C23×C1313yes—
507C2×C4⋊C4C23×C1316yes—
508C2×C4⋊C4C23×C1313yes—
509C2×C4⋊C4C23×C1311yescharacteristic
510C2×C4⋊C4C23×C1313yes—
511C2×C22⋊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×C1311yescharacteristic
518C2×C22⋊C4C23×C1313yes—
519C2×C22⋊C4C23×C1311yescharacteristic
520C2×C22⋊C4C23×C1316yes—
521C2×C22⋊C4C23×C1313yes—
522C2×C22⋊C4C23×C1313yes—
523C2×C42C23×C1313yes—
524C2×C42C23×C1316yes—
525C2×C42C23×C1313yes—
526C2×C42C23×C1313yes—
527C2×C42C23×C1313yes—
528C2×C42C23×C1313yes—
529C2×C42C23×C1313yes—
530C2×C42C23×C13124yes—
531C2×C13—24no—
532C2×C13—42no—
533C2×C13—46no—
534C2×C13#351614yesdirect product factor
535C2×C13C23×#4111yescharacteristic
536C2×C13C22×2−1+411yescharacteristic
537C2×C13C2×#58511yescharacteristic
538C24C24×C1311yescharacteristic
539C24C24×C1313yes—
540C24C24×C1311yescharacteristic
541#41—232no—
542C2×Q8—232no—
543C2×Q8—232no—
544C2×Q8—212no—
545C2×Q8—212no—
546C2×Q8—46no—
547C2×Q8C13×#4118yes—
548C2×Q8C24×C13112yes—
549C2×Q8C24×C13112yes—
550C2×Q8C24×C13112yes—
551C2×Q8C24×C1314yes—
552C2×D4—212no—
553C2×D4—24no—
554C2×D4—212no—
555C2×D4—46no—
556C2×D4C24×C13112yes—
557C2×D4C24×C1314yes—
558C2×D4C24×C13112yes—
559C2×D4C24×C13112yes—
560C22×C4—24no—
561C22×C4—212no—
562C22×C4—212no—
563C22×C4—212no—
564C22×C4—412no—
565C22×C4—46no—
566C22×C4C24×C1311yescharacteristic
567C22×C4C24×C1311yescharacteristic
568C22×C4C24×C1314yes—
569C22×C4C24×C1313yes—
570C22×C4C24×C1311yescharacteristic
571C22×C4C24×C1313yes—
572C22×C4C24×C1311yescharacteristic
573C22×C4C24×C1313yes—
574C22×C4C24×C1313yes—
575C22×C4C24×C1313yes—
576C22×C4C24×C13112yes—
577C22×C4C24×C1313yes—
578C22×C4C24×C1311yescharacteristic
579C22×C4C24×C13112yes—
580C22×C4C24×C13112yes—
581C22×C4C24×C13112yes—
582C22×C4C24×C13124yes—
583C22×C4C24×C1313yes—
584C4⋊C4C24×C13112yes—
585C4⋊C4C24×C13112yes—
586C4⋊C4C24×C13112yes—
587C4⋊C4C24×C13112yes—
588C4⋊C4C24×C13124yes—
589C4⋊C4C24×C1314yes—
590C4⋊C4C24×C13112yes—
591C4⋊C4C24×C13112yes—
592C4⋊C4C24×C13112yes—
593C4⋊C4C24×C13112yes—
594C4⋊C4C24×C13124yes—
595C4⋊C4C24×C13112yes—
596C4⋊C4C24×C13112yes—
597C4⋊C4C24×C13124yes—
598C4⋊C4C24×C13112yes—
599C4⋊C4C24×C1314yes—
600C4⋊C4C24×C13112yes—
601C22⋊C4C24×C13112yes—
602C22⋊C4C24×C1314yes—
603C22⋊C4C24×C13112yes—
604C22⋊C4C24×C13112yes—
605C22⋊C4C24×C13112yes—
606C22⋊C4C24×C13124yes—
607C22⋊C4C24×C1314yes—
608C22⋊C4C24×C13112yes—
609C22⋊C4C24×C1314yes—
610C22⋊C4C24×C13124yes—
611C22⋊C4C24×C13112yes—
612C22⋊C4C24×C13112yes—
613C42C24×C13112yes—
614C42C24×C13112yes—
615C42C24×C13112yes—
616C42C24×C13112yes—
617C42C24×C13124yes—
618C42C24×C13112yes—
619C42C24×C13112yes—
620C13C2×#351611yescharacteristic, direct product factor, Sylow
621C23—22no—
622C23—22no—
623C23—22no—
624C23—26no—
625C23—22no—
626C23—26no—
627C23—26no—
628C23—22no—
629C23C13×2−1+414yes—
630C23C25×C1312yes—
631C23C25×C1316yes—
632C23C25×C1312yes—
633C23C25×C1311yescharacteristic
634Q8—224no—
635Q8—224no—
636Q8—412no—
637Q8C2×C13×#41116yes—
638D4—224no—
639D4—28no—
640D4—224no—
641D4—412no—
642C2×C4—22no—
643C2×C4—26no—
644C2×C4—26no—
645C2×C4—28no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—26no—
649C2×C4—22no—
650C2×C4—26no—
651C2×C4—26no—
652C2×C4—26no—
653C2×C4—22no—
654C2×C4—224no—
655C2×C4—224no—
656C2×C4—224no—
657C2×C4—424no—
658C2×C4—412no—
659C2×C4C2×C13×#41112yes—
660C2×C4C25×C1312yes—
661C2×C4C25×C1312yes—
662C2×C4C25×C1316yes—
663C2×C4C25×C1312yes—
664C2×C4C25×C1316yes—
665C2×C4C25×C1312yes—
666C2×C4C25×C1316yes—
667C2×C4C25×C1316yes—
668C2×C4C25×C1316yes—
669C2×C4C25×C1316yes—
670C2×C4C25×C1312yes—
671C2×C4C25×C1316yes—
672C22—22no—
673C22—22no—
674C22—28no—
675C22—22no—
676C22—26no—
677C22—22no—
678C22—26no—
679C22—26no—
680C22—22no—
681C22—44no—
682C22—412no—
683C22C22×C13×#4112yes—
684C22C2×C13×2−1+414yes—
685C22C2×C13×2−1+412yes—
686C22C13×#58512yes—
687C22C26×C1311yescharacteristic
688C4—22no—
689C4—26no—
690C4—26no—
691C4—22no—
692C4—22no—
693C4—26no—
694C4—22no—
695C4—26no—
696C4—26no—
697C4—26no—
698C4—22no—
699C4C22×C13×#41112yes—
700C2—24no—
701C2—42no—
702C2—46no—
703C2C13×#351614yesdirect product factor
704C2C23×C13×#4111yescharacteristic
705C2C22×C13×2−1+411yescharacteristic
706C2C2×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×#3516C2direct (N × H)
2. C2×C13×#557C2semidirect
3. C2×C13×#556C2semidirect
4. C2×C13×#554C2semidirect
5. C2×C13×#553C2semidirect
6. C2×C13×#552C2semidirect
7. C2×D4×Q8×C13C2semidirect
8. C2×C13×#548C2semidirect
9. C2×C13×#548C2semidirect
10. C2×C13×#542C2semidirect
11. C2×C13×#541C2semidirect
12. C2×C13×#529C2semidirect
13. C2×C13×#529C2semidirect
14. C2×C13×#520C2semidirect
15. C2×C13×#519C2semidirect
16. C22×C4×Q8×C13C2semidirect
20. C13×#557C22semidirect
21. C13×#556C22semidirect
22. C13×#554C22semidirect
23. C13×#553C22semidirect
24. C13×#552C22semidirect
25. D4×Q8×C13C22semidirect
26. C13×#548C22semidirect
27. C13×#548C22semidirect
28. C13×#542C22semidirect
29. C13×#541C22semidirect
32. C13×#529C22semidirect
33. C13×#529C22semidirect
57. C13×#520C22semidirect
58. C13×#519C22semidirect
68. C2×C4×Q8×C13C22semidirect
185. C2×#3516C13direct (N × H)
268. #3516C2×C13direct (N × H)
269. C2×#557C2×C13semidirect
270. C2×#556C2×C13semidirect
271. C2×#554C2×C13semidirect
272. C2×#553C2×C13semidirect
273. C2×#552C2×C13semidirect
274. C2×D4×Q8C2×C13semidirect
275. C2×#548C2×C13semidirect
276. C2×#548C2×C13semidirect
277. C2×#542C2×C13semidirect
278. C2×#541C2×C13semidirect
279. C2×#529C2×C13semidirect
280. C2×#529C2×C13semidirect
281. C2×#520C2×C13semidirect
282. C2×#519C2×C13semidirect
283. C22×C4×Q8C2×C13semidirect
338. #557C22×C13semidirect
339. #556C22×C13semidirect
340. #554C22×C13semidirect
341. #553C22×C13semidirect
342. #552C22×C13semidirect
343. D4×Q8C22×C13semidirect
344. #548C22×C13semidirect
345. #548C22×C13semidirect
346. #542C22×C13semidirect
347. #541C22×C13semidirect
350. #529C22×C13semidirect
351. #529C22×C13semidirect
375. #520C22×C13semidirect
376. #519C22×C13semidirect
386. C2×C4×Q8C22×C13semidirect
534. C2×C13#3516direct (N × H)
620. C13C2×#3516direct (N × H)
703. C2C13×#3516direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35162
C2×C13×#5572
C2×C13×#5562
C2×C13×#5542
C2×C13×#5532
C2×C13×#5522
C2×D4×Q8×C132
C2×C13×#5482
C2×C13×#5422
C2×C13×#5412
C2×C13×#5292
C2×C13×#5202
C2×C13×#5192
C22×C4×Q8×C132
C2×#351613