Finite Group Databasebeta

← C13×#34294 #15720633

Subgroups — C13×#34294 #15720633

Order 3328.

3112 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#548C211yesmaximal, characteristic
2C2×C13×#520C211yesmaximal, characteristic, complemented
3C22×C4×Q8×C13C211yesmaximal, characteristic, complemented
4C13×#2367C213yesmaximal, complemented
5C13×#2361C213yesmaximal, complemented
6C13×#2360C213yesmaximal, complemented
7Q8×C13×C4⋊C4C211yesmaximal, characteristic, complemented
8D4×C13×C4⋊C4C213yesmaximal, complemented
9C13×#2341C211yesmaximal, characteristic, complemented
10Q8×C13×C22⋊C4C211yesmaximal, characteristic, complemented
11C13×#2326C213yesmaximal, complemented
12C13×#2323C213yesmaximal, complemented
13C4×C13×#121C213yesmaximal, complemented
14C13×#2290C213yesmaximal, complemented
15C13×#2276C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C23×Q8×C13C2211yescharacteristic
18C13×#548C4116yescomplemented
19C2×C13×#124C2213yes—
20C2×C13×C22⋊Q8C2213yes—
21C2×C13×#121C2213yes—
22C13×#520—28no—
23C2×C4×Q8×C13—28no—
24C2×C4×Q8×C13C2211yescharacteristic
25C2×C4×Q8×C13C2213yes—
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×Q8×C13C2213yes—
29C2×C4×Q8×C13C2211yescharacteristic
30C2×C4×Q8×C13C2211yescharacteristic
31C2×C4×D4×C13C2213yes—
32C2×C4×D4×C13C2213yes—
33C2×C4×D4×C13C2216yes—
34C2×C4×D4×C13C2213yes—
35C2×C13×#117C2213yes—
36C22×C13×C4⋊C4C2213yes—
37C22×C13×C4⋊C4C2213yes—
38C22×C42×C13C2213yes—
39C13×#391C2213yes—
40C13×#391C2213yes—
41C13×#390C2213yes—
42C13×#390C2213yes—
43C13×#389C2213yes—
44C13×#389C2216yes—
45C13×#389C2213yes—
46C13×#388C2213yes—
47C13×#388C2213yes—
48C13×#388C2216yes—
49C13×#388C2216yes—
50C13×#387C2213yes—
51C13×#387C2213yes—
52C13×#386C2213yes—
53C13×#386C2213yes—
54C13×#385C2211yescharacteristic
55C13×#385C2213yes—
56C13×#385C2216yes—
57C13×#385C2216yes—
58C13×#384C2213yes—
59C13×#380C2213yes—
60C13×#380C2213yes—
61C4×C13×C4⋊C4C2213yes—
62C4×C13×C4⋊C4C2213yes—
63C4×C13×C4⋊C4C2213yes—
64C4×C13×C4⋊C4C2213yes—
65C4×C13×C22⋊C4C2213yes—
66C4×C13×C22⋊C4C2213yes—
67C4×C13×C22⋊C4C2216yes—
68C13×#376C2213yes—
69C2×C13×#41—24no—
70C2×C13×#41—24no—
71C2×C13×#41C2×C418yescomplemented
72C22×Q8×C13—24no—
73C22×Q8×C13—24no—
74C22×Q8×C13C2×C418yescomplemented
75C22×Q8×C13C2313yes—
76C22×Q8×C13C2311yescharacteristic
77C22×D4×C13C2313yes—
78C22×D4×C13C2313yes—
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2313yes—
81C23×C4×C13C2313yes—
82C23×C4×C13C2313yes—
83C23×C4×C13C2316yes—
84C13×#124C2×C4124yescomplemented
85C13×C22⋊Q8C2×C4124yescomplemented
86C13×#121C2×C4124yescomplemented
87C4×Q8×C13—24no—
88C4×Q8×C13—24no—
89C4×Q8×C13—24no—
90C4×Q8×C13—212no—
91C4×Q8×C13—212no—
92C4×Q8×C13C2×C418yescomplemented
93C4×Q8×C13D418yescomplemented
94C4×D4×C13—212no—
95C4×D4×C13—212no—
96C4×D4×C13—412no—
97C4×D4×C13C2×C4124yescomplemented
98C13×#117—212no—
99C2×C13×C4⋊C4—212no—
100C2×C13×C4⋊C4—212no—
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C4⋊C4C2313yes—
103C2×C13×C4⋊C4C2313yes—
104C2×C13×C4⋊C4C2313yes—
105C2×C13×C4⋊C4C2316yes—
106C2×C13×C4⋊C4C2311yescharacteristic
107C2×C13×C4⋊C4C2313yes—
108C2×C13×C4⋊C4C2313yes—
109C2×C13×C4⋊C4C2316yes—
110C2×C13×C4⋊C4C2313yes—
111C2×C13×C4⋊C4C2313yes—
112C2×C13×C4⋊C4C2313yes—
113C2×C13×C22⋊C4C2311yescharacteristic
114C2×C13×C22⋊C4C2313yes—
115C2×C13×C22⋊C4C2313yes—
116C2×C13×C22⋊C4C2313yes—
117C2×C13×C22⋊C4C2313yes—
118C2×C13×C22⋊C4C2313yes—
119C2×C13×C22⋊C4C2316yes—
120C2×C13×C22⋊C4C2316yes—
121C2×C13×C22⋊C4C2311yescharacteristic
122C2×C13×C22⋊C4C2313yes—
123C2×C42×C13—212no—
124C2×C42×C13C2313yes—
125C2×C42×C13C2313yes—
126C2×C42×C13C2313yes—
127C2×C42×C13C2313yes—
128C2×C42×C13C2313yes—
129C2×C42×C13C2316yes—
130C2×C42×C13C2313yes—
131C2×C42×C13C2313yes—
132C13×#95C2311yescharacteristic
133C13×#95C2313yes—
134C13×#95C2313yes—
135C13×#95C2316yes—
136C13×#95C2313yes—
137C13×#95C2313yes—
138C13×#95C2313yes—
139C13×#95C2313yes—
140C13×#95C2313yes—
141C13×#95C2313yes—
142C13×#95C2311yescharacteristic
143#34294C1311yesmaximal, characteristic, direct product factor, Sylow
144C24×C13C2413yes—
145C24×C13C2411yescharacteristic
146C13×#41—232no—
147C2×Q8×C13—232no—
148C2×Q8×C13—26no—
149C2×Q8×C13—26no—
150C2×Q8×C13C22×C4112yes—
151C2×Q8×C13C22×C414yes—
152C2×Q8×C13C2×D414yes—
153C2×Q8×C13#4114yes—
154C2×D4×C13—26no—
155C2×D4×C13—26no—
156C2×D4×C13—26no—
157C2×D4×C13—26no—
158C2×D4×C13C22×C4112yes—
159C2×D4×C13C22×C4112yes—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—26no—
163C22×C4×C13—26no—
164C22×C4×C13—26no—
165C22×C4×C13—26no—
166C22×C4×C13—22no—
167C22×C4×C13—26no—
168C22×C4×C13—26no—
169C22×C4×C13—212no—
170C22×C4×C13—43no—
171C22×C4×C13—46no—
172C22×C4×C13—46no—
173C22×C4×C13C22×C4112yes—
174C22×C4×C13C22×C4112yes—
175C22×C4×C13C2411yescharacteristic
176C22×C4×C13C2411yescharacteristic
177C22×C4×C13C2413yes—
178C22×C4×C13C2413yes—
179C22×C4×C13C2413yes—
180C22×C4×C13C2411yescharacteristic
181C22×C4×C13C2413yes—
182C22×C4×C13C2413yes—
183C22×C4×C13C2411yescharacteristic
184C22×C4×C13C2411yescharacteristic
185C22×C4×C13C2413yes—
186C22×C4×C13C2411yescharacteristic
187C22×C4×C13C2413yes—
188C13×C4⋊C4—26no—
189C13×C4⋊C4—26no—
190C13×C4⋊C4—212no—
191C13×C4⋊C4—26no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—26no—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—43no—
196C13×C4⋊C4—46no—
197C13×C4⋊C4C22×C4112yes—
198C13×C4⋊C4C22×C4112yes—
199C13×C4⋊C4C2×D4112yes—
200C13×C22⋊C4—26no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—26no—
203C13×C22⋊C4—26no—
204C13×C22⋊C4—26no—
205C13×C22⋊C4—43no—
206C13×C22⋊C4—46no—
207C13×C22⋊C4C22×C414yes—
208C13×C22⋊C4C22×C4112yes—
209C13×C22⋊C4C22×C4124yes—
210C42×C13—26no—
211C42×C13—26no—
212C42×C13—26no—
213C42×C13—26no—
214C42×C13—26no—
215C42×C13—46no—
216C42×C13C22×C4112yes—
217C42×C13C2×D4112yes—
218C2×#548C2×C1311yescharacteristic
219C2×#520C2×C1311yescharacteristic, complemented
220C22×C4×Q8C2×C1311yescharacteristic, complemented
221#2367C2×C1313yescomplemented
222#2361C2×C1313yescomplemented
223#2360C2×C1313yescomplemented
224Q8×C4⋊C4C2×C1311yescharacteristic, complemented
225D4×C4⋊C4C2×C1313yescomplemented
226#2341C2×C1311yescharacteristic, complemented
227Q8×C22⋊C4C2×C1311yescharacteristic, complemented
228#2326C2×C1313yescomplemented
229#2323C2×C1313yescomplemented
230C4×#121C2×C1313yescomplemented
231#2290C2×C1313yescomplemented
232#2276C2×C1311yescharacteristic, complemented
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—23no—
238C23×C13—23no—
239C23×C13—23no—
240C23×C13—23no—
241C23×C13—23no—
242C23×C13—23no—
243C23×C13C23×C416yes—
244C23×C13C23×C412yes—
245C23×C13H(5,𝔽2)12yes—
246C23×C132−1+412yes—
247C23×C13C2511yescharacteristic
248Q8×C13—224no—
249Q8×C13C4×D4116yescomplemented
250D4×C13—224no—
251D4×C13—224no—
252C2×C4×C13—28no—
253C2×C4×C13—21no—
254C2×C4×C13—23no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—23no—
258C2×C4×C13—23no—
259C2×C4×C13—23no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—23no—
265C2×C4×C13—21no—
266C2×C4×C13—23no—
267C2×C4×C13—224no—
268C2×C4×C13—224no—
269C2×C4×C13—21no—
270C2×C4×C13—23no—
271C2×C4×C13—23no—
272C2×C4×C13—21no—
273C2×C4×C13—23no—
274C2×C4×C13—23no—
275C2×C4×C13—23no—
276C2×C4×C13—23no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—23no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—23no—
283C2×C4×C13—23no—
284C2×C4×C13—412no—
285C2×C4×C13—812no—
286C2×C4×C13C23×C412yes—
287C2×C4×C13C23×C416yes—
288C2×C4×C13C23×C416yes—
289C2×C4×C13C23×C412yes—
290C2×C4×C13C23×C416yes—
291C2×C4×C13C22×D412yes—
292C2×C4×C13C22×D416yes—
293C2×C4×C13C22×D416yes—
294C2×C4×C13C2×#4116yes—
295C2×C4×C132−1+412yes—
296C22×#41C22×C1311yescharacteristic
297C23×Q8C22×C1311yescharacteristic
298#548C4×C13116yescomplemented
299C2×#124C22×C1313yes—
300C2×C22⋊Q8C22×C1313yes—
301C2×#121C22×C1313yes—
302#520—28no—
303C2×C4×Q8—28no—
304C2×C4×Q8C22×C1313yes—
305C2×C4×Q8C22×C1311yescharacteristic
306C2×C4×Q8C22×C1311yescharacteristic
307C2×C4×Q8C22×C1311yescharacteristic
308C2×C4×Q8C22×C1313yes—
309C2×C4×Q8C22×C1311yescharacteristic
310C2×C4×Q8C22×C1311yescharacteristic
311C2×C4×D4C22×C1313yes—
312C2×C4×D4C22×C1313yes—
313C2×C4×D4C22×C1316yes—
314C2×C4×D4C22×C1313yes—
315C2×#117C22×C1313yes—
316C22×C4⋊C4C22×C1313yes—
317C22×C4⋊C4C22×C1313yes—
318C22×C42C22×C1313yes—
319#391C22×C1313yes—
320#391C22×C1313yes—
321#390C22×C1313yes—
322#390C22×C1313yes—
323#389C22×C1316yes—
324#389C22×C1313yes—
325#389C22×C1313yes—
326#388C22×C1316yes—
327#388C22×C1316yes—
328#388C22×C1313yes—
329#388C22×C1313yes—
330#387C22×C1313yes—
331#387C22×C1313yes—
332#386C22×C1313yes—
333#386C22×C1313yes—
334#385C22×C1316yes—
335#385C22×C1316yes—
336#385C22×C1313yes—
337#385C22×C1311yescharacteristic
338#384C22×C1313yes—
339#380C22×C1313yes—
340#380C22×C1313yes—
341C4×C4⋊C4C22×C1313yes—
342C4×C4⋊C4C22×C1313yes—
343C4×C4⋊C4C22×C1313yes—
344C4×C4⋊C4C22×C1313yes—
345C4×C22⋊C4C22×C1313yes—
346C4×C22⋊C4C22×C1313yes—
347C4×C22⋊C4C22×C1316yes—
348#376C22×C1313yes—
349C22×C13—22no—
350C22×C13—22no—
351C22×C13—22no—
352C22×C13—22no—
353C22×C13—22no—
354C22×C13—22no—
355C22×C13—26no—
356C22×C13—26no—
357C22×C13—26no—
358C22×C13—43no—
359C22×C13—43no—
360C22×C13—43no—
361C22×C13—43no—
362C22×C13#52014yescomplemented
363C22×C13C24×C411yescharacteristic
364C22×C13C23×D411yescharacteristic
365C22×C13C22×#4111yescharacteristic
366C22×C13C2×H(5,𝔽2)11yescharacteristic
367C22×C13C2×2−1+411yescharacteristic
368C22×C13C2×2−1+411yescharacteristic
369C22×C13#58511yescharacteristic
370C4×C13—22no—
371C4×C13—26no—
372C4×C13—26no—
373C4×C13—22no—
374C4×C13—22no—
375C4×C13—22no—
376C4×C13—26no—
377C4×C13—41no—
378C4×C13—43no—
379C4×C13—43no—
380C4×C13—41no—
381C4×C13—43no—
382C4×C13C2×C4×D4112yes—
383C2×#41—24no—
384C2×#41—24no—
385C2×#41C2×C4×C1318yescomplemented
386C22×Q8—24no—
387C22×Q8—24no—
388C22×Q8C2×C4×C1318yescomplemented
389C22×Q8C23×C1313yes—
390C22×Q8C23×C1311yescharacteristic
391C22×D4C23×C1313yes—
392C22×D4C23×C1313yes—
393C23×C4C23×C1311yescharacteristic
394C23×C4C23×C1313yes—
395C23×C4C23×C1313yes—
396C23×C4C23×C1313yes—
397C23×C4C23×C1316yes—
398#124C2×C4×C13124yescomplemented
399C22⋊Q8C2×C4×C13124yescomplemented
400#121C2×C4×C13124yescomplemented
401C4×Q8—24no—
402C4×Q8—24no—
403C4×Q8—24no—
404C4×Q8—212no—
405C4×Q8—212no—
406C4×Q8C2×C4×C1318yescomplemented
407C4×Q8D4×C1318yescomplemented
408C4×D4—212no—
409C4×D4—212no—
410C4×D4—412no—
411C4×D4C2×C4×C13124yescomplemented
412#117—212no—
413C2×C4⋊C4—212no—
414C2×C4⋊C4—212no—
415C2×C4⋊C4C23×C1313yes—
416C2×C4⋊C4C23×C1313yes—
417C2×C4⋊C4C23×C1313yes—
418C2×C4⋊C4C23×C1316yes—
419C2×C4⋊C4C23×C1311yescharacteristic
420C2×C4⋊C4C23×C1313yes—
421C2×C4⋊C4C23×C1311yescharacteristic
422C2×C4⋊C4C23×C1316yes—
423C2×C4⋊C4C23×C1313yes—
424C2×C4⋊C4C23×C1313yes—
425C2×C4⋊C4C23×C1313yes—
426C2×C4⋊C4C23×C1313yes—
427C2×C22⋊C4C23×C1313yes—
428C2×C22⋊C4C23×C1313yes—
429C2×C22⋊C4C23×C1313yes—
430C2×C22⋊C4C23×C1311yescharacteristic
431C2×C22⋊C4C23×C1313yes—
432C2×C22⋊C4C23×C1316yes—
433C2×C22⋊C4C23×C1313yes—
434C2×C22⋊C4C23×C1311yescharacteristic
435C2×C22⋊C4C23×C1313yes—
436C2×C22⋊C4C23×C1316yes—
437C2×C42—212no—
438C2×C42C23×C1313yes—
439C2×C42C23×C1313yes—
440C2×C42C23×C1313yes—
441C2×C42C23×C1313yes—
442C2×C42C23×C1313yes—
443C2×C42C23×C1316yes—
444C2×C42C23×C1313yes—
445C2×C42C23×C1313yes—
446#95C23×C1311yescharacteristic
447#95C23×C1313yes—
448#95C23×C1313yes—
449#95C23×C1313yes—
450#95C23×C1311yescharacteristic
451#95C23×C1313yes—
452#95C23×C1313yes—
453#95C23×C1316yes—
454#95C23×C1313yes—
455#95C23×C1313yes—
456#95C23×C1313yes—
457C2×C13—24no—
458C2×C13—46no—
459C2×C13C22×C4×D411yescharacteristic
460C2×C13C2×#52011yescharacteristic
461C2×C13C4×2−1+411yescharacteristic
462C2×C13#348611yescharacteristic
463C2×C13#348811yescharacteristic
464C2×C13#351611yescharacteristic
465C2×C13#352211yescharacteristic
466C24C24×C1313yes—
467C24C24×C1311yescharacteristic
468#41—232no—
469C2×Q8—232no—
470C2×Q8—26no—
471C2×Q8—26no—
472C2×Q8C22×C4×C13112yes—
473C2×Q8C22×C4×C1314yes—
474C2×Q8C2×D4×C1314yes—
475C2×Q8C13×#4114yes—
476C2×D4—26no—
477C2×D4—26no—
478C2×D4—26no—
479C2×D4—26no—
480C2×D4C22×C4×C13112yes—
481C2×D4C22×C4×C13112yes—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—26no—
485C22×C4—26no—
486C22×C4—26no—
487C22×C4—26no—
488C22×C4—22no—
489C22×C4—26no—
490C22×C4—26no—
491C22×C4—212no—
492C22×C4—43no—
493C22×C4—46no—
494C22×C4—46no—
495C22×C4C22×C4×C13112yes—
496C22×C4C22×C4×C13112yes—
497C22×C4C24×C1311yescharacteristic
498C22×C4C24×C1311yescharacteristic
499C22×C4C24×C1313yes—
500C22×C4C24×C1313yes—
501C22×C4C24×C1313yes—
502C22×C4C24×C1311yescharacteristic
503C22×C4C24×C1313yes—
504C22×C4C24×C1313yes—
505C22×C4C24×C1311yescharacteristic
506C22×C4C24×C1311yescharacteristic
507C22×C4C24×C1313yes—
508C22×C4C24×C1311yescharacteristic
509C22×C4C24×C1313yes—
510C4⋊C4—26no—
511C4⋊C4—26no—
512C4⋊C4—212no—
513C4⋊C4—26no—
514C4⋊C4—22no—
515C4⋊C4—26no—
516C4⋊C4—22no—
517C4⋊C4—46no—
518C4⋊C4—43no—
519C4⋊C4C22×C4×C13112yes—
520C4⋊C4C22×C4×C13112yes—
521C4⋊C4C2×D4×C13112yes—
522C22⋊C4—26no—
523C22⋊C4—22no—
524C22⋊C4—26no—
525C22⋊C4—26no—
526C22⋊C4—26no—
527C22⋊C4—46no—
528C22⋊C4—43no—
529C22⋊C4C22×C4×C1314yes—
530C22⋊C4C22×C4×C13112yes—
531C22⋊C4C22×C4×C13124yes—
532C42—26no—
533C42—26no—
534C42—26no—
535C42—26no—
536C42—26no—
537C42—46no—
538C42C22×C4×C13112yes—
539C42C2×D4×C13112yes—
540C13#3429411yescharacteristic, direct product factor, Sylow
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—23no—
546C23—23no—
547C23—23no—
548C23—23no—
549C23—23no—
550C23—23no—
551C23C23×C4×C1316yes—
552C23C23×C4×C1312yes—
553C23C13×H(5,𝔽2)12yes—
554C23C13×2−1+412yes—
555C23C25×C1311yescharacteristic
556Q8—224no—
557Q8C4×D4×C13116yescomplemented
558D4—224no—
559D4—224no—
560C2×C4—28no—
561C2×C4—21no—
562C2×C4—23no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—23no—
566C2×C4—23no—
567C2×C4—23no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—23no—
573C2×C4—21no—
574C2×C4—23no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—21no—
578C2×C4—23no—
579C2×C4—23no—
580C2×C4—21no—
581C2×C4—23no—
582C2×C4—23no—
583C2×C4—23no—
584C2×C4—23no—
585C2×C4—23no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—23no—
591C2×C4—23no—
592C2×C4—412no—
593C2×C4—812no—
594C2×C4C23×C4×C1312yes—
595C2×C4C23×C4×C1316yes—
596C2×C4C23×C4×C1316yes—
597C2×C4C23×C4×C1312yes—
598C2×C4C23×C4×C1316yes—
599C2×C4C22×D4×C1312yes—
600C2×C4C22×D4×C1316yes—
601C2×C4C22×D4×C1316yes—
602C2×C4C2×C13×#4116yes—
603C2×C4C13×2−1+412yes—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—26no—
611C22—26no—
612C22—26no—
613C22—43no—
614C22—43no—
615C22—43no—
616C22—43no—
617C22C13×#52014yescomplemented
618C22C24×C4×C1311yescharacteristic
619C22C23×D4×C1311yescharacteristic
620C22C22×C13×#4111yescharacteristic
621C22C2×C13×H(5,𝔽2)11yescharacteristic
622C22C2×C13×2−1+411yescharacteristic
623C22C2×C13×2−1+411yescharacteristic
624C22C13×#58511yescharacteristic
625C4—22no—
626C4—26no—
627C4—26no—
628C4—22no—
629C4—22no—
630C4—22no—
631C4—26no—
632C4—43no—
633C4—41no—
634C4—43no—
635C4—43no—
636C4—41no—
637C4C2×C4×D4×C13112yes—
638C2—24no—
639C2—46no—
640C2C22×C4×D4×C1311yescharacteristic
641C2C2×C13×#52011yescharacteristic
642C2C4×C13×2−1+411yescharacteristic
643C2C13×#348611yescharacteristic
644C2C13×#348811yescharacteristic
645C2C13×#351611yescharacteristic
646C2C13×#352211yescharacteristic
subgroupG/H
center, socleC23×C13C25
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
prime radicalC2×C13×#548C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#520C2semidirect
3. C22×C4×Q8×C13C2semidirect
4. C13×#2367C2semidirect
5. C13×#2361C2semidirect
6. C13×#2360C2semidirect
7. Q8×C13×C4⋊C4C2semidirect
8. D4×C13×C4⋊C4C2semidirect
9. C13×#2341C2semidirect
10. Q8×C13×C22⋊C4C2semidirect
11. C13×#2326C2semidirect
12. C13×#2323C2semidirect
13. C4×C13×#121C2semidirect
14. C13×#2290C2semidirect
15. C13×#2276C2semidirect
18. C13×#548C4semidirect
71. C2×C13×#41C2×C4semidirect
74. C22×Q8×C13C2×C4semidirect
84. C13×#124C2×C4semidirect
85. C13×C22⋊Q8C2×C4semidirect
86. C13×#121C2×C4semidirect
92. C4×Q8×C13C2×C4semidirect
93. C4×Q8×C13D4semidirect
97. C4×D4×C13C2×C4semidirect
143. #34294C13direct (N × H)
219. C2×#520C2×C13semidirect
220. C22×C4×Q8C2×C13semidirect
221. #2367C2×C13semidirect
222. #2361C2×C13semidirect
223. #2360C2×C13semidirect
224. Q8×C4⋊C4C2×C13semidirect
225. D4×C4⋊C4C2×C13semidirect
226. #2341C2×C13semidirect
227. Q8×C22⋊C4C2×C13semidirect
228. #2326C2×C13semidirect
229. #2323C2×C13semidirect
230. C4×#121C2×C13semidirect
231. #2290C2×C13semidirect
232. #2276C2×C13semidirect
249. Q8×C13C4×D4semidirect
298. #548C4×C13semidirect
362. C22×C13#520semidirect
385. C2×#41C2×C4×C13semidirect
388. C22×Q8C2×C4×C13semidirect
398. #124C2×C4×C13semidirect
399. C22⋊Q8C2×C4×C13semidirect
400. #121C2×C4×C13semidirect
406. C4×Q8C2×C4×C13semidirect
407. C4×Q8D4×C13semidirect
411. C4×D4C2×C4×C13semidirect
540. C13#34294direct (N × H)
557. Q8C4×D4×C13semidirect
617. C22C13×#520semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#5482
C2×C13×#5202
C22×C4×Q8×C132
C13×#23672
C13×#23612
C13×#23602
Q8×C13×C4⋊C42
D4×C13×C4⋊C42
C13×#23412
Q8×C13×C22⋊C42
C13×#23262
C13×#23232
C4×C13×#1212
C13×#22902
C13×#22762
#3429413