Finite Group Databasebeta

← C13×#34295 #15720634

Subgroups — C13×#34295 #15720634

Order 3328.

3200 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#550C211yesmaximal, characteristic
2C2×C13×#520C211yesmaximal, characteristic, complemented
3C2×C4×C13×#41C211yesmaximal, characteristic, complemented
4C13×#2366C213yesmaximal, complemented
5C13×#2363C213yesmaximal, complemented
6C13×#2361C213yesmaximal, complemented
7C13×#2352C213yesmaximal, complemented
8C13×#2351C211yesmaximal, characteristic, complemented
9C13×#2341C211yesmaximal, characteristic, complemented
10C13×#2341C211yesmaximal, characteristic, complemented
11C13×#2328C213yesmaximal, complemented
12C13×#2324C213yesmaximal, complemented
13C4×C13×#121C213yesmaximal, complemented
14C13×#2290C213yesmaximal, complemented
15C13×#2276C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C22×C13×#41C2211yescharacteristic
18C13×#550C4116yescomplemented
19C2×C13×#127C2213yes—
20C2×C13×#121C2213yes—
21C2×C13×#121C2213yes—
22C13×#520—28no—
23C4×C13×#41—28no—
24C2×C4×Q8×C13C2211yescharacteristic
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×Q8×C13C2211yescharacteristic
29C2×C4×D4×C13C2213yes—
30C2×C4×D4×C13C2213yes—
31C2×C4×D4×C13C2213yes—
32C2×C4×D4×C13C2213yes—
33C2×C4×D4×C13C2216yes—
34C2×C4×D4×C13C2213yes—
35C2×C13×#117C2213yes—
36C2×C13×#117C2213yes—
37C22×C13×C4⋊C4C2213yes—
38C22×C42×C13C2213yes—
39C13×#390C2213yes—
40C13×#390C2213yes—
41C13×#390C2216yes—
42C13×#390C2213yes—
43C13×#390C2213yes—
44C13×#389C2213yes—
45C13×#389C2213yes—
46C13×#388C2213yes—
47C13×#388C2213yes—
48C13×#388C2216yes—
49C13×#387C2211yescharacteristic
50C13×#387C2213yes—
51C13×#386C2213yes—
52C13×#386C2213yes—
53C13×#386C2216yes—
54C13×#386C2216yes—
55C13×#386C2216yes—
56C13×#385C2213yes—
57C13×#385C2213yes—
58C13×#382C2213yes—
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×#41—24no—
72C2×C13×#41—24no—
73C2×C13×#41C2×C418yescomplemented
74C2×C13×#41C2×C418yescomplemented
75C22×Q8×C13C2311yescharacteristic
76C22×D4×C13C2313yes—
77C22×D4×C13C2313yes—
78C22×D4×C13C2313yes—
79C22×D4×C13C2316yes—
80C23×C4×C13C2313yes—
81C23×C4×C13C2313yes—
82C23×C4×C13C2313yes—
83C23×C4×C13C2316yes—
84C23×C4×C13C2313yes—
85C13×#127C2×C4124yescomplemented
86C13×#121C2×C4124yescomplemented
87C13×#121C2×C4124yescomplemented
88C4×Q8×C13—24no—
89C4×Q8×C13—24no—
90C4×Q8×C13—24no—
91C4×Q8×C13C2×C418yescomplemented
92C4×Q8×C13D418yescomplemented
93C4×D4×C13—212no—
94C4×D4×C13—212no—
95C4×D4×C13—212no—
96C4×D4×C13—212no—
97C4×D4×C13—412no—
98C4×D4×C13C2×C4124yescomplemented
99C13×#117—212no—
100C13×#117—212no—
101C2×C13×C4⋊C4—212no—
102C2×C13×C4⋊C4C2313yes—
103C2×C13×C4⋊C4C2313yes—
104C2×C13×C4⋊C4C2313yes—
105C2×C13×C4⋊C4C2313yes—
106C2×C13×C4⋊C4C2311yescharacteristic
107C2×C13×C4⋊C4C2313yes—
108C2×C13×C4⋊C4C2313yes—
109C2×C13×C4⋊C4C2313yes—
110C2×C13×C4⋊C4C2311yescharacteristic
111C2×C13×C4⋊C4C2313yes—
112C2×C13×C22⋊C4C2313yes—
113C2×C13×C22⋊C4C2313yes—
114C2×C13×C22⋊C4C2316yes—
115C2×C13×C22⋊C4C2313yes—
116C2×C13×C22⋊C4C2316yes—
117C2×C13×C22⋊C4C2313yes—
118C2×C13×C22⋊C4C2313yes—
119C2×C13×C22⋊C4C2313yes—
120C2×C13×C22⋊C4C2316yes—
121C2×C13×C22⋊C4C2313yes—
122C2×C13×C22⋊C4C2313yes—
123C2×C42×C13—212no—
124C2×C42×C13C2313yes—
125C2×C42×C13C2313yes—
126C2×C42×C13C2313yes—
127C2×C42×C13C2313yes—
128C2×C42×C13C2311yescharacteristic
129C2×C42×C13C2316yes—
130C2×C42×C13C2313yes—
131C2×C42×C13C2313yes—
132C13×#95C2313yes—
133C13×#95C2311yescharacteristic
134C13×#95C2311yescharacteristic
135C13×#95C2313yes—
136C13×#95C2316yes—
137C13×#95C2311yescharacteristic
138C13×#95C2313yes—
139C13×#95C2313yes—
140C13×#95C2313yes—
141C13×#95C2313yes—
142C13×#95C2311yescharacteristic
143#34295C1311yesmaximal, characteristic, direct product factor, Sylow
144C24×C13C2413yes—
145C24×C13C2413yes—
146C13×#41—232no—
147C13×#41—232no—
148C2×Q8×C13C22×C414yes—
149C2×Q8×C13C2×D414yes—
150C2×Q8×C13#4114yes—
151C2×D4×C13—26no—
152C2×D4×C13—26no—
153C2×D4×C13—26no—
154C2×D4×C13—26no—
155C2×D4×C13—46no—
156C2×D4×C13—46no—
157C2×D4×C13—43no—
158C2×D4×C13—43no—
159C2×D4×C13C22×C4112yes—
160C2×D4×C13C22×C4112yes—
161C2×D4×C13C22×C4112yes—
162C2×D4×C13C22×C4124yes—
163C22×C4×C13—26no—
164C22×C4×C13—26no—
165C22×C4×C13—26no—
166C22×C4×C13—26no—
167C22×C4×C13—26no—
168C22×C4×C13—26no—
169C22×C4×C13—26no—
170C22×C4×C13—212no—
171C22×C4×C13—43no—
172C22×C4×C13—43no—
173C22×C4×C13—43no—
174C22×C4×C13—46no—
175C22×C4×C13—46no—
176C22×C4×C13C22×C4112yes—
177C22×C4×C13C22×C4112yes—
178C22×C4×C13C2411yescharacteristic
179C22×C4×C13C2413yes—
180C22×C4×C13C2413yes—
181C22×C4×C13C2413yes—
182C22×C4×C13C2411yescharacteristic
183C22×C4×C13C2411yescharacteristic
184C22×C4×C13C2411yescharacteristic
185C22×C4×C13C2413yes—
186C22×C4×C13C2411yescharacteristic
187C22×C4×C13C2411yescharacteristic
188C22×C4×C13C2413yes—
189C22×C4×C13C2411yescharacteristic
190C22×C4×C13C2413yes—
191C13×C4⋊C4—26no—
192C13×C4⋊C4—26no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—26no—
195C13×C4⋊C4—26no—
196C13×C4⋊C4—26no—
197C13×C4⋊C4—43no—
198C13×C4⋊C4C22×C414yes—
199C13×C4⋊C4C22×C4112yes—
200C13×C4⋊C4C2×D4112yes—
201C13×C22⋊C4—26no—
202C13×C22⋊C4—212no—
203C13×C22⋊C4—26no—
204C13×C22⋊C4—26no—
205C13×C22⋊C4—43no—
206C13×C22⋊C4—46no—
207C13×C22⋊C4—43no—
208C13×C22⋊C4—43no—
209C13×C22⋊C4—46no—
210C13×C22⋊C4C22×C4112yes—
211C13×C22⋊C4C22×C4112yes—
212C42×C13—22no—
213C42×C13—26no—
214C42×C13—26no—
215C42×C13—26no—
216C42×C13—26no—
217C42×C13—46no—
218C42×C13C22×C4112yes—
219C42×C13C2×D4112yes—
220C2×#550C2×C1311yescharacteristic
221C2×#520C2×C1311yescharacteristic, complemented
222C2×C4×#41C2×C1311yescharacteristic, complemented
223#2366C2×C1313yescomplemented
224#2363C2×C1313yescomplemented
225#2361C2×C1313yescomplemented
226#2352C2×C1313yescomplemented
227#2351C2×C1311yescharacteristic, complemented
228#2341C2×C1311yescharacteristic, complemented
229#2341C2×C1311yescharacteristic, complemented
230#2328C2×C1313yescomplemented
231#2324C2×C1313yescomplemented
232C4×#121C2×C1313yescomplemented
233#2290C2×C1313yescomplemented
234#2276C2×C1311yescharacteristic, complemented
235C23×C13—23no—
236C23×C13—23no—
237C23×C13—23no—
238C23×C13—23no—
239C23×C13—23no—
240C23×C13—23no—
241C23×C13—23no—
242C23×C13—23no—
243C23×C13—23no—
244C23×C13—23no—
245C23×C13—23no—
246C23×C13—23no—
247C23×C13C23×C416yes—
248C23×C13C23×C416yes—
249C23×C13C2511yescharacteristic
250Q8×C13C4×D4116yescomplemented
251D4×C13—224no—
252D4×C13—224no—
253D4×C13—412no—
254D4×C13—424no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—23no—
261C2×C4×C13—23no—
262C2×C4×C13—23no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—23no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—224no—
270C2×C4×C13—224no—
271C2×C4×C13—21no—
272C2×C4×C13—23no—
273C2×C4×C13—23no—
274C2×C4×C13—21no—
275C2×C4×C13—23no—
276C2×C4×C13—23no—
277C2×C4×C13—23no—
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—23no—
285C2×C4×C13—21no—
286C2×C4×C13—412no—
287C2×C4×C13—412no—
288C2×C4×C13—812no—
289C2×C4×C13C23×C412yes—
290C2×C4×C13C23×C416yes—
291C2×C4×C13C23×C412yes—
292C2×C4×C13C23×C412yes—
293C2×C4×C13C23×C416yes—
294C2×C4×C13C22×D412yes—
295C2×C4×C13C22×D416yes—
296C2×C4×C13C22×D416yes—
297C2×C4×C13C2×#4116yes—
298C2×C4×C13H(5,𝔽2)12yes—
299C22×#41C22×C1311yescharacteristic
300C22×#41C22×C1311yescharacteristic
301#550C4×C13116yescomplemented
302C2×#127C22×C1313yes—
303C2×#121C22×C1313yes—
304C2×#121C22×C1313yes—
305#520—28no—
306C4×#41—28no—
307C2×C4×Q8C22×C1311yescharacteristic
308C2×C4×Q8C22×C1311yescharacteristic
309C2×C4×Q8C22×C1311yescharacteristic
310C2×C4×Q8C22×C1311yescharacteristic
311C2×C4×Q8C22×C1311yescharacteristic
312C2×C4×D4C22×C1313yes—
313C2×C4×D4C22×C1313yes—
314C2×C4×D4C22×C1313yes—
315C2×C4×D4C22×C1313yes—
316C2×C4×D4C22×C1316yes—
317C2×C4×D4C22×C1313yes—
318C2×#117C22×C1313yes—
319C2×#117C22×C1313yes—
320C22×C4⋊C4C22×C1313yes—
321C22×C42C22×C1313yes—
322#390C22×C1313yes—
323#390C22×C1316yes—
324#390C22×C1313yes—
325#390C22×C1313yes—
326#390C22×C1313yes—
327#389C22×C1313yes—
328#389C22×C1313yes—
329#388C22×C1316yes—
330#388C22×C1313yes—
331#388C22×C1313yes—
332#387C22×C1313yes—
333#387C22×C1311yescharacteristic
334#386C22×C1316yes—
335#386C22×C1313yes—
336#386C22×C1316yes—
337#386C22×C1316yes—
338#386C22×C1313yes—
339#385C22×C1313yes—
340#385C22×C1313yes—
341#382C22×C1313yes—
342#380C22×C1313yes—
343#380C22×C1313yes—
344C4×C4⋊C4C22×C1313yes—
345C4×C4⋊C4C22×C1313yes—
346C4×C4⋊C4C22×C1313yes—
347C4×C4⋊C4C22×C1313yes—
348C4×C22⋊C4C22×C1313yes—
349C4×C22⋊C4C22×C1313yes—
350C4×C22⋊C4C22×C1316yes—
351#376C22×C1313yes—
352C22×C13—26no—
353C22×C13—26no—
354C22×C13—26no—
355C22×C13—26no—
356C22×C13—26no—
357C22×C13—26no—
358C22×C13—43no—
359C22×C13—43no—
360C22×C13—43no—
361C22×C13—43no—
362C22×C13—43no—
363C22×C13—43no—
364C22×C13—43no—
365C22×C13—43no—
366C22×C13C24×C411yescharacteristic
367C22×C13C23×D411yescharacteristic
368C22×C13C22×#4111yescharacteristic
369C22×C13C2×H(5,𝔽2)11yescharacteristic
370C22×C13#58511yescharacteristic
371C22×C13#58511yescharacteristic
372C22×C13#58511yescharacteristic
373C4×C13—22no—
374C4×C13—22no—
375C4×C13—22no—
376C4×C13—26no—
377C4×C13—22no—
378C4×C13—22no—
379C4×C13—26no—
380C4×C13—41no—
381C4×C13—43no—
382C4×C13—43no—
383C4×C13—43no—
384C4×C13—41no—
385C4×C13C2×C4×D4112yes—
386C2×#41—24no—
387C2×#41—24no—
388C2×#41—24no—
389C2×#41—24no—
390C2×#41C2×C4×C1318yescomplemented
391C2×#41C2×C4×C1318yescomplemented
392C22×Q8C23×C1311yescharacteristic
393C22×D4C23×C1313yes—
394C22×D4C23×C1313yes—
395C22×D4C23×C1316yes—
396C22×D4C23×C1313yes—
397C23×C4C23×C1313yes—
398C23×C4C23×C1313yes—
399C23×C4C23×C1313yes—
400C23×C4C23×C1316yes—
401C23×C4C23×C1313yes—
402#127C2×C4×C13124yescomplemented
403#121C2×C4×C13124yescomplemented
404#121C2×C4×C13124yescomplemented
405C4×Q8—24no—
406C4×Q8—24no—
407C4×Q8—24no—
408C4×Q8C2×C4×C1318yescomplemented
409C4×Q8D4×C1318yescomplemented
410C4×D4—212no—
411C4×D4—212no—
412C4×D4—212no—
413C4×D4—212no—
414C4×D4—412no—
415C4×D4C2×C4×C13124yescomplemented
416#117—212no—
417#117—212no—
418C2×C4⋊C4—212no—
419C2×C4⋊C4C23×C1313yes—
420C2×C4⋊C4C23×C1313yes—
421C2×C4⋊C4C23×C1311yescharacteristic
422C2×C4⋊C4C23×C1313yes—
423C2×C4⋊C4C23×C1313yes—
424C2×C4⋊C4C23×C1313yes—
425C2×C4⋊C4C23×C1313yes—
426C2×C4⋊C4C23×C1311yescharacteristic
427C2×C4⋊C4C23×C1313yes—
428C2×C4⋊C4C23×C1313yes—
429C2×C22⋊C4C23×C1313yes—
430C2×C22⋊C4C23×C1316yes—
431C2×C22⋊C4C23×C1313yes—
432C2×C22⋊C4C23×C1313yes—
433C2×C22⋊C4C23×C1316yes—
434C2×C22⋊C4C23×C1316yes—
435C2×C22⋊C4C23×C1313yes—
436C2×C22⋊C4C23×C1313yes—
437C2×C22⋊C4C23×C1313yes—
438C2×C22⋊C4C23×C1313yes—
439C2×C22⋊C4C23×C1313yes—
440C2×C42—212no—
441C2×C42C23×C1313yes—
442C2×C42C23×C1313yes—
443C2×C42C23×C1313yes—
444C2×C42C23×C1313yes—
445C2×C42C23×C1311yescharacteristic
446C2×C42C23×C1316yes—
447C2×C42C23×C1313yes—
448C2×C42C23×C1313yes—
449#95C23×C1311yescharacteristic
450#95C23×C1313yes—
451#95C23×C1313yes—
452#95C23×C1313yes—
453#95C23×C1313yes—
454#95C23×C1311yescharacteristic
455#95C23×C1311yescharacteristic
456#95C23×C1313yes—
457#95C23×C1316yes—
458#95C23×C1311yescharacteristic
459#95C23×C1313yes—
460C2×C13—46no—
461C2×C13—46no—
462C2×C13C22×C4×D411yescharacteristic
463C2×C13#342811yescharacteristic
464C2×C13C4×H(5,𝔽2)11yescharacteristic
465C2×C13#348711yescharacteristic
466C2×C13#348811yescharacteristic
467C2×C13#351711yescharacteristic
468C2×C13#352411yescharacteristic
469C24C24×C1313yes—
470C24C24×C1313yes—
471#41—232no—
472#41—232no—
473C2×Q8C22×C4×C1314yes—
474C2×Q8C2×D4×C1314yes—
475C2×Q8C13×#4114yes—
476C2×D4—26no—
477C2×D4—26no—
478C2×D4—26no—
479C2×D4—26no—
480C2×D4—46no—
481C2×D4—46no—
482C2×D4—43no—
483C2×D4—43no—
484C2×D4C22×C4×C13112yes—
485C2×D4C22×C4×C13112yes—
486C2×D4C22×C4×C13112yes—
487C2×D4C22×C4×C13124yes—
488C22×C4—26no—
489C22×C4—26no—
490C22×C4—26no—
491C22×C4—26no—
492C22×C4—26no—
493C22×C4—26no—
494C22×C4—26no—
495C22×C4—212no—
496C22×C4—43no—
497C22×C4—43no—
498C22×C4—43no—
499C22×C4—46no—
500C22×C4—46no—
501C22×C4C22×C4×C13112yes—
502C22×C4C22×C4×C13112yes—
503C22×C4C24×C1311yescharacteristic
504C22×C4C24×C1313yes—
505C22×C4C24×C1313yes—
506C22×C4C24×C1313yes—
507C22×C4C24×C1311yescharacteristic
508C22×C4C24×C1311yescharacteristic
509C22×C4C24×C1311yescharacteristic
510C22×C4C24×C1313yes—
511C22×C4C24×C1311yescharacteristic
512C22×C4C24×C1311yescharacteristic
513C22×C4C24×C1313yes—
514C22×C4C24×C1311yescharacteristic
515C22×C4C24×C1313yes—
516C4⋊C4—26no—
517C4⋊C4—26no—
518C4⋊C4—22no—
519C4⋊C4—26no—
520C4⋊C4—26no—
521C4⋊C4—26no—
522C4⋊C4—43no—
523C4⋊C4C22×C4×C1314yes—
524C4⋊C4C22×C4×C13112yes—
525C4⋊C4C2×D4×C13112yes—
526C22⋊C4—26no—
527C22⋊C4—212no—
528C22⋊C4—26no—
529C22⋊C4—26no—
530C22⋊C4—46no—
531C22⋊C4—43no—
532C22⋊C4—46no—
533C22⋊C4—43no—
534C22⋊C4—43no—
535C22⋊C4C22×C4×C13112yes—
536C22⋊C4C22×C4×C13112yes—
537C42—22no—
538C42—26no—
539C42—26no—
540C42—26no—
541C42—26no—
542C42—46no—
543C42C22×C4×C13112yes—
544C42C2×D4×C13112yes—
545C13#3429511yescharacteristic, direct product factor, Sylow
546C23—23no—
547C23—23no—
548C23—23no—
549C23—23no—
550C23—23no—
551C23—23no—
552C23—23no—
553C23—23no—
554C23—23no—
555C23—23no—
556C23—23no—
557C23—23no—
558C23C23×C4×C1316yes—
559C23C23×C4×C1316yes—
560C23C25×C1311yescharacteristic
561Q8C4×D4×C13116yescomplemented
562D4—224no—
563D4—224no—
564D4—412no—
565D4—424no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—23no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—23no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—21no—
583C2×C4—23no—
584C2×C4—23no—
585C2×C4—21no—
586C2×C4—23no—
587C2×C4—23no—
588C2×C4—23no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—23no—
593C2×C4—23no—
594C2×C4—23no—
595C2×C4—23no—
596C2×C4—21no—
597C2×C4—412no—
598C2×C4—412no—
599C2×C4—812no—
600C2×C4C23×C4×C1312yes—
601C2×C4C23×C4×C1316yes—
602C2×C4C23×C4×C1312yes—
603C2×C4C23×C4×C1312yes—
604C2×C4C23×C4×C1316yes—
605C2×C4C22×D4×C1312yes—
606C2×C4C22×D4×C1316yes—
607C2×C4C22×D4×C1316yes—
608C2×C4C2×C13×#4116yes—
609C2×C4C13×H(5,𝔽2)12yes—
610C22—26no—
611C22—26no—
612C22—26no—
613C22—26no—
614C22—26no—
615C22—26no—
616C22—43no—
617C22—43no—
618C22—43no—
619C22—43no—
620C22—43no—
621C22—43no—
622C22—43no—
623C22—43no—
624C22C24×C4×C1311yescharacteristic
625C22C23×D4×C1311yescharacteristic
626C22C22×C13×#4111yescharacteristic
627C22C2×C13×H(5,𝔽2)11yescharacteristic
628C22C13×#58511yescharacteristic
629C22C13×#58511yescharacteristic
630C22C13×#58511yescharacteristic
631C4—22no—
632C4—22no—
633C4—22no—
634C4—26no—
635C4—22no—
636C4—22no—
637C4—26no—
638C4—41no—
639C4—41no—
640C4—43no—
641C4—43no—
642C4—43no—
643C4C2×C4×D4×C13112yes—
644C2—46no—
645C2—46no—
646C2C22×C4×D4×C1311yescharacteristic
647C2C13×#342811yescharacteristic
648C2C4×C13×H(5,𝔽2)11yescharacteristic
649C2C13×#348711yescharacteristic
650C2C13×#348811yescharacteristic
651C2C13×#351711yescharacteristic
652C2C13×#352411yescharacteristic
subgroupG/H
center, socleC23×C13C25
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
prime radicalC2×C13×#550C2
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. C2×C4×C13×#41C2semidirect
4. C13×#2366C2semidirect
5. C13×#2363C2semidirect
6. C13×#2361C2semidirect
7. C13×#2352C2semidirect
8. C13×#2351C2semidirect
9. C13×#2341C2semidirect
10. C13×#2341C2semidirect
11. C13×#2328C2semidirect
12. C13×#2324C2semidirect
13. C4×C13×#121C2semidirect
14. C13×#2290C2semidirect
15. C13×#2276C2semidirect
18. C13×#550C4semidirect
73. C2×C13×#41C2×C4semidirect
74. C2×C13×#41C2×C4semidirect
85. C13×#127C2×C4semidirect
86. C13×#121C2×C4semidirect
87. C13×#121C2×C4semidirect
91. C4×Q8×C13C2×C4semidirect
92. C4×Q8×C13D4semidirect
98. C4×D4×C13C2×C4semidirect
143. #34295C13direct (N × H)
221. C2×#520C2×C13semidirect
222. C2×C4×#41C2×C13semidirect
223. #2366C2×C13semidirect
224. #2363C2×C13semidirect
225. #2361C2×C13semidirect
226. #2352C2×C13semidirect
227. #2351C2×C13semidirect
228. #2341C2×C13semidirect
229. #2341C2×C13semidirect
230. #2328C2×C13semidirect
231. #2324C2×C13semidirect
232. C4×#121C2×C13semidirect
233. #2290C2×C13semidirect
234. #2276C2×C13semidirect
250. Q8×C13C4×D4semidirect
301. #550C4×C13semidirect
390. C2×#41C2×C4×C13semidirect
391. C2×#41C2×C4×C13semidirect
402. #127C2×C4×C13semidirect
403. #121C2×C4×C13semidirect
404. #121C2×C4×C13semidirect
408. C4×Q8C2×C4×C13semidirect
409. C4×Q8D4×C13semidirect
415. C4×D4C2×C4×C13semidirect
545. C13#34295direct (N × H)
561. Q8C4×D4×C13semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#5502
C2×C13×#5202
C2×C4×C13×#412
C13×#23662
C13×#23632
C13×#23612
C13×#23522
C13×#23512
C13×#23412
C13×#23282
C13×#23242
C4×C13×#1212
C13×#22902
C13×#22762
#3429513