Finite Group Databasebeta

← C2×C13×#2666 #15720927

Subgroups — C2×C13×#2666 #15720927

Order 3328.

1918 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
1C13×#2666C2116yesmaximal, direct product factor
2C2×C13×#400C211yesmaximal, characteristic
3C2×C13×#400C211yesmaximal, characteristic
4C2×C13×#398C211yesmaximal, characteristic
5C2×C13×#398C211yesmaximal, characteristic
6C2×C13×#398C211yesmaximal, characteristic
7C2×C13×#398C211yesmaximal, characteristic
8C2×C13×#395C211yesmaximal, characteristic
9C2×C13×#395C211yesmaximal, characteristic
10C2×C13×#391C211yesmaximal, characteristic
11C2×C13×#389C211yesmaximal, characteristic
12C2×C13×#387C211yesmaximal, characteristic
13C2×C13×#387C211yesmaximal, characteristic
14C2×C13×#383C211yesmaximal, characteristic
15C2×C13×#382C211yesmaximal, characteristic
16C2×C4×C13×C4⋊C4C211yesmaximal, characteristic
17C23×Q8×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C22×C13×C4⋊C4C2211yescharacteristic
30C22×C13×C4⋊C4C2211yescharacteristic
31C22×C42×C13C2211yescharacteristic
32C22×C42×C13C2211yescharacteristic
33C22×C42×C13C2211yescharacteristic
34C13×#400C2218yes—
35C13×#400C2218yes—
36C13×#398C2218yes—
37C13×#398C2218yes—
38C13×#398C2218yes—
39C13×#398C2218yes—
40C13×#395C2218yes—
41C13×#395C2218yes—
42C13×#391C2218yes—
43C13×#389C2218yes—
44C13×#387C2218yes—
45C13×#387C2218yes—
46C13×#383C2218yes—
47C13×#382C2218yes—
48C4×C13×C4⋊C4C2218yes—
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C2×C13×#95C2211yescharacteristic
58C2×C13×#95C2211yescharacteristic
59C2×C13×#95C2211yescharacteristic
60C2×C13×#95C2211yescharacteristic
61C2×C13×#95C2211yescharacteristic
62C2×C13×#95C2211yescharacteristic
63C2×C13×#95C2211yescharacteristic
64C2×C13×#95C2211yescharacteristic
65C2×C13×#95C2211yescharacteristic
66C2×C13×#95C2211yescharacteristic
67C22×Q8×C13—24no—
68C22×Q8×C13—42no—
69C22×Q8×C13—42no—
70C22×Q8×C13C2314yes—
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C2×C13×C4⋊C4—24no—
87C2×C13×C4⋊C4—24no—
88C2×C13×C4⋊C4—24no—
89C2×C13×C4⋊C4—24no—
90C2×C13×C4⋊C4—24no—
91C2×C13×C4⋊C4—42no—
92C2×C13×C4⋊C4—42no—
93C2×C13×C4⋊C4—42no—
94C2×C13×C4⋊C4—42no—
95C2×C13×C4⋊C4—42no—
96C2×C13×C4⋊C4—42no—
97C2×C13×C4⋊C4—42no—
98C2×C13×C4⋊C4—42no—
99C2×C13×C4⋊C4C2314yes—
100C2×C13×C4⋊C4C2314yes—
101C2×C13×C4⋊C4C2314yes—
102C2×C13×C4⋊C4C2314yes—
103C2×C13×C4⋊C4C2314yes—
104C2×C13×C4⋊C4C2314yes—
105C2×C13×C4⋊C4C2314yes—
106C2×C13×C4⋊C4C2314yes—
107C2×C13×C4⋊C4C2314yes—
108C2×C13×C4⋊C4C2314yes—
109C2×C13×C4⋊C4C2314yes—
110C2×C13×C4⋊C4C2314yes—
111C2×C13×C4⋊C4C2314yes—
112C2×C42×C13—42no—
113C2×C42×C13—42no—
114C2×C42×C13Q818yescomplemented
115C2×C42×C13C2314yes—
116C2×C42×C13C2314yes—
117C2×C42×C13C2314yes—
118C13×#95C2314yes—
119C13×#95C2314yes—
120C13×#95C2314yes—
121C13×#95C2314yes—
122C13×#95C2314yes—
123C13×#95C2314yes—
124C13×#95C2314yes—
125C13×#95C2314yes—
126C13×#95C2314yes—
127C13×#95C2314yes—
128C13×#95C2314yes—
129C13×#95C2314yes—
130C13×#95C2314yes—
131C13×#95C2314yes—
132C13×#95C2314yes—
133C13×#95C2314yes—
134C13×#95C2314yes—
135C13×#95C2314yes—
136C2×#2666C1311yesmaximal, characteristic, direct product factor, Sylow
137C24×C13C2411yescharacteristic
138C2×Q8×C13—28no—
139C2×Q8×C13—44no—
140C2×Q8×C13—44no—
141C2×Q8×C13—416no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
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×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13C2×Q814yes—
183C22×C4×C13C2×Q814yes—
184C22×C4×C13C2×Q814yes—
185C22×C4×C13#4114yes—
186C22×C4×C13#4114yes—
187C22×C4×C13C2412yes—
188C22×C4×C13C2412yes—
189C22×C4×C13C2412yes—
190C22×C4×C13C2412yes—
191C22×C4×C13C2412yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2412yes—
194C22×C4×C13C2412yes—
195C22×C4×C13C2412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
198C22×C4×C13C2412yes—
199C22×C4×C13C2412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C13×C4⋊C4—28no—
203C13×C4⋊C4—28no—
204C13×C4⋊C4—28no—
205C13×C4⋊C4—28no—
206C13×C4⋊C4—28no—
207C13×C4⋊C4—44no—
208C13×C4⋊C4—44no—
209C13×C4⋊C4—44no—
210C13×C4⋊C4—44no—
211C13×C4⋊C4—44no—
212C13×C4⋊C4—44no—
213C13×C4⋊C4—44no—
214C13×C4⋊C4—44no—
215C42×C13—44no—
216C42×C13—44no—
217C42×C13C2×Q8116yescomplemented
218#2666C2×C13116yesdirect product factor
219C2×#400C2×C1311yescharacteristic
220C2×#400C2×C1311yescharacteristic
221C2×#398C2×C1311yescharacteristic
222C2×#398C2×C1311yescharacteristic
223C2×#398C2×C1311yescharacteristic
224C2×#398C2×C1311yescharacteristic
225C2×#395C2×C1311yescharacteristic
226C2×#395C2×C1311yescharacteristic
227C2×#391C2×C1311yescharacteristic
228C2×#389C2×C1311yescharacteristic
229C2×#387C2×C1311yescharacteristic
230C2×#387C2×C1311yescharacteristic
231C2×#383C2×C1311yescharacteristic
232C2×#382C2×C1311yescharacteristic
233C2×C4×C4⋊C4C2×C1311yescharacteristic
234C23×C13C22×Q812yes—
235C23×C13C2×#4112yes—
236C23×C13C2×#4112yes—
237C23×C13H(5,𝔽2)12yes—
238C23×C13H(5,𝔽2)12yes—
239C23×C132−1+412yes—
240C23×C132−1+412yes—
241C23×C13C2511yescharacteristic
242Q8×C13—416no—
243C2×C4×C13—28no—
244C2×C4×C13—28no—
245C2×C4×C13—28no—
246C2×C4×C13—28no—
247C2×C4×C13—28no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—44no—
289C2×C4×C13—44no—
290C2×C4×C13—44no—
291C2×C4×C13—44no—
292C2×C4×C13—44no—
293C2×C4×C13—44no—
294C2×C4×C13—44no—
295C2×C4×C13—44no—
296C2×C4×C13—44no—
297C2×C4×C13—44no—
298C2×C4×C13C22×Q814yes—
299C2×C4×C13C22×Q814yes—
300C2×C4×C13C22×Q814yes—
301C2×C4×C13C2×#4114yes—
302C2×C4×C13C2×#4114yes—
303C23×Q8C22×C1311yescharacteristic
304C22×C4⋊C4C22×C1311yescharacteristic
305C22×C4⋊C4C22×C1311yescharacteristic
306C22×C4⋊C4C22×C1311yescharacteristic
307C22×C4⋊C4C22×C1311yescharacteristic
308C22×C4⋊C4C22×C1311yescharacteristic
309C22×C4⋊C4C22×C1311yescharacteristic
310C22×C4⋊C4C22×C1311yescharacteristic
311C22×C4⋊C4C22×C1311yescharacteristic
312C22×C4⋊C4C22×C1311yescharacteristic
313C22×C4⋊C4C22×C1311yescharacteristic
314C22×C4⋊C4C22×C1311yescharacteristic
315C22×C4⋊C4C22×C1311yescharacteristic
316C22×C4⋊C4C22×C1311yescharacteristic
317C22×C42C22×C1311yescharacteristic
318C22×C42C22×C1311yescharacteristic
319C22×C42C22×C1311yescharacteristic
320#400C22×C1318yes—
321#400C22×C1318yes—
322#398C22×C1318yes—
323#398C22×C1318yes—
324#398C22×C1318yes—
325#398C22×C1318yes—
326#395C22×C1318yes—
327#395C22×C1318yes—
328#391C22×C1318yes—
329#389C22×C1318yes—
330#387C22×C1318yes—
331#387C22×C1318yes—
332#383C22×C1318yes—
333#382C22×C1318yes—
334C4×C4⋊C4C22×C1318yes—
335C2×#95C22×C1311yescharacteristic
336C2×#95C22×C1311yescharacteristic
337C2×#95C22×C1311yescharacteristic
338C2×#95C22×C1311yescharacteristic
339C2×#95C22×C1311yescharacteristic
340C2×#95C22×C1311yescharacteristic
341C2×#95C22×C1311yescharacteristic
342C2×#95C22×C1311yescharacteristic
343C2×#95C22×C1311yescharacteristic
344C2×#95C22×C1311yescharacteristic
345C2×#95C22×C1311yescharacteristic
346C2×#95C22×C1311yescharacteristic
347C2×#95C22×C1311yescharacteristic
348C2×#95C22×C1311yescharacteristic
349C2×#95C22×C1311yescharacteristic
350C2×#95C22×C1311yescharacteristic
351C2×#95C22×C1311yescharacteristic
352C2×#95C22×C1311yescharacteristic
353C22×C13#53314yes—
354C22×C13#53814yes—
355C22×C13#53914yes—
356C22×C13#54114yes—
357C22×C13#54214yes—
358C22×C13#54414yes—
359C22×C13#54414yes—
360C22×C13C23×Q811yescharacteristic
361C22×C13C22×#4111yescharacteristic
362C22×C13C22×#4111yescharacteristic
363C22×C13C2×H(5,𝔽2)11yescharacteristic
364C22×C13C2×H(5,𝔽2)11yescharacteristic
365C22×C13C2×2−1+411yescharacteristic
366C22×C13C2×2−1+411yescharacteristic
367C4×C13—24no—
368C4×C13—24no—
369C4×C13—24no—
370C4×C13—24no—
371C4×C13—24no—
372C4×C13—42no—
373C4×C13—42no—
374C4×C13—42no—
375C4×C13—42no—
376C4×C13—42no—
377C4×C13—42no—
378C4×C13—42no—
379C4×C13—42no—
380C4×C13—42no—
381C4×C13—42no—
382C22×Q8—24no—
383C22×Q8—42no—
384C22×Q8—42no—
385C22×Q8C23×C1314yes—
386C23×C4C23×C1311yescharacteristic
387C23×C4C23×C1311yescharacteristic
388C23×C4C23×C1311yescharacteristic
389C23×C4C23×C1311yescharacteristic
390C23×C4C23×C1311yescharacteristic
391C23×C4C23×C1311yescharacteristic
392C23×C4C23×C1311yescharacteristic
393C23×C4C23×C1311yescharacteristic
394C23×C4C23×C1311yescharacteristic
395C23×C4C23×C1311yescharacteristic
396C23×C4C23×C1311yescharacteristic
397C23×C4C23×C1311yescharacteristic
398C23×C4C23×C1311yescharacteristic
399C23×C4C23×C1311yescharacteristic
400C23×C4C23×C1311yescharacteristic
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—42no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4C23×C1314yes—
415C2×C4⋊C4C23×C1314yes—
416C2×C4⋊C4C23×C1314yes—
417C2×C4⋊C4C23×C1314yes—
418C2×C4⋊C4C23×C1314yes—
419C2×C4⋊C4C23×C1314yes—
420C2×C4⋊C4C23×C1314yes—
421C2×C4⋊C4C23×C1314yes—
422C2×C4⋊C4C23×C1314yes—
423C2×C4⋊C4C23×C1314yes—
424C2×C4⋊C4C23×C1314yes—
425C2×C4⋊C4C23×C1314yes—
426C2×C4⋊C4C23×C1314yes—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42Q8×C1318yescomplemented
430C2×C42C23×C1314yes—
431C2×C42C23×C1314yes—
432C2×C42C23×C1314yes—
433#95C23×C1314yes—
434#95C23×C1314yes—
435#95C23×C1314yes—
436#95C23×C1314yes—
437#95C23×C1314yes—
438#95C23×C1314yes—
439#95C23×C1314yes—
440#95C23×C1314yes—
441#95C23×C1314yes—
442#95C23×C1314yes—
443#95C23×C1314yes—
444#95C23×C1314yes—
445#95C23×C1314yes—
446#95C23×C1314yes—
447#95C23×C1314yes—
448#95C23×C1314yes—
449#95C23×C1314yes—
450#95C23×C1314yes—
451C2×C13#266618yesdirect product factor
452C2×C13C2×#53311yescharacteristic
453C2×C13C2×#53811yescharacteristic
454C2×C13C2×#53911yescharacteristic
455C2×C13C2×#54111yescharacteristic
456C2×C13C2×#54211yescharacteristic
457C2×C13C2×#54411yescharacteristic
458C2×C13C2×#54411yescharacteristic
459C24C24×C1311yescharacteristic
460C2×Q8—28no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—416no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4C2×Q8×C1314yes—
505C22×C4C2×Q8×C1314yes—
506C22×C4C2×Q8×C1314yes—
507C22×C4C13×#4114yes—
508C22×C4C13×#4114yes—
509C22×C4C24×C1312yes—
510C22×C4C24×C1312yes—
511C22×C4C24×C1312yes—
512C22×C4C24×C1312yes—
513C22×C4C24×C1312yes—
514C22×C4C24×C1312yes—
515C22×C4C24×C1312yes—
516C22×C4C24×C1312yes—
517C22×C4C24×C1312yes—
518C22×C4C24×C1312yes—
519C22×C4C24×C1312yes—
520C22×C4C24×C1312yes—
521C22×C4C24×C1312yes—
522C22×C4C24×C1312yes—
523C22×C4C24×C1312yes—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—28no—
528C4⋊C4—28no—
529C4⋊C4—44no—
530C4⋊C4—44no—
531C4⋊C4—44no—
532C4⋊C4—44no—
533C4⋊C4—44no—
534C4⋊C4—44no—
535C4⋊C4—44no—
536C4⋊C4—44no—
537C42—44no—
538C42—44no—
539C42C2×Q8×C13116yescomplemented
540C13C2×#266611yescharacteristic, direct product factor, Sylow
541C23C22×Q8×C1312yes—
542C23C2×C13×#4112yes—
543C23C2×C13×#4112yes—
544C23C13×H(5,𝔽2)12yes—
545C23C13×H(5,𝔽2)12yes—
546C23C13×2−1+412yes—
547C23C13×2−1+412yes—
548C23C25×C1311yescharacteristic
549Q8—416no—
550C2×C4—28no—
551C2×C4—28no—
552C2×C4—28no—
553C2×C4—28no—
554C2×C4—28no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—44no—
603C2×C4—44no—
604C2×C4—44no—
605C2×C4C22×Q8×C1314yes—
606C2×C4C22×Q8×C1314yes—
607C2×C4C22×Q8×C1314yes—
608C2×C4C2×C13×#4114yes—
609C2×C4C2×C13×#4114yes—
610C22C13×#53314yes—
611C22C13×#53814yes—
612C22C13×#53914yes—
613C22C13×#54114yes—
614C22C13×#54214yes—
615C22C13×#54414yes—
616C22C13×#54414yes—
617C22C23×Q8×C1311yescharacteristic
618C22C22×C13×#4111yescharacteristic
619C22C22×C13×#4111yescharacteristic
620C22C2×C13×H(5,𝔽2)11yescharacteristic
621C22C2×C13×H(5,𝔽2)11yescharacteristic
622C22C2×C13×2−1+411yescharacteristic
623C22C2×C13×2−1+411yescharacteristic
624C4—24no—
625C4—24no—
626C4—24no—
627C4—24no—
628C4—24no—
629C4—42no—
630C4—42no—
631C4—42no—
632C4—42no—
633C4—42no—
634C4—42no—
635C4—42no—
636C4—42no—
637C4—42no—
638C4—42no—
639C2C13×#266618yesdirect product factor
640C2C2×C13×#53311yescharacteristic
641C2C2×C13×#53811yescharacteristic
642C2C2×C13×#53911yescharacteristic
643C2C2×C13×#54111yescharacteristic
644C2C2×C13×#54211yescharacteristic
645C2C2×C13×#54411yescharacteristic
646C2C2×C13×#54411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C13C24
commutator, Frattini, cosocleC23C25×C13
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#2666C2direct (N × H)
114. C2×C42×C13Q8semidirect
136. C2×#2666C13direct (N × H)
217. C42×C13C2×Q8semidirect
218. #2666C2×C13direct (N × H)
429. C2×C42Q8×C13semidirect
451. C2×C13#2666direct (N × H)
539. C42C2×Q8×C13semidirect
540. C13C2×#2666direct (N × H)
639. C2C13×#2666direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#26662
C2×C13×#4002
C2×C13×#3982
C2×C13×#3952
C2×C13×#3912
C2×C13×#3892
C2×C13×#3872
C2×C13×#3832
C2×C13×#3822
C2×C4×C13×C4⋊C42
C2×#266613