Finite Group Databasebeta

← C13×#34511 #15720850

Subgroups — C13×#34511 #15720850

Order 3328.

2544 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#560C211yesmaximal, characteristic
2C13×#2375C211yesmaximal, characteristic, complemented
3C13×#2375C212yesmaximal, complemented
4C13×#2374C211yesmaximal, characteristic, complemented
5C13×#2373C212yesmaximal, complemented
6C13×#2366C211yesmaximal, characteristic, complemented
7C13×#2364C212yesmaximal, complemented
8C13×#2363C212yesmaximal, complemented
9C13×#2361C212yesmaximal, complemented
10C13×#2359C212yesmaximal, complemented
11C13×#2335C212yesmaximal, complemented
12C13×#2334C212yesmaximal, complemented
13C13×#2333C212yesmaximal, complemented
14C13×#2328C211yesmaximal, characteristic, complemented
15C13×#2325C212yesmaximal, complemented
16C13×#2324C212yesmaximal, complemented
17C13×#2322C211yesmaximal, characteristic, complemented
18C4×C13×#120C212yesmaximal, complemented
19C4×C13×#120C211yesmaximal, characteristic, complemented
20C24×C4×C13C2211yescharacteristic
21C13×#560C4116yescomplemented
22C2×C13×#127C2211yescharacteristic
23C2×C13×#126C2212yes—
24C2×C13×#123C2211yescharacteristic
25C2×C13×#123C2212yes—
26C2×C13×#121C2212yes—
27C2×C13×#121C2212yes—
28C2×C13×#121C2212yes—
29C2×C13×#120C2212yes—
30C2×C13×#120C2211yescharacteristic
31C2×C4×D4×C13C2211yescharacteristic
32C2×C4×D4×C13C2212yes—
33C2×C4×D4×C13C2212yes—
34C2×C4×D4×C13C2212yes—
35C2×C4×D4×C13C2212yes—
36C2×C4×D4×C13C2212yescomplemented
37C2×C4×D4×C13C2211yescharacteristic, complemented
38C2×C13×#117C2212yescomplemented
39C22×C13×C4⋊C4C2211yescharacteristic, complemented
40C13×#390C2212yes—
41C13×#390C2212yes—
42C13×#390C2211yescharacteristic
43C13×#390C2212yes—
44C13×#390C2212yes—
45C13×#390C2211yescharacteristic, complemented
46C13×#390C2212yescomplemented
47C13×#389C2212yescomplemented
48C13×#389C2212yescomplemented
49C13×#389C2212yescomplemented
50C13×#388C2212yes—
51C13×#388C2212yes—
52C13×#388C2212yes—
53C13×#388C2212yes—
54C13×#388C2212yes—
55C13×#388C2212yes—
56C13×#388C2212yes—
57C13×#388C2212yes—
58C13×#388C2212yes—
59C13×#388C2212yescomplemented
60C13×#388C2212yescomplemented
61C13×#388C2212yescomplemented
62C13×#387C2212yescomplemented
63C13×#387C2212yescomplemented
64C13×#387C2212yescomplemented
65C13×#387C2212yescomplemented
66C13×#387C2212yescomplemented
67C13×#387C2212yescomplemented
68C13×#386C2212yes—
69C13×#386C2212yes—
70C13×#386C2212yes—
71C13×#386C2212yes—
72C13×#386C2211yescharacteristic
73C13×#386C2211yescharacteristic
74C13×#386C2212yes—
75C13×#386C2212yes—
76C13×#386C2212yes—
77C13×#386C2212yes—
78C13×#386C2212yescomplemented
79C13×#386C2212yescomplemented
80C13×#386C2212yescomplemented
81C13×#385C2212yes—
82C13×#385C2212yes—
83C13×#385C2212yes—
84C13×#385C2211yescharacteristic
85C13×#385C2212yes—
86C13×#385C2211yescharacteristic, complemented
87C13×#385C2212yescomplemented
88C13×#382C2211yescharacteristic, complemented
89C13×#381C2211yescharacteristic, complemented
90C13×#380C2212yescomplemented
91C13×#379C2211yescharacteristic
92C13×#379C2212yes—
93C4×C13×C4⋊C4C2212yescomplemented
94C4×C13×C4⋊C4C2212yescomplemented
95C4×C13×C4⋊C4C2212yescomplemented
96C4×C13×C4⋊C4C2212yescomplemented
97C4×C13×C22⋊C4C2212yes—
98C4×C13×C22⋊C4C2211yescharacteristic
99C4×C13×C22⋊C4C2212yes—
100C4×C13×C22⋊C4C2212yes—
101C4×C13×C22⋊C4C2212yes—
102C4×C13×C22⋊C4C2211yescharacteristic, complemented
103C4×C13×C22⋊C4C2212yescomplemented
104C4×C13×C22⋊C4C2212yescomplemented
105C4×C13×C22⋊C4C2212yescomplemented
106C13×#376C2211yescharacteristic, complemented
107C2×C13×#95C2212yescomplemented
108C25×C13C2311yescharacteristic
109C22×D4×C13C2312yes—
110C22×D4×C13C2312yes—
111C22×D4×C13C2312yes—
112C22×D4×C13C2312yes—
113C22×D4×C13C2311yescharacteristic
114C22×D4×C13C2311yescharacteristic
115C22×D4×C13C2312yes—
116C23×C4×C13—44no—
117C23×C4×C13—42no—
118C23×C4×C13C2311yescharacteristic
119C23×C4×C13C2312yes—
120C23×C4×C13C2312yes—
121C23×C4×C13C2311yescharacteristic
122C23×C4×C13C2311yescharacteristic
123C23×C4×C13C2312yes—
124C23×C4×C13C2312yes—
125C23×C4×C13C2311yescharacteristic
126C23×C4×C13C2311yescharacteristic
127C23×C4×C13C2312yes—
128C13×#127C2×C418yescomplemented
129C13×#126C2×C4116yescomplemented
130C13×#123C2×C418yescomplemented
131C13×#123C2×C4116yescomplemented
132C13×#121C2×C4116yescomplemented
133C13×#121C2×C4116yescomplemented
134C13×#121C2×C4116yescomplemented
135C13×#120C2×C4116yescomplemented
136C13×#120C2×C418yescomplemented
137C4×D4×C13—42no—
138C4×D4×C13—44no—
139C4×D4×C13—42no—
140C4×D4×C13—44no—
141C4×D4×C13—44no—
142C4×D4×C13—44no—
143C4×D4×C13—44no—
144C13×#117—44no—
145C2×C13×C4⋊C4—42no—
146C2×C13×C4⋊C4C2312yes—
147C2×C13×C4⋊C4C2312yes—
148C2×C13×C4⋊C4C2312yes—
149C2×C13×C4⋊C4C2312yes—
150C2×C13×C4⋊C4C2312yes—
151C2×C13×C4⋊C4C2312yes—
152C2×C13×C4⋊C4C2311yescharacteristic
153C2×C13×C4⋊C4C2311yescharacteristic
154C2×C13×C4⋊C4C2312yes—
155C2×C13×C4⋊C4C2312yes—
156C2×C13×C4⋊C4C2312yes—
157C2×C13×C4⋊C4C2312yes—
158C2×C13×C4⋊C4C2312yes—
159C2×C13×C22⋊C4C2312yes—
160C2×C13×C22⋊C4C2312yes—
161C2×C13×C22⋊C4C2312yes—
162C2×C13×C22⋊C4C2312yes—
163C2×C13×C22⋊C4C2312yes—
164C2×C13×C22⋊C4C2312yes—
165C2×C13×C22⋊C4C2311yescharacteristic
166C2×C13×C22⋊C4C2312yes—
167C2×C13×C22⋊C4C2311yescharacteristic
168C2×C13×C22⋊C4C2312yes—
169C2×C13×C22⋊C4C2312yes—
170C2×C13×C22⋊C4C2311yescharacteristic
171C2×C13×C22⋊C4C2312yes—
172C2×C13×C22⋊C4C2312yes—
173C2×C13×C22⋊C4C2312yes—
174C2×C13×C22⋊C4C2312yes—
175C2×C13×C22⋊C4C2312yes—
176C2×C13×C22⋊C4C2312yes—
177C2×C13×C22⋊C4C2311yescharacteristic
178C2×C13×C22⋊C4C2312yes—
179C2×C13×C22⋊C4C2312yes—
180C2×C13×C22⋊C4C2312yes—
181C2×C13×C22⋊C4C2312yes—
182C2×C13×C22⋊C4C2311yescharacteristic
183C2×C13×C22⋊C4C2312yes—
184C2×C13×C22⋊C4C2311yescharacteristic
185C2×C13×C22⋊C4C2312yes—
186C2×C42×C13C2312yes—
187C2×C42×C13C2311yescharacteristic
188C2×C42×C13C2312yes—
189C2×C42×C13C2312yes—
190C2×C42×C13C2312yes—
191C2×C42×C13C2312yes—
192C2×C42×C13C2312yes—
193C2×C42×C13C2312yes—
194C2×C42×C13C2312yes—
195C2×C42×C13C2311yescharacteristic
196C2×C42×C13C2311yescharacteristic
197C13×#95C2312yes—
198C13×#95C2312yes—
199C13×#95C2312yes—
200C13×#95C2312yes—
201C13×#95C2312yes—
202C13×#95C2312yes—
203C13×#95C2312yes—
204C13×#95C2312yes—
205C13×#95C2312yes—
206C13×#95C2312yes—
207C13×#95C2312yes—
208C13×#95C2312yes—
209C13×#95C2312yes—
210C13×#95C2312yes—
211C13×#95C2312yes—
212C13×#95C2312yes—
213C13×#95C2312yes—
214C13×#95C2312yes—
215#34511C1311yesmaximal, characteristic, direct product factor, Sylow
216C24×C13—42no—
217C24×C13—41no—
218C24×C13—41no—
219C24×C13—42no—
220C24×C13C22×C414yes—
221C24×C13C2412yes—
222C24×C13C2411yescharacteristic
223C24×C13C2412yes—
224C24×C13C2411yescharacteristic
225C2×D4×C13—42no—
226C2×D4×C13—41no—
227C2×D4×C13—41no—
228C2×D4×C13—42no—
229C2×D4×C13—42no—
230C2×D4×C13—42no—
231C2×D4×C13—42no—
232C2×D4×C13—42no—
233C2×D4×C13—42no—
234C2×D4×C13—41no—
235C2×D4×C13—41no—
236C2×D4×C13—42no—
237C2×D4×C13—42no—
238C2×D4×C13—42no—
239C2×D4×C13C22×C418yes—
240C2×D4×C13C22×C418yes—
241C2×D4×C13C22×C418yes—
242C2×D4×C13C22×C414yes—
243C2×D4×C13C22×C418yes—
244C2×D4×C13C22×C414yescomplemented
245C2×D4×C13C22×C418yescomplemented
246C22×C4×C13—24no—
247C22×C4×C13—24no—
248C22×C4×C13—24no—
249C22×C4×C13—24no—
250C22×C4×C13—22no—
251C22×C4×C13—22no—
252C22×C4×C13—24no—
253C22×C4×C13—41no—
254C22×C4×C13—42no—
255C22×C4×C13—42no—
256C22×C4×C13—41no—
257C22×C4×C13—42no—
258C22×C4×C13—42no—
259C22×C4×C13—42no—
260C22×C4×C13—41no—
261C22×C4×C13—42no—
262C22×C4×C13—41no—
263C22×C4×C13—42no—
264C22×C4×C13—42no—
265C22×C4×C13—42no—
266C22×C4×C13—42no—
267C22×C4×C13—42no—
268C22×C4×C13—42no—
269C22×C4×C13—42no—
270C22×C4×C13—416no—
271C22×C4×C13C22×C414yescomplemented
272C22×C4×C13C22×C418yescomplemented
273C22×C4×C13C2411yescharacteristic
274C22×C4×C13C2412yes—
275C22×C4×C13C2411yescharacteristic
276C22×C4×C13C2412yes—
277C22×C4×C13C2412yes—
278C22×C4×C13C2412yes—
279C22×C4×C13C2412yes—
280C22×C4×C13C2411yescharacteristic
281C22×C4×C13C2411yescharacteristic
282C22×C4×C13C2412yes—
283C22×C4×C13C2412yes—
284C22×C4×C13C2412yes—
285C22×C4×C13C2412yes—
286C22×C4×C13C2411yescharacteristic
287C22×C4×C13C2412yes—
288C13×C4⋊C4—24no—
289C13×C4⋊C4—24no—
290C13×C4⋊C4—24no—
291C13×C4⋊C4—42no—
292C13×C4⋊C4—42no—
293C13×C4⋊C4—42no—
294C13×C4⋊C4—42no—
295C13×C4⋊C4—42no—
296C13×C4⋊C4—41no—
297C13×C4⋊C4—41no—
298C13×C4⋊C4C22×C418yescomplemented
299C13×C4⋊C4C22×C418yescomplemented
300C13×C4⋊C4C22×C418yescomplemented
301C13×C22⋊C4—24no—
302C13×C22⋊C4—24no—
303C13×C22⋊C4—24no—
304C13×C22⋊C4—42no—
305C13×C22⋊C4—41no—
306C13×C22⋊C4—42no—
307C13×C22⋊C4—42no—
308C13×C22⋊C4—42no—
309C13×C22⋊C4—41no—
310C13×C22⋊C4—42no—
311C13×C22⋊C4—42no—
312C13×C22⋊C4—42no—
313C13×C22⋊C4—42no—
314C13×C22⋊C4—42no—
315C13×C22⋊C4—41no—
316C13×C22⋊C4—41no—
317C13×C22⋊C4—42no—
318C13×C22⋊C4—42no—
319C13×C22⋊C4—42no—
320C13×C22⋊C4—42no—
321C13×C22⋊C4C22×C418yes—
322C13×C22⋊C4C22×C418yes—
323C13×C22⋊C4C22×C418yes—
324C13×C22⋊C4C22×C414yes—
325C13×C22⋊C4C22×C418yes—
326C13×C22⋊C4C22×C414yescomplemented
327C13×C22⋊C4C22×C418yescomplemented
328C42×C13—24no—
329C42×C13—22no—
330C42×C13—42no—
331C42×C13—42no—
332C42×C13—41no—
333C42×C13—42no—
334C42×C13—42no—
335C42×C13—42no—
336C42×C13—42no—
337C42×C13—42no—
338C42×C13C22×C414yescomplemented
339C2×#560C2×C1311yescharacteristic
340#2375C2×C1311yescharacteristic, complemented
341#2375C2×C1312yescomplemented
342#2374C2×C1311yescharacteristic, complemented
343#2373C2×C1312yescomplemented
344#2366C2×C1311yescharacteristic, complemented
345#2364C2×C1312yescomplemented
346#2363C2×C1312yescomplemented
347#2361C2×C1312yescomplemented
348#2359C2×C1312yescomplemented
349#2335C2×C1312yescomplemented
350#2334C2×C1312yescomplemented
351#2333C2×C1312yescomplemented
352#2328C2×C1311yescharacteristic, complemented
353#2325C2×C1312yescomplemented
354#2324C2×C1312yescomplemented
355#2322C2×C1311yescharacteristic, complemented
356C4×#120C2×C1311yescharacteristic, complemented
357C4×#120C2×C1312yescomplemented
358C23×C13—22no—
359C23×C13—22no—
360C23×C13—22no—
361C23×C13—22no—
362C23×C13—21no—
363C23×C13—22no—
364C23×C13—22no—
365C23×C13—22no—
366C23×C13—21no—
367C23×C13—22no—
368C23×C13—21no—
369C23×C13—22no—
370C23×C13—22no—
371C23×C13—22no—
372C23×C13—21no—
373C23×C13—22no—
374C23×C13—22no—
375C23×C13—22no—
376C23×C13—22no—
377C23×C13—22no—
378C23×C13—48no—
379C23×C13—44no—
380C23×C13—44no—
381C23×C13—48no—
382C23×C13—44no—
383C23×C13C23×C414yes—
384C23×C13C23×C412yes—
385C23×C13C23×C414yes—
386C23×C13C23×C412yes—
387C23×C13C2511yescharacteristic
388D4×C13—48no—
389D4×C13—48no—
390D4×C13—48no—
391D4×C13—44no—
392D4×C13—48no—
393D4×C13—44no—
394D4×C13—48no—
395C2×C4×C13—22no—
396C2×C4×C13—21no—
397C2×C4×C13—22no—
398C2×C4×C13—22no—
399C2×C4×C13—22no—
400C2×C4×C13—22no—
401C2×C4×C13—22no—
402C2×C4×C13—22no—
403C2×C4×C13—22no—
404C2×C4×C13—22no—
405C2×C4×C13—21no—
406C2×C4×C13—22no—
407C2×C4×C13—22no—
408C2×C4×C13—22no—
409C2×C4×C13—21no—
410C2×C4×C13—22no—
411C2×C4×C13—22no—
412C2×C4×C13—22no—
413C2×C4×C13—22no—
414C2×C4×C13—22no—
415C2×C4×C13—22no—
416C2×C4×C13—22no—
417C2×C4×C13—21no—
418C2×C4×C13—22no—
419C2×C4×C13—21no—
420C2×C4×C13—22no—
421C2×C4×C13—22no—
422C2×C4×C13—22no—
423C2×C4×C13—22no—
424C2×C4×C13—22no—
425C2×C4×C13—22no—
426C2×C4×C13—22no—
427C2×C4×C13—22no—
428C2×C4×C13—22no—
429C2×C4×C13—44no—
430C2×C4×C13—48no—
431C2×C4×C13—48no—
432C2×C4×C13—44no—
433C2×C4×C13—44no—
434C2×C4×C13—48no—
435C2×C4×C13—82no—
436C2×C4×C13—84no—
437C2×C4×C13—82no—
438C2×C4×C13—84no—
439C2×C4×C13C23×C412yes—
440C2×C4×C13C23×C414yes—
441C2×C4×C13C23×C414yes—
442C2×C4×C13C23×C414yes—
443C2×C4×C13C23×C414yes—
444C2×C4×C13H(5,𝔽2)14yes—
445C2×C4×C13H(5,𝔽2)12yes—
446C24×C4C22×C1311yescharacteristic
447#560C4×C13116yescomplemented
448C2×#127C22×C1311yescharacteristic
449C2×#126C22×C1312yes—
450C2×#123C22×C1311yescharacteristic
451C2×#123C22×C1312yes—
452C2×#121C22×C1312yes—
453C2×#121C22×C1312yes—
454C2×#121C22×C1312yes—
455C2×#120C22×C1311yescharacteristic
456C2×#120C22×C1312yes—
457C2×C4×D4C22×C1311yescharacteristic
458C2×C4×D4C22×C1312yes—
459C2×C4×D4C22×C1312yes—
460C2×C4×D4C22×C1312yes—
461C2×C4×D4C22×C1312yes—
462C2×C4×D4C22×C1312yescomplemented
463C2×C4×D4C22×C1311yescharacteristic, complemented
464C2×#117C22×C1312yescomplemented
465C22×C4⋊C4C22×C1311yescharacteristic, complemented
466#390C22×C1312yes—
467#390C22×C1312yes—
468#390C22×C1311yescharacteristic
469#390C22×C1312yes—
470#390C22×C1312yes—
471#390C22×C1311yescharacteristic, complemented
472#390C22×C1312yescomplemented
473#389C22×C1312yescomplemented
474#389C22×C1312yescomplemented
475#389C22×C1312yescomplemented
476#388C22×C1312yes—
477#388C22×C1312yes—
478#388C22×C1312yes—
479#388C22×C1312yes—
480#388C22×C1312yes—
481#388C22×C1312yes—
482#388C22×C1312yes—
483#388C22×C1312yes—
484#388C22×C1312yes—
485#388C22×C1312yescomplemented
486#388C22×C1312yescomplemented
487#388C22×C1312yescomplemented
488#387C22×C1312yescomplemented
489#387C22×C1312yescomplemented
490#387C22×C1312yescomplemented
491#387C22×C1312yescomplemented
492#387C22×C1312yescomplemented
493#387C22×C1312yescomplemented
494#386C22×C1311yescharacteristic
495#386C22×C1312yes—
496#386C22×C1312yes—
497#386C22×C1312yes—
498#386C22×C1312yes—
499#386C22×C1312yes—
500#386C22×C1312yes—
501#386C22×C1312yes—
502#386C22×C1312yes—
503#386C22×C1311yescharacteristic
504#386C22×C1312yescomplemented
505#386C22×C1312yescomplemented
506#386C22×C1312yescomplemented
507#385C22×C1312yes—
508#385C22×C1312yes—
509#385C22×C1312yes—
510#385C22×C1311yescharacteristic
511#385C22×C1312yes—
512#385C22×C1311yescharacteristic, complemented
513#385C22×C1312yescomplemented
514#382C22×C1311yescharacteristic, complemented
515#381C22×C1311yescharacteristic, complemented
516#380C22×C1312yescomplemented
517#379C22×C1312yes—
518#379C22×C1311yescharacteristic
519C4×C4⋊C4C22×C1312yescomplemented
520C4×C4⋊C4C22×C1312yescomplemented
521C4×C4⋊C4C22×C1312yescomplemented
522C4×C4⋊C4C22×C1312yescomplemented
523C4×C22⋊C4C22×C1312yes—
524C4×C22⋊C4C22×C1311yescharacteristic
525C4×C22⋊C4C22×C1312yes—
526C4×C22⋊C4C22×C1312yes—
527C4×C22⋊C4C22×C1312yes—
528C4×C22⋊C4C22×C1311yescharacteristic, complemented
529C4×C22⋊C4C22×C1312yescomplemented
530C4×C22⋊C4C22×C1312yescomplemented
531C4×C22⋊C4C22×C1312yescomplemented
532#376C22×C1311yescharacteristic, complemented
533C2×#95C22×C1312yescomplemented
534C22×C13—24no—
535C22×C13—22no—
536C22×C13—24no—
537C22×C13—24no—
538C22×C13—24no—
539C22×C13—24no—
540C22×C13—24no—
541C22×C13—24no—
542C22×C13—24no—
543C22×C13—22no—
544C22×C13—416no—
545C22×C13—42no—
546C22×C13—41no—
547C22×C13—41no—
548C22×C13—42no—
549C22×C13—42no—
550C22×C13—42no—
551C22×C13—42no—
552C22×C13—42no—
553C22×C13—42no—
554C22×C13—42no—
555C22×C13—42no—
556C22×C13—41no—
557C22×C13—41no—
558C22×C13—42no—
559C22×C13C24×C411yescharacteristic
560C22×C13C2×H(5,𝔽2)12yes—
561C22×C13C2×H(5,𝔽2)11yescharacteristic
562C22×C13#58511yescharacteristic
563C22×C13#58512yes—
564C4×C13—24no—
565C4×C13—24no—
566C4×C13—24no—
567C4×C13—22no—
568C4×C13—24no—
569C4×C13—22no—
570C4×C13—24no—
571C4×C13—41no—
572C4×C13—41no—
573C4×C13—42no—
574C4×C13—42no—
575C4×C13—42no—
576C4×C13—42no—
577C4×C13—42no—
578C4×C13—41no—
579C25C23×C1311yescharacteristic
580C22×D4C23×C1312yes—
581C22×D4C23×C1312yes—
582C22×D4C23×C1312yes—
583C22×D4C23×C1311yescharacteristic
584C22×D4C23×C1312yes—
585C22×D4C23×C1312yes—
586C22×D4C23×C1311yescharacteristic
587C23×C4—44no—
588C23×C4—42no—
589C23×C4C23×C1311yescharacteristic
590C23×C4C23×C1312yes—
591C23×C4C23×C1311yescharacteristic
592C23×C4C23×C1312yes—
593C23×C4C23×C1311yescharacteristic
594C23×C4C23×C1312yes—
595C23×C4C23×C1311yescharacteristic
596C23×C4C23×C1312yes—
597C23×C4C23×C1311yescharacteristic
598C23×C4C23×C1312yes—
599#127C2×C4×C1318yescomplemented
600#126C2×C4×C13116yescomplemented
601#123C2×C4×C1318yescomplemented
602#123C2×C4×C13116yescomplemented
603#121C2×C4×C13116yescomplemented
604#121C2×C4×C13116yescomplemented
605#121C2×C4×C13116yescomplemented
606#120C2×C4×C1318yescomplemented
607#120C2×C4×C13116yescomplemented
608C4×D4—42no—
609C4×D4—44no—
610C4×D4—42no—
611C4×D4—44no—
612C4×D4—44no—
613C4×D4—44no—
614C4×D4—44no—
615#117—44no—
616C2×C4⋊C4—42no—
617C2×C4⋊C4C23×C1312yes—
618C2×C4⋊C4C23×C1312yes—
619C2×C4⋊C4C23×C1312yes—
620C2×C4⋊C4C23×C1312yes—
621C2×C4⋊C4C23×C1312yes—
622C2×C4⋊C4C23×C1312yes—
623C2×C4⋊C4C23×C1311yescharacteristic
624C2×C4⋊C4C23×C1311yescharacteristic
625C2×C4⋊C4C23×C1312yes—
626C2×C4⋊C4C23×C1312yes—
627C2×C4⋊C4C23×C1312yes—
628C2×C4⋊C4C23×C1312yes—
629C2×C4⋊C4C23×C1312yes—
630C2×C22⋊C4C23×C1312yes—
631C2×C22⋊C4C23×C1312yes—
632C2×C22⋊C4C23×C1312yes—
633C2×C22⋊C4C23×C1312yes—
634C2×C22⋊C4C23×C1311yescharacteristic
635C2×C22⋊C4C23×C1312yes—
636C2×C22⋊C4C23×C1312yes—
637C2×C22⋊C4C23×C1312yes—
638C2×C22⋊C4C23×C1312yes—
639C2×C22⋊C4C23×C1312yes—
640C2×C22⋊C4C23×C1311yescharacteristic
641C2×C22⋊C4C23×C1312yes—
642C2×C22⋊C4C23×C1312yes—
643C2×C22⋊C4C23×C1312yes—
644C2×C22⋊C4C23×C1312yes—
645C2×C22⋊C4C23×C1311yescharacteristic
646C2×C22⋊C4C23×C1312yes—
647C2×C22⋊C4C23×C1311yescharacteristic
648C2×C22⋊C4C23×C1312yes—
649C2×C22⋊C4C23×C1312yes—
650C2×C22⋊C4C23×C1312yes—
651C2×C22⋊C4C23×C1312yes—
652C2×C22⋊C4C23×C1312yes—
653C2×C22⋊C4C23×C1312yes—
654C2×C22⋊C4C23×C1311yescharacteristic
655C2×C22⋊C4C23×C1312yes—
656C2×C22⋊C4C23×C1311yescharacteristic
657C2×C42C23×C1312yes—
658C2×C42C23×C1311yescharacteristic
659C2×C42C23×C1312yes—
660C2×C42C23×C1312yes—
661C2×C42C23×C1312yes—
662C2×C42C23×C1312yes—
663C2×C42C23×C1312yes—
664C2×C42C23×C1311yescharacteristic
665C2×C42C23×C1312yes—
666C2×C42C23×C1312yes—
667C2×C42C23×C1311yescharacteristic
668#95C23×C1312yes—
669#95C23×C1312yes—
670#95C23×C1312yes—
671#95C23×C1312yes—
672#95C23×C1312yes—
673#95C23×C1312yes—
674#95C23×C1312yes—
675#95C23×C1312yes—
676#95C23×C1312yes—
677#95C23×C1312yes—
678#95C23×C1312yes—
679#95C23×C1312yes—
680#95C23×C1312yes—
681#95C23×C1312yes—
682#95C23×C1312yes—
683#95C23×C1312yes—
684#95C23×C1312yes—
685#95C23×C1312yes—
686C2×C13—42no—
687C2×C13—44no—
688C2×C13—44no—
689C2×C13—42no—
690C2×C13C4×H(5,𝔽2)12yes—
691C2×C13C4×H(5,𝔽2)11yescharacteristic
692C2×C13#353211yescharacteristic
693C2×C13#353912yes—
694C2×C13#354011yescharacteristic
695C24—42no—
696C24—41no—
697C24—41no—
698C24—42no—
699C24C22×C4×C1314yes—
700C24C24×C1311yescharacteristic
701C24C24×C1312yes—
702C24C24×C1312yes—
703C24C24×C1311yescharacteristic
704C2×D4—42no—
705C2×D4—41no—
706C2×D4—41no—
707C2×D4—42no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—42no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4C22×C4×C1318yes—
719C2×D4C22×C4×C1318yes—
720C2×D4C22×C4×C1318yes—
721C2×D4C22×C4×C1314yes—
722C2×D4C22×C4×C1318yes—
723C2×D4C22×C4×C1314yescomplemented
724C2×D4C22×C4×C1318yescomplemented
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—24no—
732C22×C4—41no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—41no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—41no—
740C22×C4—42no—
741C22×C4—41no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—416no—
750C22×C4C22×C4×C1314yescomplemented
751C22×C4C22×C4×C1318yescomplemented
752C22×C4C24×C1311yescharacteristic
753C22×C4C24×C1312yes—
754C22×C4C24×C1311yescharacteristic
755C22×C4C24×C1312yes—
756C22×C4C24×C1312yes—
757C22×C4C24×C1312yes—
758C22×C4C24×C1312yes—
759C22×C4C24×C1311yescharacteristic
760C22×C4C24×C1311yescharacteristic
761C22×C4C24×C1312yes—
762C22×C4C24×C1312yes—
763C22×C4C24×C1312yes—
764C22×C4C24×C1312yes—
765C22×C4C24×C1312yes—
766C22×C4C24×C1311yescharacteristic
767C4⋊C4—24no—
768C4⋊C4—24no—
769C4⋊C4—24no—
770C4⋊C4—42no—
771C4⋊C4—42no—
772C4⋊C4—42no—
773C4⋊C4—41no—
774C4⋊C4—41no—
775C4⋊C4—42no—
776C4⋊C4—42no—
777C4⋊C4C22×C4×C1318yescomplemented
778C4⋊C4C22×C4×C1318yescomplemented
779C4⋊C4C22×C4×C1318yescomplemented
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—24no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—41no—
787C22⋊C4—41no—
788C22⋊C4—42no—
789C22⋊C4—42no—
790C22⋊C4—42no—
791C22⋊C4—42no—
792C22⋊C4—42no—
793C22⋊C4—41no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—42no—
799C22⋊C4—42no—
800C22⋊C4C22×C4×C1318yes—
801C22⋊C4C22×C4×C1318yes—
802C22⋊C4C22×C4×C1318yes—
803C22⋊C4C22×C4×C1318yes—
804C22⋊C4C22×C4×C1314yes—
805C22⋊C4C22×C4×C1318yescomplemented
806C22⋊C4C22×C4×C1314yescomplemented
807C42—24no—
808C42—22no—
809C42—42no—
810C42—42no—
811C42—42no—
812C42—42no—
813C42—42no—
814C42—42no—
815C42—42no—
816C42—41no—
817C42C22×C4×C1314yescomplemented
818C13#3451111yescharacteristic, direct product factor, Sylow
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—21no—
828C23—22no—
829C23—21no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—21no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—48no—
840C23—44no—
841C23—44no—
842C23—48no—
843C23—44no—
844C23C23×C4×C1314yes—
845C23C23×C4×C1312yes—
846C23C23×C4×C1314yes—
847C23C23×C4×C1312yes—
848C23C25×C1311yescharacteristic
849D4—48no—
850D4—48no—
851D4—48no—
852D4—44no—
853D4—48no—
854D4—44no—
855D4—48no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—21no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—44no—
891C2×C4—48no—
892C2×C4—48no—
893C2×C4—44no—
894C2×C4—44no—
895C2×C4—48no—
896C2×C4—82no—
897C2×C4—84no—
898C2×C4—82no—
899C2×C4—84no—
900C2×C4C23×C4×C1312yes—
901C2×C4C23×C4×C1314yes—
902C2×C4C23×C4×C1314yes—
903C2×C4C23×C4×C1314yes—
904C2×C4C23×C4×C1314yes—
905C2×C4C13×H(5,𝔽2)14yes—
906C2×C4C13×H(5,𝔽2)12yes—
907C22—24no—
908C22—22no—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—22no—
917C22—416no—
918C22—42no—
919C22—41no—
920C22—41no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—41no—
930C22—41no—
931C22—42no—
932C22C24×C4×C1311yescharacteristic
933C22C2×C13×H(5,𝔽2)12yes—
934C22C2×C13×H(5,𝔽2)11yescharacteristic
935C22C13×#58511yescharacteristic
936C22C13×#58512yes—
937C4—22no—
938C4—24no—
939C4—24no—
940C4—24no—
941C4—24no—
942C4—22no—
943C4—24no—
944C4—41no—
945C4—41no—
946C4—42no—
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—41no—
952C2—44no—
953C2—42no—
954C2—42no—
955C2—44no—
956C2C4×C13×H(5,𝔽2)12yes—
957C2C4×C13×H(5,𝔽2)11yescharacteristic
958C2C13×#353211yescharacteristic
959C2C13×#353912yes—
960C2C13×#354011yescharacteristic
subgroupG/H
center, socleC23×C13C25
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
prime radicalC2×C13×#560C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2375C2semidirect
3. C13×#2375C2semidirect
4. C13×#2374C2semidirect
5. C13×#2373C2semidirect
6. C13×#2366C2semidirect
7. C13×#2364C2semidirect
8. C13×#2363C2semidirect
9. C13×#2361C2semidirect
10. C13×#2359C2semidirect
11. C13×#2335C2semidirect
12. C13×#2334C2semidirect
13. C13×#2333C2semidirect
14. C13×#2328C2semidirect
15. C13×#2325C2semidirect
16. C13×#2324C2semidirect
17. C13×#2322C2semidirect
18. C4×C13×#120C2semidirect
19. C4×C13×#120C2semidirect
21. C13×#560C4semidirect
36. C2×C4×D4×C13C22semidirect
37. C2×C4×D4×C13C22semidirect
38. C2×C13×#117C22semidirect
39. C22×C13×C4⋊C4C22semidirect
45. C13×#390C22semidirect
46. C13×#390C22semidirect
47. C13×#389C22semidirect
48. C13×#389C22semidirect
49. C13×#389C22semidirect
59. C13×#388C22semidirect
60. C13×#388C22semidirect
61. C13×#388C22semidirect
62. C13×#387C22semidirect
63. C13×#387C22semidirect
64. C13×#387C22semidirect
65. C13×#387C22semidirect
66. C13×#387C22semidirect
67. C13×#387C22semidirect
78. C13×#386C22semidirect
79. C13×#386C22semidirect
80. C13×#386C22semidirect
86. C13×#385C22semidirect
87. C13×#385C22semidirect
88. C13×#382C22semidirect
89. C13×#381C22semidirect
90. C13×#380C22semidirect
93. C4×C13×C4⋊C4C22semidirect
94. C4×C13×C4⋊C4C22semidirect
95. C4×C13×C4⋊C4C22semidirect
96. C4×C13×C4⋊C4C22semidirect
102. C4×C13×C22⋊C4C22semidirect
103. C4×C13×C22⋊C4C22semidirect
104. C4×C13×C22⋊C4C22semidirect
105. C4×C13×C22⋊C4C22semidirect
106. C13×#376C22semidirect
107. C2×C13×#95C22semidirect
128. C13×#127C2×C4semidirect
129. C13×#126C2×C4semidirect
130. C13×#123C2×C4semidirect
131. C13×#123C2×C4semidirect
132. C13×#121C2×C4semidirect
133. C13×#121C2×C4semidirect
134. C13×#121C2×C4semidirect
135. C13×#120C2×C4semidirect
136. C13×#120C2×C4semidirect
215. #34511C13direct (N × H)
244. C2×D4×C13C22×C4semidirect
245. C2×D4×C13C22×C4semidirect
271. C22×C4×C13C22×C4semidirect
272. C22×C4×C13C22×C4semidirect
298. C13×C4⋊C4C22×C4semidirect
299. C13×C4⋊C4C22×C4semidirect
300. C13×C4⋊C4C22×C4semidirect
326. C13×C22⋊C4C22×C4semidirect
327. C13×C22⋊C4C22×C4semidirect
338. C42×C13C22×C4semidirect
340. #2375C2×C13semidirect
341. #2375C2×C13semidirect
342. #2374C2×C13semidirect
343. #2373C2×C13semidirect
344. #2366C2×C13semidirect
345. #2364C2×C13semidirect
346. #2363C2×C13semidirect
347. #2361C2×C13semidirect
348. #2359C2×C13semidirect
349. #2335C2×C13semidirect
350. #2334C2×C13semidirect
351. #2333C2×C13semidirect
352. #2328C2×C13semidirect
353. #2325C2×C13semidirect
354. #2324C2×C13semidirect
355. #2322C2×C13semidirect
356. C4×#120C2×C13semidirect
357. C4×#120C2×C13semidirect
447. #560C4×C13semidirect
462. C2×C4×D4C22×C13semidirect
463. C2×C4×D4C22×C13semidirect
464. C2×#117C22×C13semidirect
465. C22×C4⋊C4C22×C13semidirect
471. #390C22×C13semidirect
472. #390C22×C13semidirect
473. #389C22×C13semidirect
474. #389C22×C13semidirect
475. #389C22×C13semidirect
485. #388C22×C13semidirect
486. #388C22×C13semidirect
487. #388C22×C13semidirect
488. #387C22×C13semidirect
489. #387C22×C13semidirect
490. #387C22×C13semidirect
491. #387C22×C13semidirect
492. #387C22×C13semidirect
493. #387C22×C13semidirect
504. #386C22×C13semidirect
505. #386C22×C13semidirect
506. #386C22×C13semidirect
512. #385C22×C13semidirect
513. #385C22×C13semidirect
514. #382C22×C13semidirect
515. #381C22×C13semidirect
516. #380C22×C13semidirect
519. C4×C4⋊C4C22×C13semidirect
520. C4×C4⋊C4C22×C13semidirect
521. C4×C4⋊C4C22×C13semidirect
522. C4×C4⋊C4C22×C13semidirect
528. C4×C22⋊C4C22×C13semidirect
529. C4×C22⋊C4C22×C13semidirect
530. C4×C22⋊C4C22×C13semidirect
531. C4×C22⋊C4C22×C13semidirect
532. #376C22×C13semidirect
533. C2×#95C22×C13semidirect
599. #127C2×C4×C13semidirect
600. #126C2×C4×C13semidirect
601. #123C2×C4×C13semidirect
602. #123C2×C4×C13semidirect
603. #121C2×C4×C13semidirect
604. #121C2×C4×C13semidirect
605. #121C2×C4×C13semidirect
606. #120C2×C4×C13semidirect
607. #120C2×C4×C13semidirect
723. C2×D4C22×C4×C13semidirect
724. C2×D4C22×C4×C13semidirect
750. C22×C4C22×C4×C13semidirect
751. C22×C4C22×C4×C13semidirect
777. C4⋊C4C22×C4×C13semidirect
778. C4⋊C4C22×C4×C13semidirect
779. C4⋊C4C22×C4×C13semidirect
805. C22⋊C4C22×C4×C13semidirect
806. C22⋊C4C22×C4×C13semidirect
817. C42C22×C4×C13semidirect
818. C13#34511direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5602
C13×#23752
C13×#23742
C13×#23732
C13×#23662
C13×#23642
C13×#23632
C13×#23612
C13×#23592
C13×#23352
C13×#23342
C13×#23332
C13×#23282
C13×#23252
C13×#23242
C13×#23222
C4×C13×#1202
#3451113