Finite Group Databasebeta

← C13×#14520 #15700859

Subgroups — C13×#14520 #15700859

Order 3328.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#392C211yesmaximal, characteristic
2C2×C13×#390C211yesmaximal, characteristic, complemented
3C2×C13×#388C211yesmaximal, characteristic, complemented
4C2×C13×#386C211yesmaximal, characteristic, complemented
5C2×C13×#386C211yesmaximal, characteristic, complemented
6C13×#1442C211yesmaximal, characteristic, complemented
7C13×#1440C211yesmaximal, characteristic, complemented
8C13×#1438C211yesmaximal, characteristic, complemented
9C13×#1438C211yesmaximal, characteristic, complemented
10C13×#1438C211yesmaximal, characteristic, complemented
11C13×#1437C211yesmaximal, characteristic, complemented
12C13×#1437C211yesmaximal, characteristic, complemented
13C13×#1437C211yesmaximal, characteristic, complemented
14C13×#1434C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C13×C22⋊C4C2211yescharacteristic
33C22×C13×C22⋊C4C2211yescharacteristic
34C22×C13×C22⋊C4C2211yescharacteristic
35C22×C42×C13C2211yescharacteristic
36C22×C42×C13C2211yescharacteristic
37C13×#392C418yescomplemented
38C13×#390—24no—
39C13×#388—24no—
40C13×#386—24no—
41C13×#386—24no—
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C25×C13C2311yescharacteristic
57C25×C13C2311yescharacteristic
58C25×C13C2311yescharacteristic
59C22×D4×C13—22no—
60C22×D4×C13—22no—
61C22×D4×C13—22no—
62C22×D4×C13—22no—
63C22×D4×C13—22no—
64C22×D4×C13—22no—
65C22×D4×C13—41no—
66C22×D4×C13—41no—
67C22×D4×C13—41no—
68C22×D4×C13—41no—
69C22×D4×C13—41no—
70C22×D4×C13—41no—
71C22×D4×C13—41no—
72C22×D4×C13—41no—
73C22×D4×C13—41no—
74C22×D4×C13—41no—
75C22×D4×C13—41no—
76C22×D4×C13—41no—
77C22×D4×C13C2×C414yes—
78C22×D4×C13C2×C414yes—
79C22×D4×C13C2×C414yescomplemented
80C23×C4×C13—22no—
81C23×C4×C13—22no—
82C23×C4×C13—22no—
83C23×C4×C13—41no—
84C23×C4×C13—41no—
85C23×C4×C13—41no—
86C23×C4×C13—41no—
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C23×C4×C13C2311yescharacteristic
92C23×C4×C13C2311yescharacteristic
93C23×C4×C13C2311yescharacteristic
94C23×C4×C13C2311yescharacteristic
95C23×C4×C13C2311yescharacteristic
96C23×C4×C13C2311yescharacteristic
97C23×C4×C13C2311yescharacteristic
98C23×C4×C13C2311yescharacteristic
99C2×C13×C4⋊C4—22no—
100C2×C13×C4⋊C4—22no—
101C2×C13×C4⋊C4—41no—
102C2×C13×C22⋊C4—22no—
103C2×C13×C22⋊C4—22no—
104C2×C13×C22⋊C4—22no—
105C2×C13×C22⋊C4—22no—
106C2×C13×C22⋊C4—22no—
107C2×C13×C22⋊C4—22no—
108C2×C13×C22⋊C4—22no—
109C2×C13×C22⋊C4—22no—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—22no—
114C2×C13×C22⋊C4—22no—
115C2×C13×C22⋊C4—22no—
116C2×C13×C22⋊C4—22no—
117C2×C13×C22⋊C4—22no—
118C2×C13×C22⋊C4—22no—
119C2×C13×C22⋊C4—22no—
120C2×C13×C22⋊C4—41no—
121C2×C13×C22⋊C4—41no—
122C2×C13×C22⋊C4—41no—
123C2×C13×C22⋊C4—41no—
124C2×C13×C22⋊C4—41no—
125C2×C13×C22⋊C4—41no—
126C2×C13×C22⋊C4—41no—
127C2×C13×C22⋊C4—41no—
128C2×C13×C22⋊C4—41no—
129C2×C13×C22⋊C4—41no—
130C2×C13×C22⋊C4—41no—
131C2×C13×C22⋊C4—41no—
132C2×C13×C22⋊C4—41no—
133C2×C13×C22⋊C4—41no—
134C2×C13×C22⋊C4—41no—
135C2×C13×C22⋊C4—41no—
136C2×C13×C22⋊C4—41no—
137C2×C13×C22⋊C4—41no—
138C2×C13×C22⋊C4—41no—
139C2×C13×C22⋊C4—41no—
140C2×C13×C22⋊C4C2×C414yes—
141C2×C13×C22⋊C4C2×C414yescomplemented
142C2×C13×C22⋊C4C2×C414yescomplemented
143C2×C13×C22⋊C4D414yescomplemented
144C2×C42×C13—22no—
145C2×C42×C13—22no—
146C2×C42×C13—22no—
147C2×C42×C13—41no—
148C2×C42×C13—41no—
149C2×C42×C13—41no—
150C13×#95—22no—
151C13×#95—22no—
152C13×#95—22no—
153C13×#95—22no—
154C13×#95—41no—
155C13×#95—41no—
156C13×#95—41no—
157C13×#95—41no—
158C13×#95—41no—
159C13×#95—41no—
160C13×#95—41no—
161C13×#95—41no—
162C13×#95C2×C414yescomplemented
163C13×#95D414yescomplemented
164#14520C1311yesmaximal, characteristic, direct product factor, Sylow
165C24×C13—21no—
166C24×C13—21no—
167C24×C13—21no—
168C24×C13—21no—
169C24×C13—21no—
170C24×C13—21no—
171C24×C13—21no—
172C24×C13—21no—
173C24×C13—21no—
174C24×C13—21no—
175C24×C13—21no—
176C24×C13—21no—
177C24×C13—21no—
178C24×C13—21no—
179C24×C13—21no—
180C24×C13—21no—
181C24×C13—21no—
182C24×C13—21no—
183C24×C13—21no—
184C24×C13—21no—
185C24×C13—21no—
186C24×C13—21no—
187C24×C13—21no—
188C24×C13—21no—
189C24×C13—21no—
190C24×C13—21no—
191C24×C13—21no—
192C24×C13—21no—
193C24×C13—21no—
194C24×C13—21no—
195C24×C13—21no—
196C24×C13—21no—
197C24×C13—21no—
198C24×C13—21no—
199C24×C13—21no—
200C24×C13—21no—
201C24×C13—21no—
202C24×C13—21no—
203C24×C13—21no—
204C24×C13—21no—
205C24×C13C22×C412yes—
206C24×C13C22×C412yes—
207C24×C13C22×C412yes—
208C24×C13C2×D412yes—
209C24×C13#4112yes—
210C24×C13C2411yescharacteristic
211C2×D4×C13—28no—
212C2×D4×C13—28no—
213C2×D4×C13—28no—
214C2×D4×C13—44no—
215C2×D4×C13—44no—
216C2×D4×C13—44no—
217C2×D4×C13—44no—
218C2×D4×C13—44no—
219C2×D4×C13—44no—
220C2×D4×C13—44no—
221C2×D4×C13—44no—
222C2×D4×C13—44no—
223C2×D4×C13—44no—
224C2×D4×C13—44no—
225C2×D4×C13—44no—
226C2×D4×C13—44no—
227C2×D4×C13—44no—
228C2×D4×C13—44no—
229C2×D4×C13—44no—
230C2×D4×C13—44no—
231C2×D4×C13—44no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×C13—21no—
253C22×C4×C13—21no—
254C22×C4×C13—21no—
255C22×C4×C13—21no—
256C22×C4×C13—21no—
257C22×C4×C13—21no—
258C22×C4×C13—21no—
259C22×C4×C13—21no—
260C22×C4×C13—21no—
261C22×C4×C13—21no—
262C22×C4×C13—21no—
263C22×C4×C13—21no—
264C22×C4×C13—21no—
265C22×C4×C13—21no—
266C22×C4×C13—21no—
267C22×C4×C13—21no—
268C22×C4×C13—21no—
269C22×C4×C13—21no—
270C22×C4×C13—21no—
271C22×C4×C13—21no—
272C22×C4×C13—21no—
273C22×C4×C13—21no—
274C22×C4×C13—21no—
275C22×C4×C13—21no—
276C22×C4×C13—21no—
277C22×C4×C13—21no—
278C22×C4×C13—21no—
279C22×C4×C13—21no—
280C22×C4×C13—21no—
281C22×C4×C13—21no—
282C22×C4×C13—21no—
283C22×C4×C13—21no—
284C22×C4×C13—21no—
285C22×C4×C13—21no—
286C22×C4×C13—21no—
287C22×C4×C13—21no—
288C22×C4×C13—21no—
289C22×C4×C13—21no—
290C22×C4×C13—21no—
291C22×C4×C13—21no—
292C22×C4×C13—21no—
293C22×C4×C13—21no—
294C22×C4×C13—21no—
295C22×C4×C13—21no—
296C22×C4×C13—21no—
297C22×C4×C13—21no—
298C22×C4×C13—21no—
299C22×C4×C13—21no—
300C22×C4×C13—21no—
301C22×C4×C13—21no—
302C22×C4×C13—21no—
303C22×C4×C13—21no—
304C22×C4×C13—44no—
305C22×C4×C13—44no—
306C22×C4×C13—44no—
307C22×C4×C13—44no—
308C22×C4×C13—44no—
309C22×C4×C13—44no—
310C22×C4×C13—44no—
311C22×C4×C13C22×C412yes—
312C22×C4×C13C22×C412yes—
313C22×C4×C13C22×C412yes—
314C22×C4×C13C22×C412yes—
315C22×C4×C13C2×D412yes—
316C22×C4×C13C2×D412yes—
317C22×C4×C13C2×D412yes—
318C22×C4×C13C2×D412yes—
319C22×C4×C13C2×D412yes—
320C22×C4×C13#4112yes—
321C22×C4×C13#4112yes—
322C22×C4×C13#4112yes—
323C13×C4⋊C4—44no—
324C13×C22⋊C4—28no—
325C13×C22⋊C4—44no—
326C13×C22⋊C4—44no—
327C13×C22⋊C4—44no—
328C13×C22⋊C4—44no—
329C13×C22⋊C4—44no—
330C13×C22⋊C4—44no—
331C13×C22⋊C4—44no—
332C13×C22⋊C4—44no—
333C13×C22⋊C4—44no—
334C13×C22⋊C4—44no—
335C13×C22⋊C4—44no—
336C13×C22⋊C4—44no—
337C13×C22⋊C4—44no—
338C42×C13—44no—
339C42×C13—44no—
340C2×#392C2×C1311yescharacteristic
341C2×#390C2×C1311yescharacteristic, complemented
342C2×#388C2×C1311yescharacteristic, complemented
343C2×#386C2×C1311yescharacteristic, complemented
344C2×#386C2×C1311yescharacteristic, complemented
345#1442C2×C1311yescharacteristic, complemented
346#1440C2×C1311yescharacteristic, complemented
347#1438C2×C1311yescharacteristic, complemented
348#1438C2×C1311yescharacteristic, complemented
349#1438C2×C1311yescharacteristic, complemented
350#1437C2×C1311yescharacteristic, complemented
351#1437C2×C1311yescharacteristic, complemented
352#1437C2×C1311yescharacteristic, complemented
353#1434C2×C1311yescharacteristic, complemented
354C22⋊#95C2×C1311yescharacteristic, complemented
355C23×C13—22no—
356C23×C13—22no—
357C23×C13—22no—
358C23×C13—22no—
359C23×C13—22no—
360C23×C13—22no—
361C23×C13—22no—
362C23×C13—22no—
363C23×C13—22no—
364C23×C13—22no—
365C23×C13—22no—
366C23×C13—22no—
367C23×C13—22no—
368C23×C13—22no—
369C23×C13—22no—
370C23×C13—22no—
371C23×C13—22no—
372C23×C13—22no—
373C23×C13—22no—
374C23×C13—22no—
375C23×C13—22no—
376C23×C13—22no—
377C23×C13—22no—
378C23×C13—22no—
379C23×C13—22no—
380C23×C13—22no—
381C23×C13—22no—
382C23×C13—22no—
383C23×C13—22no—
384C23×C13—22no—
385C23×C13—22no—
386C23×C13—22no—
387C23×C13—41no—
388C23×C13—41no—
389C23×C13—41no—
390C23×C13—41no—
391C23×C13—41no—
392C23×C13—41no—
393C23×C13—41no—
394C23×C13—41no—
395C23×C13—41no—
396C23×C13—41no—
397C23×C13—41no—
398C23×C13—41no—
399C23×C13—41no—
400C23×C13—41no—
401C23×C13—41no—
402C23×C13—41no—
403C23×C13—41no—
404C23×C13—41no—
405C23×C13—41no—
406C23×C13—41no—
407C23×C13—41no—
408C23×C13—41no—
409C23×C13—41no—
410C23×C13—41no—
411C23×C13—41no—
412C23×C13—41no—
413C23×C13—41no—
414C23×C13—41no—
415C23×C13—41no—
416C23×C13—41no—
417C23×C13—41no—
418C23×C13—41no—
419C23×C13—41no—
420C23×C13—41no—
421C23×C13—41no—
422C23×C13—41no—
423C23×C13—41no—
424C23×C13—41no—
425C23×C13—41no—
426C23×C13—41no—
427C23×C13—41no—
428C23×C13—41no—
429C23×C13—41no—
430C23×C13—41no—
431C23×C13—41no—
432C23×C13—41no—
433C23×C13—41no—
434C23×C13—41no—
435C23×C13—41no—
436C23×C13—41no—
437C23×C13—41no—
438C23×C13—41no—
439C23×C13—41no—
440C23×C13—41no—
441C23×C13—41no—
442C23×C13—41no—
443C23×C13—41no—
444C23×C13—41no—
445C23×C13—41no—
446C23×C13—41no—
447C23×C13—41no—
448C23×C13—41no—
449C23×C13—41no—
450C23×C13—41no—
451C23×C13—41no—
452C23×C13—41no—
453C23×C13—41no—
454C23×C13—41no—
455C23×C13—41no—
456C23×C13—41no—
457C23×C13—41no—
458C23×C13—41no—
459C23×C13C4×D414yes—
460C23×C13C23×C411yescharacteristic
461C23×C13C22×D411yescharacteristic
462C23×C13C22×D411yescharacteristic
463C23×C13C2×#4111yescharacteristic
464C23×C13C2×#4111yescharacteristic
465C23×C13C2×#4111yescharacteristic
466C23×C13C2×#4111yescharacteristic
467C23×C13H(5,𝔽2)11yescharacteristic
468C23×C13H(5,𝔽2)11yescharacteristic
469C23×C13H(5,𝔽2)11yescharacteristic
470C23×C13H(5,𝔽2)11yescharacteristic
471C23×C13H(5,𝔽2)11yescharacteristic
472C23×C13H(5,𝔽2)11yescharacteristic
473C23×C13H(5,𝔽2)11yescharacteristic
474C23×C13H(5,𝔽2)11yescharacteristic
475D4×C13—416no—
476D4×C13—416no—
477D4×C13—416no—
478C2×C4×C13—22no—
479C2×C4×C13—22no—
480C2×C4×C13—22no—
481C2×C4×C13—22no—
482C2×C4×C13—22no—
483C2×C4×C13—22no—
484C2×C4×C13—22no—
485C2×C4×C13—22no—
486C2×C4×C13—22no—
487C2×C4×C13—22no—
488C2×C4×C13—22no—
489C2×C4×C13—22no—
490C2×C4×C13—22no—
491C2×C4×C13—22no—
492C2×C4×C13—22no—
493C2×C4×C13—22no—
494C2×C4×C13—22no—
495C2×C4×C13—22no—
496C2×C4×C13—22no—
497C2×C4×C13—22no—
498C2×C4×C13—22no—
499C2×C4×C13—22no—
500C2×C4×C13—22no—
501C2×C4×C13—22no—
502C2×C4×C13—22no—
503C2×C4×C13—22no—
504C2×C4×C13—22no—
505C2×C4×C13—22no—
506C2×C4×C13—22no—
507C2×C4×C13—22no—
508C2×C4×C13—22no—
509C2×C4×C13—22no—
510C2×C4×C13—22no—
511C2×C4×C13—416no—
512C2×C4×C13—41no—
513C2×C4×C13—41no—
514C2×C4×C13—41no—
515C2×C4×C13—41no—
516C2×C4×C13—41no—
517C2×C4×C13—41no—
518C2×C4×C13—41no—
519C2×C4×C13—41no—
520C2×C4×C13—41no—
521C2×C4×C13—41no—
522C2×C4×C13—41no—
523C2×C4×C13—41no—
524C2×C4×C13—41no—
525C2×C4×C13—41no—
526C2×C4×C13—41no—
527C2×C4×C13—41no—
528C2×C4×C13—41no—
529C2×C4×C13—41no—
530C2×C4×C13—41no—
531C2×C4×C13—41no—
532C2×C4×C13—41no—
533C2×C4×C13—41no—
534C2×C4×C13—41no—
535C2×C4×C13—41no—
536C2×C4×C13—41no—
537C2×C4×C13—41no—
538C2×C4×C13—41no—
539C2×C4×C13—41no—
540C2×C4×C13—41no—
541C2×C4×C13—41no—
542C2×C4×C13—41no—
543C2×C4×C13—41no—
544C2×C4×C13—41no—
545C2×C4×C13—41no—
546C2×C4×C13—41no—
547C2×C4×C13—41no—
548C2×C4×C13—41no—
549C2×C4×C13—41no—
550C2×C4×C13—41no—
551C2×C4×C13—41no—
552C2×C4×C13—41no—
553C2×C4×C13—41no—
554C2×C4×C13—41no—
555C2×C4×C13—41no—
556C2×C4×C13—41no—
557C2×C4×C13—41no—
558C2×C4×C13—41no—
559C2×C4×C13—41no—
560C2×C4×C13—41no—
561C2×C4×C13—41no—
562C2×C4×C13C4×D414yes—
563C23×D4C22×C1311yescharacteristic
564C23×D4C22×C1311yescharacteristic
565C23×D4C22×C1311yescharacteristic
566C24×C4C22×C1311yescharacteristic
567C22×C4⋊C4C22×C1311yescharacteristic
568C22×C22⋊C4C22×C1311yescharacteristic
569C22×C22⋊C4C22×C1311yescharacteristic
570C22×C22⋊C4C22×C1311yescharacteristic
571C22×C22⋊C4C22×C1311yescharacteristic
572C22×C22⋊C4C22×C1311yescharacteristic
573C22×C22⋊C4C22×C1311yescharacteristic
574C22×C22⋊C4C22×C1311yescharacteristic
575C22×C22⋊C4C22×C1311yescharacteristic
576C22×C22⋊C4C22×C1311yescharacteristic
577C22×C22⋊C4C22×C1311yescharacteristic
578C22×C22⋊C4C22×C1311yescharacteristic
579C22×C22⋊C4C22×C1311yescharacteristic
580C22×C22⋊C4C22×C1311yescharacteristic
581C22×C22⋊C4C22×C1311yescharacteristic
582C22×C42C22×C1311yescharacteristic
583C22×C42C22×C1311yescharacteristic
584#392C4×C1318yescomplemented
585#390—24no—
586#388—24no—
587#386—24no—
588#386—24no—
589C2×#95C22×C1311yescharacteristic
590C2×#95C22×C1311yescharacteristic
591C2×#95C22×C1311yescharacteristic
592C2×#95C22×C1311yescharacteristic
593C2×#95C22×C1311yescharacteristic
594C2×#95C22×C1311yescharacteristic
595C2×#95C22×C1311yescharacteristic
596C2×#95C22×C1311yescharacteristic
597C2×#95C22×C1311yescharacteristic
598C2×#95C22×C1311yescharacteristic
599C2×#95C22×C1311yescharacteristic
600C2×#95C22×C1311yescharacteristic
601C2×#95C22×C1311yescharacteristic
602C2×#95C22×C1311yescharacteristic
603C22×C13—24no—
604C22×C13—24no—
605C22×C13—24no—
606C22×C13—42no—
607C22×C13—42no—
608C22×C13—42no—
609C22×C13—42no—
610C22×C13—42no—
611C22×C13—42no—
612C22×C13—42no—
613C22×C13—42no—
614C22×C13—42no—
615C22×C13—42no—
616C22×C13—42no—
617C22×C13—42no—
618C22×C13—42no—
619C22×C13—42no—
620C22×C13—42no—
621C22×C13—42no—
622C22×C13—42no—
623C22×C13—42no—
624C22×C13—42no—
625C22×C13—42no—
626C22×C13—42no—
627C22×C13—42no—
628C22×C13—42no—
629C22×C13—42no—
630C22×C13—42no—
631C22×C13—42no—
632C22×C13—81no—
633C22×C13—81no—
634C22×C13—81no—
635C22×C13—81no—
636C22×C13—81no—
637C22×C13—81no—
638C22×C13—81no—
639C22×C13—81no—
640C22×C13—81no—
641C22×C13—81no—
642C22×C13—81no—
643C22×C13—81no—
644C22×C13—81no—
645C22×C13—81no—
646C22×C13—81no—
647C22×C13—81no—
648C22×C13C2×C4×D411yescharacteristic
649C22×C13C2×C4×D411yescharacteristic
650C22×C13C4×#4111yescharacteristic
651C22×C13#51811yescharacteristic
652C22×C13#51811yescharacteristic
653C22×C13#51811yescharacteristic
654C22×C13#51811yescharacteristic
655C22×C13#53411yescharacteristic
656C22×C13#53511yescharacteristic
657C22×C13#53511yescharacteristic
658C22×C13#53511yescharacteristic
659C22×C13#53811yescharacteristic
660C22×C13#53811yescharacteristic
661C22×C13#53811yescharacteristic
662C22×C13#53811yescharacteristic
663C22×C13#54011yescharacteristic
664C22×C13#54011yescharacteristic
665C22×C13#54011yescharacteristic
666C22×C13#54011yescharacteristic
667C22×C13D4211yescharacteristic
668C22×C13#54611yescharacteristic
669C22×C13#54611yescharacteristic
670C22×C13#54611yescharacteristic
671C22×C13#54611yescharacteristic
672C22×C13#54611yescharacteristic
673C22×C13#55011yescharacteristic
674C22×C13#55111yescharacteristic
675C22×C13#55311yescharacteristic
676C22×C13#55311yescharacteristic
677C22×C13#55311yescharacteristic
678C22×C13#55511yescharacteristic
679C22×C13#56011yescharacteristic
680C22×C13#56011yescharacteristic
681C22×C13#56011yescharacteristic
682C22×C13H(3,𝔽4)11yescharacteristic
683C4×C13—24no—
684C4×C13—42no—
685C4×C13—42no—
686C4×C13—42no—
687C4×C13—42no—
688C4×C13—42no—
689C4×C13—42no—
690C4×C13—42no—
691C4×C13—42no—
692C4×C13—42no—
693C4×C13—81no—
694C4×C13—81no—
695C25C23×C1311yescharacteristic
696C25C23×C1311yescharacteristic
697C25C23×C1311yescharacteristic
698C22×D4—22no—
699C22×D4—22no—
700C22×D4—22no—
701C22×D4—22no—
702C22×D4—22no—
703C22×D4—22no—
704C22×D4—41no—
705C22×D4—41no—
706C22×D4—41no—
707C22×D4—41no—
708C22×D4—41no—
709C22×D4—41no—
710C22×D4—41no—
711C22×D4—41no—
712C22×D4—41no—
713C22×D4—41no—
714C22×D4—41no—
715C22×D4—41no—
716C22×D4C2×C4×C1314yes—
717C22×D4C2×C4×C1314yes—
718C22×D4C2×C4×C1314yescomplemented
719C23×C4—22no—
720C23×C4—22no—
721C23×C4—22no—
722C23×C4—41no—
723C23×C4—41no—
724C23×C4—41no—
725C23×C4—41no—
726C23×C4C23×C1311yescharacteristic
727C23×C4C23×C1311yescharacteristic
728C23×C4C23×C1311yescharacteristic
729C23×C4C23×C1311yescharacteristic
730C23×C4C23×C1311yescharacteristic
731C23×C4C23×C1311yescharacteristic
732C23×C4C23×C1311yescharacteristic
733C23×C4C23×C1311yescharacteristic
734C23×C4C23×C1311yescharacteristic
735C23×C4C23×C1311yescharacteristic
736C23×C4C23×C1311yescharacteristic
737C23×C4C23×C1311yescharacteristic
738C2×C4⋊C4—22no—
739C2×C4⋊C4—22no—
740C2×C4⋊C4—41no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—41no—
760C2×C22⋊C4—41no—
761C2×C22⋊C4—41no—
762C2×C22⋊C4—41no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—41no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4C2×C4×C1314yes—
780C2×C22⋊C4C2×C4×C1314yescomplemented
781C2×C22⋊C4C2×C4×C1314yescomplemented
782C2×C22⋊C4D4×C1314yescomplemented
783C2×C42—22no—
784C2×C42—22no—
785C2×C42—22no—
786C2×C42—41no—
787C2×C42—41no—
788C2×C42—41no—
789#95—22no—
790#95—22no—
791#95—22no—
792#95—22no—
793#95—41no—
794#95—41no—
795#95—41no—
796#95—41no—
797#95—41no—
798#95—41no—
799#95—41no—
800#95—41no—
801#95C2×C4×C1314yescomplemented
802#95D4×C1314yescomplemented
803C2×C13—44no—
804C2×C13—82no—
805C2×C13—82no—
806C2×C13#232111yescharacteristic
807C2×C13#232811yescharacteristic
808C2×C13#233311yescharacteristic
809C2×C13#235811yescharacteristic
810C2×C13#236311yescharacteristic
811C2×C13#236411yescharacteristic
812C2×C13#237511yescharacteristic
813C2×C13#267011yescharacteristic
814C2×C13#267311yescharacteristic
815C2×C13#269911yescharacteristic
816C2×C13#270311yescharacteristic
817C2×C13#270311yescharacteristic
818C2×C13#271411yescharacteristic
819C2×C13#275311yescharacteristic
820C2×C13#275611yescharacteristic
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24C22×C4×C1312yes—
862C24C22×C4×C1312yes—
863C24C22×C4×C1312yes—
864C24C2×D4×C1312yes—
865C24C13×#4112yes—
866C24C24×C1311yescharacteristic
867C2×D4—28no—
868C2×D4—28no—
869C2×D4—28no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4C22×C4×C1312yes—
968C22×C4C22×C4×C1312yes—
969C22×C4C22×C4×C1312yes—
970C22×C4C22×C4×C1312yes—
971C22×C4C2×D4×C1312yes—
972C22×C4C2×D4×C1312yes—
973C22×C4C2×D4×C1312yes—
974C22×C4C2×D4×C1312yes—
975C22×C4C2×D4×C1312yes—
976C22×C4C13×#4112yes—
977C22×C4C13×#4112yes—
978C22×C4C13×#4112yes—
979C4⋊C4—44no—
980C22⋊C4—28no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C42—44no—
995C42—44no—
996C13#1452011yescharacteristic, direct product factor, Sylow
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23C4×D4×C1314yes—
1102C23C23×C4×C1311yescharacteristic
1103C23C22×D4×C1311yescharacteristic
1104C23C22×D4×C1311yescharacteristic
1105C23C2×C13×#4111yescharacteristic
1106C23C2×C13×#4111yescharacteristic
1107C23C2×C13×#4111yescharacteristic
1108C23C2×C13×#4111yescharacteristic
1109C23C13×H(5,𝔽2)11yescharacteristic
1110C23C13×H(5,𝔽2)11yescharacteristic
1111C23C13×H(5,𝔽2)11yescharacteristic
1112C23C13×H(5,𝔽2)11yescharacteristic
1113C23C13×H(5,𝔽2)11yescharacteristic
1114C23C13×H(5,𝔽2)11yescharacteristic
1115C23C13×H(5,𝔽2)11yescharacteristic
1116C23C13×H(5,𝔽2)11yescharacteristic
1117D4—416no—
1118D4—416no—
1119D4—416no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—416no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4C4×D4×C1314yes—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22C2×C4×D4×C1311yescharacteristic
1251C22C2×C4×D4×C1311yescharacteristic
1252C22C4×C13×#4111yescharacteristic
1253C22C13×#51811yescharacteristic
1254C22C13×#51811yescharacteristic
1255C22C13×#51811yescharacteristic
1256C22C13×#51811yescharacteristic
1257C22C13×#53411yescharacteristic
1258C22C13×#53511yescharacteristic
1259C22C13×#53511yescharacteristic
1260C22C13×#53511yescharacteristic
1261C22C13×#53811yescharacteristic
1262C22C13×#53811yescharacteristic
1263C22C13×#53811yescharacteristic
1264C22C13×#53811yescharacteristic
1265C22C13×#54011yescharacteristic
1266C22C13×#54011yescharacteristic
1267C22C13×#54011yescharacteristic
1268C22C13×#54011yescharacteristic
1269C22D42×C1311yescharacteristic
1270C22C13×#54611yescharacteristic
1271C22C13×#54611yescharacteristic
1272C22C13×#54611yescharacteristic
1273C22C13×#54611yescharacteristic
1274C22C13×#54611yescharacteristic
1275C22C13×#55011yescharacteristic
1276C22C13×#55111yescharacteristic
1277C22C13×#55311yescharacteristic
1278C22C13×#55311yescharacteristic
1279C22C13×#55311yescharacteristic
1280C22C13×#55511yescharacteristic
1281C22C13×#56011yescharacteristic
1282C22C13×#56011yescharacteristic
1283C22C13×#56011yescharacteristic
1284C22C13×H(3,𝔽4)11yescharacteristic
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C2—44no—
1298C2—82no—
1299C2—82no—
1300C2C13×#232111yescharacteristic
1301C2C13×#232811yescharacteristic
1302C2C13×#233311yescharacteristic
1303C2C13×#235811yescharacteristic
1304C2C13×#236311yescharacteristic
1305C2C13×#236411yescharacteristic
1306C2C13×#237511yescharacteristic
1307C2C13×#267011yescharacteristic
1308C2C13×#267311yescharacteristic
1309C2C13×#269911yescharacteristic
1310C2C13×#270311yescharacteristic
1311C2C13×#270311yescharacteristic
1312C2C13×#271411yescharacteristic
1313C2C13×#275311yescharacteristic
1314C2C13×#275611yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC2×C13×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#390C2semidirect
3. C2×C13×#388C2semidirect
4. C2×C13×#386C2semidirect
5. C2×C13×#386C2semidirect
6. C13×#1442C2semidirect
7. C13×#1440C2semidirect
8. C13×#1438C2semidirect
9. C13×#1438C2semidirect
10. C13×#1438C2semidirect
11. C13×#1437C2semidirect
12. C13×#1437C2semidirect
13. C13×#1437C2semidirect
14. C13×#1434C2semidirect
15. C13×C22⋊#95C2semidirect
37. C13×#392C4semidirect
79. C22×D4×C13C2×C4semidirect
141. C2×C13×C22⋊C4C2×C4semidirect
142. C2×C13×C22⋊C4C2×C4semidirect
143. C2×C13×C22⋊C4D4semidirect
162. C13×#95C2×C4semidirect
163. C13×#95D4semidirect
164. #14520C13direct (N × H)
341. C2×#390C2×C13semidirect
342. C2×#388C2×C13semidirect
343. C2×#386C2×C13semidirect
344. C2×#386C2×C13semidirect
345. #1442C2×C13semidirect
346. #1440C2×C13semidirect
347. #1438C2×C13semidirect
348. #1438C2×C13semidirect
349. #1438C2×C13semidirect
350. #1437C2×C13semidirect
351. #1437C2×C13semidirect
352. #1437C2×C13semidirect
353. #1434C2×C13semidirect
354. C22⋊#95C2×C13semidirect
584. #392C4×C13semidirect
718. C22×D4C2×C4×C13semidirect
780. C2×C22⋊C4C2×C4×C13semidirect
781. C2×C22⋊C4C2×C4×C13semidirect
782. C2×C22⋊C4D4×C13semidirect
801. #95C2×C4×C13semidirect
802. #95D4×C13semidirect
996. C13#14520direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3922
C2×C13×#3902
C2×C13×#3882
C2×C13×#3862
C13×#14422
C13×#14402
C13×#14382
C13×#14372
C13×#14342
C13×C22⋊#952
#1452013