Finite Group Databasebeta

← C13×#16526 #15702865

Subgroups — C13×#16526 #15702865

Order 3328.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#397C211yesmaximal, characteristic, complemented
2C2×C13×#394C211yesmaximal, characteristic, complemented
3C2×C13×#394C211yesmaximal, characteristic, complemented
4C2×C13×#394C211yesmaximal, characteristic, complemented
5C2×C13×#392C211yesmaximal, characteristic
6C2×C13×#390C211yesmaximal, characteristic, complemented
7C13×#1444C211yesmaximal, characteristic, complemented
8C13×#1440C211yesmaximal, characteristic, complemented
9C13×#1439C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic, complemented
12C13×#1438C211yesmaximal, characteristic, complemented
13C13×#1438C211yesmaximal, characteristic, complemented
14C13×#1437C211yesmaximal, characteristic, complemented
15C13×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊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×C13×C22⋊C4C2211yescharacteristic
36C22×C13×C22⋊C4C2211yescharacteristic
37C22×C13×C22⋊C4C2211yescharacteristic
38C22×C42×C13C2211yescharacteristic
39C13×#397—24no—
40C13×#394—24no—
41C13×#394—24no—
42C13×#394—24no—
43C13×#392—24no—
44C13×#390—24no—
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
56C2×C13×#95C2211yescharacteristic
57C25×C13C2311yescharacteristic
58C25×C13C2311yescharacteristic
59C25×C13C2311yescharacteristic
60C22×D4×C13—22no—
61C22×D4×C13—22no—
62C22×D4×C13—22no—
63C22×D4×C13—22no—
64C22×D4×C13—22no—
65C22×D4×C13—22no—
66C22×D4×C13—22no—
67C22×D4×C13—22no—
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×C13—41no—
78C22×D4×C13—41no—
79C22×D4×C13—41no—
80C22×D4×C13D414yes—
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C23×C4×C13C2311yescharacteristic
92C23×C4×C13C2311yescharacteristic
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4—22no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C4⋊C4—41no—
101C2×C13×C4⋊C4—41no—
102C2×C13×C4⋊C4—41no—
103C2×C13×C4⋊C4—41no—
104C2×C13×C4⋊C4—41no—
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—22no—
121C2×C13×C22⋊C4—22no—
122C2×C13×C22⋊C4—22no—
123C2×C13×C22⋊C4—22no—
124C2×C13×C22⋊C4—22no—
125C2×C13×C22⋊C4—22no—
126C2×C13×C22⋊C4—22no—
127C2×C13×C22⋊C4—22no—
128C2×C13×C22⋊C4—22no—
129C2×C13×C22⋊C4—22no—
130C2×C13×C22⋊C4—22no—
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⋊C4—41no—
141C2×C13×C22⋊C4—41no—
142C2×C13×C22⋊C4—41no—
143C2×C13×C22⋊C4—41no—
144C2×C13×C22⋊C4—41no—
145C2×C13×C22⋊C4—41no—
146C2×C13×C22⋊C4—41no—
147C2×C13×C22⋊C4—41no—
148C2×C13×C22⋊C4—41no—
149C2×C13×C22⋊C4D414yescomplemented
150C2×C42×C13—22no—
151C2×C42×C13—41no—
152C2×C42×C13—41no—
153C13×#95—22no—
154C13×#95—22no—
155C13×#95—22no—
156C13×#95—22no—
157C13×#95—22no—
158C13×#95—22no—
159C13×#95—22no—
160C13×#95—41no—
161C13×#95—41no—
162C13×#95—41no—
163C13×#95—41no—
164C13×#95D414yescomplemented
165#16526C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
206C24×C13—21no—
207C24×C13—21no—
208C24×C13C2×D412yes—
209C24×C13C2×D412yes—
210C24×C13C2×D412yes—
211C24×C13C2411yescharacteristic
212C2×D4×C13—28no—
213C2×D4×C13—44no—
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—
232C2×D4×C13—44no—
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—21no—
305C22×C4×C13—21no—
306C22×C4×C13—21no—
307C22×C4×C13C2×D412yes—
308C22×C4×C13C2×D412yes—
309C22×C4×C13C2×D412yes—
310C22×C4×C13C2×D412yes—
311C22×C4×C13C2×D412yes—
312C22×C4×C13C2×D412yes—
313C22×C4×C13#4112yes—
314C22×C4×C13#4112yes—
315C22×C4×C13#4112yes—
316C22×C4×C13#4112yes—
317C13×C4⋊C4—44no—
318C13×C4⋊C4—44no—
319C13×C4⋊C4—44no—
320C13×C4⋊C4—44no—
321C13×C22⋊C4—44no—
322C13×C22⋊C4—44no—
323C13×C22⋊C4—44no—
324C13×C22⋊C4—44no—
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—
336C42×C13—44no—
337C2×#397C2×C1311yescharacteristic, complemented
338C2×#394C2×C1311yescharacteristic, complemented
339C2×#394C2×C1311yescharacteristic, complemented
340C2×#394C2×C1311yescharacteristic, complemented
341C2×#392C2×C1311yescharacteristic
342C2×#390C2×C1311yescharacteristic, complemented
343#1444C2×C1311yescharacteristic, complemented
344#1440C2×C1311yescharacteristic, complemented
345#1439C2×C1311yescharacteristic, complemented
346#1439C2×C1311yescharacteristic, complemented
347#1439C2×C1311yescharacteristic, complemented
348#1438C2×C1311yescharacteristic, complemented
349#1438C2×C1311yescharacteristic, complemented
350#1437C2×C1311yescharacteristic, complemented
351#1436C2×C1311yescharacteristic, complemented
352C23×C13—22no—
353C23×C13—22no—
354C23×C13—22no—
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—41no—
374C23×C13—41no—
375C23×C13—41no—
376C23×C13—41no—
377C23×C13—41no—
378C23×C13—41no—
379C23×C13—41no—
380C23×C13—41no—
381C23×C13—41no—
382C23×C13—41no—
383C23×C13—41no—
384C23×C13—41no—
385C23×C13—41no—
386C23×C13—41no—
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×C13C22×D411yescharacteristic
458C23×C13C22×D411yescharacteristic
459C23×C13C22×D411yescharacteristic
460C23×C13C2×#4111yescharacteristic
461C23×C13C2×#4111yescharacteristic
462C23×C13C2×#4111yescharacteristic
463C23×C13C2×#4111yescharacteristic
464C23×C13H(5,𝔽2)11yescharacteristic
465C23×C13H(5,𝔽2)11yescharacteristic
466C23×C13H(5,𝔽2)11yescharacteristic
467C23×C13H(5,𝔽2)11yescharacteristic
468C23×C13H(5,𝔽2)11yescharacteristic
469C23×C13H(5,𝔽2)11yescharacteristic
470C23×C13H(5,𝔽2)11yescharacteristic
471C23×C132−1+411yescharacteristic
472D4×C13—416no—
473D4×C13—416no—
474D4×C13—416no—
475C2×C4×C13—22no—
476C2×C4×C13—22no—
477C2×C4×C13—22no—
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—41no—
503C2×C4×C13—41no—
504C2×C4×C13—41no—
505C2×C4×C13—41no—
506C2×C4×C13—41no—
507C2×C4×C13—41no—
508C2×C4×C13—41no—
509C2×C4×C13—41no—
510C2×C4×C13—41no—
511C2×C4×C13—41no—
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#12314yes—
559C23×D4C22×C1311yescharacteristic
560C23×D4C22×C1311yescharacteristic
561C23×D4C22×C1311yescharacteristic
562C22×C4⋊C4C22×C1311yescharacteristic
563C22×C4⋊C4C22×C1311yescharacteristic
564C22×C4⋊C4C22×C1311yescharacteristic
565C22×C4⋊C4C22×C1311yescharacteristic
566C22×C22⋊C4C22×C1311yescharacteristic
567C22×C22⋊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×C42C22×C1311yescharacteristic
582#397—24no—
583#394—24no—
584#394—24no—
585#394—24no—
586#392—24no—
587#390—24no—
588C2×#95C22×C1311yescharacteristic
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
600C22×C13—42no—
601C22×C13—42no—
602C22×C13—42no—
603C22×C13—42no—
604C22×C13—42no—
605C22×C13—42no—
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—81no—
622C22×C13—81no—
623C22×C13—81no—
624C22×C13—81no—
625C22×C13—81no—
626C22×C13—81no—
627C22×C13—81no—
628C22×C13—81no—
629C22×C13—81no—
630C22×C13—81no—
631C22×C13—81no—
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×C13C2×#12311yescharacteristic
646C22×C13#53211yescharacteristic
647C22×C13#53211yescharacteristic
648C22×C13#53411yescharacteristic
649C22×C13#53411yescharacteristic
650C22×C13#53411yescharacteristic
651C22×C13#53511yescharacteristic
652C22×C13#53511yescharacteristic
653C22×C13#53711yescharacteristic
654C22×C13#53811yescharacteristic
655C22×C13#53811yescharacteristic
656C22×C13#53811yescharacteristic
657C22×C13#53811yescharacteristic
658C22×C13#53811yescharacteristic
659C22×C13#53811yescharacteristic
660C22×C13#54011yescharacteristic
661C22×C13#54011yescharacteristic
662C22×C13#54211yescharacteristic
663C22×C13#54211yescharacteristic
664C22×C13D4211yescharacteristic
665C22×C13D4211yescharacteristic
666C22×C13D4211yescharacteristic
667C22×C13#54611yescharacteristic
668C22×C13#54611yescharacteristic
669C22×C13#54611yescharacteristic
670C22×C13#54711yescharacteristic
671C22×C13#54711yescharacteristic
672C22×C13#55011yescharacteristic
673C22×C13#55311yescharacteristic
674C22×C13#55511yescharacteristic
675C22×C13#55911yescharacteristic
676C22×C13#56011yescharacteristic
677C22×C13#56011yescharacteristic
678C22×C13#56211yescharacteristic
679C22×C13#56211yescharacteristic
680C4×C13—24no—
681C4×C13—42no—
682C4×C13—42no—
683C4×C13—42no—
684C4×C13—42no—
685C4×C13—42no—
686C4×C13—42no—
687C4×C13—42no—
688C4×C13—81no—
689C4×C13—81no—
690C4×C13—81no—
691C4×C13—81no—
692C25C23×C1311yescharacteristic
693C25C23×C1311yescharacteristic
694C25C23×C1311yescharacteristic
695C22×D4—22no—
696C22×D4—22no—
697C22×D4—22no—
698C22×D4—22no—
699C22×D4—22no—
700C22×D4—22no—
701C22×D4—22no—
702C22×D4—22no—
703C22×D4—41no—
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×D4D4×C1314yes—
716C23×C4C23×C1311yescharacteristic
717C23×C4C23×C1311yescharacteristic
718C23×C4C23×C1311yescharacteristic
719C23×C4C23×C1311yescharacteristic
720C23×C4C23×C1311yescharacteristic
721C23×C4C23×C1311yescharacteristic
722C23×C4C23×C1311yescharacteristic
723C23×C4C23×C1311yescharacteristic
724C23×C4C23×C1311yescharacteristic
725C23×C4C23×C1311yescharacteristic
726C23×C4C23×C1311yescharacteristic
727C23×C4C23×C1311yescharacteristic
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—22no—
731C2×C4⋊C4—22no—
732C2×C4⋊C4—22no—
733C2×C4⋊C4—22no—
734C2×C4⋊C4—41no—
735C2×C4⋊C4—41no—
736C2×C4⋊C4—41no—
737C2×C4⋊C4—41no—
738C2×C4⋊C4—41no—
739C2×C4⋊C4—41no—
740C2×C22⋊C4—22no—
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—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
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⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4D4×C1314yescomplemented
785C2×C42—22no—
786C2×C42—41no—
787C2×C42—41no—
788#95—22no—
789#95—22no—
790#95—22no—
791#95—22no—
792#95—22no—
793#95—22no—
794#95—22no—
795#95—41no—
796#95—41no—
797#95—41no—
798#95—41no—
799#95D4×C1314yescomplemented
800C2×C13—82no—
801C2×C13—82no—
802C2×C13—82no—
803C2×C13#242211yescharacteristic
804C2×C13#244511yescharacteristic
805C2×C13#255511yescharacteristic
806C2×C13#262211yescharacteristic
807C2×C13#266111yescharacteristic
808C2×C13#266211yescharacteristic
809C2×C13#266811yescharacteristic
810C2×C13#266911yescharacteristic
811C2×C13#267111yescharacteristic
812C2×C13#268211yescharacteristic
813C2×C13#268611yescharacteristic
814C2×C13#271011yescharacteristic
815C2×C13#271411yescharacteristic
816C2×C13#280311yescharacteristic
817C2×C13#282911yescharacteristic
818C24—21no—
819C24—21no—
820C24—21no—
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—
860C24C2×D4×C1312yes—
861C24C2×D4×C1312yes—
862C24C2×D4×C1312yes—
863C24C24×C1311yescharacteristic
864C2×D4—28no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
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—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
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×C4C2×D4×C1312yes—
960C22×C4C2×D4×C1312yes—
961C22×C4C2×D4×C1312yes—
962C22×C4C2×D4×C1312yes—
963C22×C4C2×D4×C1312yes—
964C22×C4C2×D4×C1312yes—
965C22×C4C13×#4112yes—
966C22×C4C13×#4112yes—
967C22×C4C13×#4112yes—
968C22×C4C13×#4112yes—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C42—44no—
989C13#1652611yescharacteristic, direct product factor, Sylow
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
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—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
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—
1095C23C22×D4×C1311yescharacteristic
1096C23C22×D4×C1311yescharacteristic
1097C23C22×D4×C1311yescharacteristic
1098C23C2×C13×#4111yescharacteristic
1099C23C2×C13×#4111yescharacteristic
1100C23C2×C13×#4111yescharacteristic
1101C23C2×C13×#4111yescharacteristic
1102C23C13×H(5,𝔽2)11yescharacteristic
1103C23C13×H(5,𝔽2)11yescharacteristic
1104C23C13×H(5,𝔽2)11yescharacteristic
1105C23C13×H(5,𝔽2)11yescharacteristic
1106C23C13×H(5,𝔽2)11yescharacteristic
1107C23C13×H(5,𝔽2)11yescharacteristic
1108C23C13×H(5,𝔽2)11yescharacteristic
1109C23C13×2−1+411yescharacteristic
1110D4—416no—
1111D4—416no—
1112D4—416no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
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—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
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×C4C13×#12314yes—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22C2×C13×#12311yescharacteristic
1243C22C13×#53211yescharacteristic
1244C22C13×#53211yescharacteristic
1245C22C13×#53411yescharacteristic
1246C22C13×#53411yescharacteristic
1247C22C13×#53411yescharacteristic
1248C22C13×#53511yescharacteristic
1249C22C13×#53511yescharacteristic
1250C22C13×#53711yescharacteristic
1251C22C13×#53811yescharacteristic
1252C22C13×#53811yescharacteristic
1253C22C13×#53811yescharacteristic
1254C22C13×#53811yescharacteristic
1255C22C13×#53811yescharacteristic
1256C22C13×#53811yescharacteristic
1257C22C13×#54011yescharacteristic
1258C22C13×#54011yescharacteristic
1259C22C13×#54211yescharacteristic
1260C22C13×#54211yescharacteristic
1261C22D42×C1311yescharacteristic
1262C22D42×C1311yescharacteristic
1263C22D42×C1311yescharacteristic
1264C22C13×#54611yescharacteristic
1265C22C13×#54611yescharacteristic
1266C22C13×#54611yescharacteristic
1267C22C13×#54711yescharacteristic
1268C22C13×#54711yescharacteristic
1269C22C13×#55011yescharacteristic
1270C22C13×#55311yescharacteristic
1271C22C13×#55511yescharacteristic
1272C22C13×#55911yescharacteristic
1273C22C13×#56011yescharacteristic
1274C22C13×#56011yescharacteristic
1275C22C13×#56211yescharacteristic
1276C22C13×#56211yescharacteristic
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C2—82no—
1290C2—82no—
1291C2—82no—
1292C2C13×#242211yescharacteristic
1293C2C13×#244511yescharacteristic
1294C2C13×#255511yescharacteristic
1295C2C13×#262211yescharacteristic
1296C2C13×#266111yescharacteristic
1297C2C13×#266211yescharacteristic
1298C2C13×#266811yescharacteristic
1299C2C13×#266911yescharacteristic
1300C2C13×#267111yescharacteristic
1301C2C13×#268211yescharacteristic
1302C2C13×#268611yescharacteristic
1303C2C13×#271011yescharacteristic
1304C2C13×#271411yescharacteristic
1305C2C13×#280311yescharacteristic
1306C2C13×#282911yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC2×C13×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#397C2semidirect
2. C2×C13×#394C2semidirect
3. C2×C13×#394C2semidirect
4. C2×C13×#394C2semidirect
6. C2×C13×#390C2semidirect
7. C13×#1444C2semidirect
8. C13×#1440C2semidirect
9. C13×#1439C2semidirect
10. C13×#1439C2semidirect
11. C13×#1439C2semidirect
12. C13×#1438C2semidirect
13. C13×#1438C2semidirect
14. C13×#1437C2semidirect
15. C13×#1436C2semidirect
149. C2×C13×C22⋊C4D4semidirect
164. C13×#95D4semidirect
165. #16526C13direct (N × H)
337. C2×#397C2×C13semidirect
338. C2×#394C2×C13semidirect
339. C2×#394C2×C13semidirect
340. C2×#394C2×C13semidirect
342. C2×#390C2×C13semidirect
343. #1444C2×C13semidirect
344. #1440C2×C13semidirect
345. #1439C2×C13semidirect
346. #1439C2×C13semidirect
347. #1439C2×C13semidirect
348. #1438C2×C13semidirect
349. #1438C2×C13semidirect
350. #1437C2×C13semidirect
351. #1436C2×C13semidirect
784. C2×C22⋊C4D4×C13semidirect
799. #95D4×C13semidirect
989. C13#16526direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3972
C2×C13×#3942
C2×C13×#3922
C2×C13×#3902
C13×#14442
C13×#14402
C13×#14392
C13×#14382
C13×#14372
C13×#14362
#1652613